Our Flagship product Freespace is installed in over 40 cities around the world and serves over 30000 people every day

Freespace

Authors:
(1) Renan F. F. da Silva, Institute of Computing, University of Campinas;
(2) Yulle G. F. Borges, Institute of Computing, University of Campinas;
(3) Rafael C. S. Schouery, Institute of Computing, University of Campinas. 6 Variable Neighborhood Search 6.1 Objective function Our objective function f has two levels: the primary objective that seeks to minimize the number of used bins and the secondary objective that seeks the lowest lexicographic order in the residual vector. The residual vector consists of the residual capacity of used bins in non-decreasing order. 6.2 Neighborhoods The VNS performs local searches in neighborhoods, as will be explained below. One relevant factor is the heuristic used in the local search. In our VNS, we use the Best Improvement heuristic, which analyzes all neighbors of a solution and changes to the best neighbor (in terms of the objective function). Our VNS has neighborhoods with the moves: Move-Item, Swap-Items, Swap-and-Move, and MoveTwo-to-One. The number of items changed in one move is constant for these neighborhoods, which just change a constant number of bins and elements in the residual vector (of the second objective function). As we can compare two neighborhoods using their variations in the objective function, it can be done in O(1). Next, we present our neighborhoods, showing optimizations to obtain fast algorithms even for large instances. 6.2.1 Move-Item Neighborhood For the CBPP, one possible algorithm for this neighborhood is to adapt the algorithm used by Fleszar and Hindi [19] for the BPP, that have time complexity O(n2). In this, for each item i, we iterate in the bins given in non-ascending order of residual capacity. Then, we check if the move (i, Br) is valid, where Br is the current bin, and evaluate it if so. Besides, we stop the search when we find the first bin Br such that wi > res(r), since the ordering guarantee that the bins forward also do not have space for the item i. However, it is not necessary to evaluate all moves to find the best one. Applying the Auxiliary Algorithm using the current solution B, it returns the best move for each item i ∈ I, so the best one is the best move between them. It gives us an implementation of the Move-Item Neighborhood with time complexity Θ(n). 6.2.2 Swap-Items Neighborhood Fleszar and Hindi [19] propose for the BPP a Swap-Items Neighborhood with complexity O(n+M), where M is the number of valid moves, which can be very fast in some solutions with little free space. We present the pseudocode of this neighborhood in the Algorithm 4. Although the time complexity of this algorithm is O(n log n + M), in our tests, it performed better than Fleszar and Hindi’s algorithm, especially in large instances. Algorithm 5 presents the pseudocode of this algorithm. 6.2.3 Move-Two-to-One Neighborhood 6.2.4 Swap-and-Move Neighborhood The Swap-and-Move Neighborhood selects three items i, j, k from different bins, then swaps i and j, and moves k to B(i) (its bin before the move). This neighborhood has complexity O(n3) when implemented in the completed way, which offers a low cost-benefit, so we use a restricted version from this one. Instead of testing all the possibilities of k, we test only the heaviest item that can be moved to B(i). The first candidate for k is the heaviest item that fits in B(i), and we can use a binary search to find it. 6.3 Shake Algorithm The Shake Algorithm is a function that makes random moves, seeking to escape from local optimal. In particular, our Shake chooses to execute one of two subroutines with equal probability. In the first subroutine, we performed 20 moves with the constraint that each bin belongs to a maximum of one move. The possible moves are to move one item or swap two items. In the second subroutine, we select two bins and then repack their items in a random order using the Best Fit heuristic. Note that we use a very aggressive Shake since its moves can make the solution much worse. Our Shake is based on the one proposed by Fleszar and Hindi [19] for the BPP, which is equal to the first subroutine without the constraint that bins must be distinct in different moves. The second routine was added because the perturbation generated by the first one can be small in instances with little free space. 6.4 Algorithm 6.5 Neighborhood Ordering This paper is available on arxiv under CC 4.0 license. Authors: (1) Renan F. F. da Silva, Institute of Computing, University of Campinas; (2) Yulle G. F. Borges, Institute of Computing, University of Campinas; (3) Rafael C. S. Schouery, Institute of Computing, University of Campinas. Authors: (1) Renan F. F. da Silva, Institute of Computing, University of Campinas; (2) Yulle G. F. Borges, Institute of Computing, University of Campinas; (3) Rafael C. S. Schouery, Institute of Computing, University of Campinas. 6 Variable Neighborhood Search 6.1 Objective function Our objective function f has two levels: the primary objective that seeks to minimize the number of used bins and the secondary objective that seeks the lowest lexicographic order in the residual vector. The residual vector consists of the residual capacity of used bins in non-decreasing order. 6.2 Neighborhoods The VNS performs local searches in neighborhoods, as will be explained below. One relevant factor is the heuristic used in the local search. In our VNS, we use the Best Improvement heuristic, which analyzes all neighbors of a solution and changes to the best neighbor (in terms of the objective function). Our VNS has neighborhoods with the moves: Move-Item, Swap-Items, Swap-and-Move, and MoveTwo-to-One. The number of items changed in one move is constant for these neighborhoods, which just change a constant number of bins and elements in the residual vector (of the second objective function). As we can compare two neighborhoods using their variations in the objective function, it can be done in O(1). Next, we present our neighborhoods, showing optimizations to obtain fast algorithms even for large instances. 6.2.1 Move-Item Neighborhood For the CBPP, one possible algorithm for this neighborhood is to adapt the algorithm used by Fleszar and Hindi [19] for the BPP, that have time complexity O(n2). In this, for each item i, we iterate in the bins given in non-ascending order of residual capacity. Then, we check if the move (i, Br) is valid, where Br is the current bin, and evaluate it if so. Besides, we stop the search when we find the first bin Br such that wi > res(r), since the ordering guarantee that the bins forward also do not have space for the item i. However, it is not necessary to evaluate all moves to find the best one. Applying the Auxiliary Algorithm using the current solution B, it returns the best move for each item i ∈ I, so the best one is the best move between them. It gives us an implementation of the Move-Item Neighborhood with time complexity Θ(n). 6.2.2 Swap-Items Neighborhood Fleszar and Hindi [19] propose for the BPP a Swap-Items Neighborhood with complexity O(n+M), where M is the number of valid moves, which can be very fast in some solutions with little free space. We present the pseudocode of this neighborhood in the Algorithm 4. Although the time complexity of this algorithm is O(n log n + M), in our tests, it performed better than Fleszar and Hindi’s algorithm, especially in large instances. Algorithm 5 presents the pseudocode of this algorithm. 6.2.3 Move-Two-to-One Neighborhood 6.2.4 Swap-and-Move Neighborhood The Swap-and-Move Neighborhood selects three items i, j, k from different bins, then swaps i and j, and moves k to B(i) (its bin before the move). This neighborhood has complexity O(n3) when implemented in the completed way, which offers a low cost-benefit, so we use a restricted version from this one. Instead of testing all the possibilities of k, we test only the heaviest item that can be moved to B(i). The first candidate for k is the heaviest item that fits in B(i), and we can use a binary search to find it. 6.3 Shake Algorithm The Shake Algorithm is a function that makes random moves, seeking to escape from local optimal. In particular, our Shake chooses to execute one of two subroutines with equal probability. In the first subroutine, we performed 20 moves with the constraint that each bin belongs to a maximum of one move. The possible moves are to move one item or swap two items. In the second subroutine, we select two bins and then repack their items in a random order using the Best Fit heuristic. Note that we use a very aggressive Shake since its moves can make the solution much worse. Our Shake is based on the one proposed by Fleszar and Hindi [19] for the BPP, which is equal to the first subroutine without the constraint that bins must be distinct in different moves. The second routine was added because the perturbation generated by the first one can be small in instances with little free space. 6.4 Algorithm 6.5 Neighborhood Ordering This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Understanding Variable Neighborhood Search

This paper is available on arxiv under CC 4.0 license. Authors: (1) Xiaoyu Ai, School of Electrical Engineering & Telecommunications, University of New South Wales, Sydney, NSW 2052, Australia; (2) Robert Malaney, School of Electrical Engineering & Telecommunications, University of New South Wales, Sydney, NSW 2052, Australia. Table of Links Abstract & Introduction System Overview Overcoming the limitation of key reconciliation Final Key Rate Experimental Results Discussion Conclusion & References Appendix VII. CONCLUSION In this work, we have carried out a full-blown analysis and experimental implementation of a Slice Reconciliation scheme applied to a specific CV QKD protocol (with post-selection) under simulated channel conditions anticipated for satelliteto-Earth channels. We have provided the optimal solution for the classical reconciliation process for this CV-QKD protocol in the context of massive parallelisation under the finite key regime. More specifically, we have identified the optimal block length when a large-code block is to be subdivided so as to improve the final secure key rate in bits per second. Although our results were based on a specific CV-QKD protocol and a specific GPU architecture, the type of analysis we have introduced here will apply in general terms a large suite of CV-QKD protocols run over any form of architecture that offers massive parallelisation. Our results, therefore, pave the way to optimal reconciliation system design for a wide range of practical CV-QKD systems that operate in the finite key regime. As the demand on the finite key size grows (better security thresholds), and technology advances lead to larger quantum signalling rates, the importance of optimised multithreaded CV-QKD reconciliation will grow. REFERENCES [1] N. Hosseinidehaj, Z. Babar, R. Malaney, S. X. Ng, and L. Hanzo, “Satellite-Based Continuous-Variable Quantum Communications: Stateof-the-Art and a Predictive Outlook,” IEEE Communications Surveys & Tutorials, vol. 21, no. 1, 881–919, 2018. [2] C. H. Bennett and G. Brassard, “Quantum Cryptography: Public Key Distribution and Coin Tossing,” in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing,, vol. 175, 8, 1984. [3] H. Weinfurter, “Quantum Communication Experiments with Discrete Variables,” Quantum Information: From Foundations to Quantum Technology Applications, 369–381, 2016. [4] L. Gy ¨ongy ¨osi, L. Bacsardi, and S. Imre, “A Survey on Quantum Key Distribution,” Infocommunications Journal, vol. 11, no. 2, 14–21, 2019. [5] S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, et al., “Advances in Quantum Cryptography,” Advances in Optics and Photonics, vol. 12, no. 4, 1012–1236, 2020. [6] B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably Secure and Practical Quantum Key Distribution over 307 km of Optical Fibre,” Nature Photonics, vol. 9, no. 3, 163–168, 2015. [7] T. A. Eriksson, T. Hirano, B. J. Puttnam, G. Rademacher, R. S. Lu´ıs, M. Fujiwara, R. Namiki, Y. Awaji, M. Takeoka, N. Wada, et al., “Wavelength Division Multiplexing of Continuous Variable Quantum Key Distribution and 18.3 Tbit/s Data Channels,” Communications Physics, vol. 2, no. 1, 1–8, 2019. [8] S.-Y. Shen, M.-W. Dai, X.-T. Zheng, Q.-Y. Sun, G.-C. Guo, and Z.- F. Han, “Free-Space Continuous-Variable Quantum Key Distribution of Unidimensional Gaussian Modulation Using Polarized Coherent States in an Urban Environment,” Physical Review A, vol. 100, 012325, 2019. [9] L. Gyongyosi and S. Imre, “Secret Key Rates of Free-Space Optical Continuous-Variable Quantum Key Distribution,” International Journal of Communication Systems, vol. 32, no. 18, e4152, 2019. [10] P. Jouguet, S. Kunz-Jacques, and A. Leverrier, “Long-Distance Continuous-Variable Quantum Key Distribution with a Gaussian Modulation,” Physical Review A, vol. 84, no. 6, 062317, 2011. [11] P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. All´eaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, et al., “Field Test of Classical Symmetric Encryption with Continuous Variables Quantum Key Distribution,” Optics Express, vol. 20, no. 13, 14030–14041, 2012. [12] Q. Liao, Y. Guo, D. Huang, P. Huang, and G. Zeng, “Long-Distance Continuous-Variable Quantum Key Distribution Using Non-Gaussian State-Discrimination Detection,” New Journal of Physics, vol. 20, no. 2, 023015, 2018. [13] D. Guo, C. He, T. Guo, Z. Xue, Q. Feng, and J. Mu, “Comprehensive High-Speed Reconciliation for Continuous-Variable Quantum Key Distribution,” Quantum Information Processing, vol. 19, no. 9, 1–19, 2020. [14] Y. Zhang, Z. Chen, S. Pirandola, X. Wang, C. Zhou, B. Chu, Y. Zhao, B. Xu, S. Yu, and H. Guo, “Long-Distance Continuous-Variable Quantum Key Distribution over 202.81 km of Fiber,” Physical Review Letters, vol. 125, no. 1, 010502, 2020. [15] A. Leverrier, F. Grosshans, and P. Grangier, “Finite-Size Analysis of a Continuous-Variable Quantum Key Distribution,” Physical Review A, vol. 81, no. 6, 062343, 2010. [16] F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous Variable Quantum Key Distribution: Finite-Key Analysis of Composable Security against Coherent Attacks,” Physical Review Letters, vol. 109, no. 10, 100502, 2012. [17] S. Kish, E. Villase˜nor, R. Malaney, K. Mudge, and K. Grant, “Feasibility Assessment for Practical Continuous Variable Quantum Key Distribution over the Satellite-to-Earth Channel,” Quantum Engineering, vol. 2, no. 3, e50, 2020. [18] M. Tomamichel, C. C. W. Lim, N. Gisin, and R. Renner, “Tight FiniteKey Analysis for Quantum Cryptography,” Nature Communications, vol. 3, no. 1, 1–6, 2012. [19] Z. Yuan, A. Plews, R. Takahashi, K. Doi, W. Tam, A. Sharpe, A. Dixon, E. Lavelle, J. Dynes, A. Murakami, et al., “10-Mb/s Quantum Key Distribution,” Journal of Lightwave Technology, vol. 36, no. 16, 3427– 3433, 2018. [20] S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, et al., “Satellite-to-Ground Quantum Key Distribution,” Nature, vol. 549, no. 7670, 43–47, 2017. [21] D. Lin, D. Huang, P. Huang, J. Peng, and G. Zeng, “High Performance Reconciliation for Continuous-Variable Quantum Key Distribution with LDPC Code,” International Journal of Quantum Information, vol. 13, no. 02, 1550010, 2015. [22] X. Wang, Y. Zhang, S. Yu, B. Xu, Z. Li, and H. Guo, “Efficient Rate-Adaptive Reconciliation for Continuous-Variable Quantum Key Distribution,” Quantum Information & Computation, vol. 17, no. 13– 14, 1123–1134, 2017. [23] C. Zhou, X. Wang, Y. Zhang, Z. Zhang, S. Yu, and H. Guo, “ContinuousVariable Quantum Key Distribution with Rateless Reconciliation Protocol,” Physical Review Applied, vol. 12, no. 5, 054013, 2019. [24] M. Milicevic, C. Feng, L. M. Zhang, and P. G. Gulak, “Quasi-Cyclic Multi-Edge LDPC Codes for Long-Distance Quantum Cryptography,” NPJ Quantum Information, vol. 4, no. 1, 1–9, 2018. [25] S.-S. Yang, Z.-G. Lu, and Y.-M. Li, “High-Speed Post-Processing in Continuous-Variable Quantum Key Distribution Based on FPGA Implementation,” Journal of Lightwave Technology, vol. 38, no. 15, 3935–3941, 2020. [26] H. Li and Y. Pang, “FPGA-Accelerated Quantum Computing Emulation and Quantum Key Distillation,” IEEE Micro, vol. 41, no. 4, 49–57, 2021. [27] C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum Cryptography without Switching,” Physical Review Letters, vol. 93, no. 17, 170504, 2004. [28] N. Hosseinidehaj, A. M. Lance, T. Symul, N. Walk, and T. C. Ralph, “Finite-Size Effects in Continuous-Variable Quantum Key Distribution with Gaussian Postselection,” Physical Review A, vol. 101, no. 5, 052335, 2020. [29] D. Dequal, L. T. Vidarte, V. R. Rodriguez, G. Vallone, P. Villoresi, A. Leverrier, and E. Diamanti, “Feasibility of Satellite-to-Ground Continuous-Variable Quantum Key Distribution,” NPJ Quantum Information, vol. 7, no. 1, 1–10, 2020. [30] M. Bloch, A. Thangaraj, and S. W. McLaughlin, “Efficient Reconciliation of Correlated Continuous Random Variables Using LDPC Codes,” arXiv preprint cs/0509041, 2005. [31] P. Jouguet, D. Elkouss, and S. Kunz-Jacques, “High-Bit-Rate Continuous-Variable Quantum Key Distribution,” Physical Review A, vol. 90, no. 4, 042329, 2014. [32] H. Mani, T. Gehring, P. Grabenweger, B. Omer, C. Pacher, and ¨ U. L. Andersen, “Multiedge-Type Low-Density Parity-Check Codes for Continuous-Variable Quantum Key Distribution,” Physical Review A, vol. 103, no. 6, 062419, 2021. [33] H. Imai and S. Hirakawa, “A New Multilevel Coding Method Using Error-Correcting Codes,” IEEE Transactions on Information Theory, vol. 23, no. 3, 371–377, 1977. [34] U. Wachsmann, R. F. Fischer, and J. B. Huber, “Multilevel codes: Theoretical concepts and practical design rules,” IEEE Transactions on Information Theory, vol. 45, no. 5, 1361–1391, 1999. [35] R. D. Wesel, X. Liu, J. M. Cioffi, and C. Komninakis, “Constellation Labeling for Linear Encoders,” IEEE Transactions on Information Theory, vol. 47, no. 6, 2417–2431, 2001. [36] M. Bloch, A. Thangaraj, S. W. McLaughlin, and J.-M. Merolla, “LDPCBased Gaussian Key Reconciliation,” in IEEE Information Theory Workshop-ITW’06 Punta del Este, 116–120, IEEE, 2006. [37] A. Leverrier, R. All´eaume, J. Boutros, G. Z´emor, and P. Grangier, “Multidimensional Reconciliation for a Continuous-Variable Quantum Key Distribution,” Physical Review A, vol. 77, no. 4, 042325, 2008. [38] J. Fiur´aˇsek and N. J. Cerf, “Gaussian Postselection and Virtual Noiseless Amplification in Continuous-Variable Quantum Key Distribution,” Physical Review A, vol. 86, no. 6, 060302, 2012. [39] F. Darema, “The SPMD Model: Past, Present and Future,” in European Parallel Virtual Machine/Message Passing Interface Users’ Group Meeting, 1–1, Springer, 2001. [40] M. Pharr and W. R. Mark, “A SPMD Compiler for High-Performance CPU Programming,” in Innovative Parallel Computing (InPar), 1–13, IEEE, 2012. [41] J. Lodewyck, M. Bloch, R. Garc´ıa-Patr ´on, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, et al., “Quantum Key Distribution over 25 km with an AllFiber Continuous-Variable System,” Physical Review A, vol. 76, no. 4, 042305, 2007. [42] F. Laudenbach, C. Pacher, C.-H. F. Fung, A. Poppe, M. Peev, B. Schrenk, M. Hentschel, P. Walther, and H. H ¨ubel, “Continuous-Variable Quantum Key Distribution with Gaussian Modulation—The Theory of Practical Implementations,” Advanced Quantum Technologies, vol. 1, no. 1, 1800011, 2018. [43] Y. Polyanskiy, H. V. Poor, and S. Verd ´u, “Channel Coding Rate in the Finite Blocklength Regime,” IEEE Transactions on Information Theory, vol. 56, no. 5, 2307–2359, 2010. [44] D. Slepian and J. Wolf, “Noiseless Coding of Correlated Information Sources,” IEEE Transactions on Information Theory, vol. 19, no. 4, 471–480, 1973. [45] T. Richardson and R. Urbanke, Modern Coding Theory. Cambridge University Press, 2008. [46] X. Ai, R. Malaney, and S. X. Ng, “A Reconciliation Strategy for RealTime Satellite-Based QKD,” IEEE Communications Letters, vol. 24, no. 5, 1062–1066, 2020. [47] S.-Y. Chung, T. J. Richardson, and R. L. Urbanke, “Analysis of SumProduct Decoding of Low-Density Parity-Check Codes Using a Gaussian Approximation,” IEEE Transactions on Information Theory, vol. 47, no. 2, 657–670, 2001. [48] V. A. Chandrasetty and S. M. Aziz, “FPGA Implementation of an LDPC Decoder Using a Reduced Complexity Message Passing Algorithm,” Journal of Networks, vol. 6, no. 1, 36, 2011. [49] A. Leverrier, “Composable Security Proof for Continuous-Variable Quantum Key Distribution with Coherent States,” Physical Review Letters, vol. 114, no. 7, 070501, 2015. [50] C. Lupo, C. Ottaviani, P. Papanastasiou, and S. Pirandola, “ContinuousVariable Measurement-Device-Independent Quantum Key Distribution: Composable Security against Coherent Attacks,” Physical Review A, vol. 97, no. 5, 052327, 2018. [51] N. Hosseinidehaj, N. Walk, and T. C. Ralph, “Optimal Realistic Attacks in Continuous-Variable Quantum Key Distribution,” Physical Review A, vol. 99, no. 5, 052336, 2019. [52] S. Pirandola, “Limits and Security of Free-Space Quantum Communications,” Physical Review Research, vol. 3, no. 1, 013279, 2021. [53] S. Pirandola, “Satellite Quantum Communications: Fundamental Bounds and Practical Security,” Physical Review Research, vol. 3, no. 2, 023130, 2021. [54] J. H. Mathews and K. D. Fink, Numerical Methods Using MATLAB, vol. 4. Pearson Prentice Hall Upper Saddle River, NJ, 2004. [55] A. Leverrier, “Security of Continuous-Variable Quantum Key Distribution via a Gaussian de Finetti Reduction,” Physical Review Letters, vol. 118, no. 20, 200501, 2017. [56] E. Villase˜nor, R. Malaney, K. A. Mudge, and K. J. Grant, “Atmospheric Effects on Satellite-to-Ground Quantum Key Distribution Using Coherent States,” in GLOBECOM 2020-2020 IEEE Global Communications Conference, 1–6, IEEE, 2020. [57] J. Mateo, Efficient Information Reconciliation for Quantum Key Distribution. PhD thesis, Universidad Politecnica de Madrid, 2011. [58] T. Tian, C. R. Jones, J. D. Villasenor, and R. D. Wesel, “Selective Avoidance of Cycles in Irregular LDPC Code Construction,” IEEE Transactions on Communications, vol. 52, no. 8, 1242–1247, 2004. [59] D. V. Nguyen, S. K. Chilappagari, M. W. Marcellin, and B. Vasic, “On the Construction of Structured LDPC Codes Free of Small Trapping Sets,” IEEE Transactions on Information Theory, vol. 58, no. 4, 2280– 2302, 2012. [60] S. Landner and O. Milenkovic, “Algorithmic and Combinatorial Analysis of Trapping Sets in Structured LDPC Codes,” in International Conference on Wireless Networks, Communications and Mobile Computing, vol. 1, 630–635, IEEE, 2005. [61] X. Wang, Y. Zhang, S. Yu, and H. Guo, “High Speed Error Correction for Continuous-Variable Quantum Key Distribution with Multi-Edge Type LDPC Code,” Scientific Reports, vol. 8, no. 1, 1–7, 2018. [62] Y. Li, X. Zhang, Y. Li, B. Xu, L. Ma, J. Yang, and W. Huang, “HighThroughput GPU Layered Decoder of Quasi-Cyclic Multi-Edge Type Low Density Parity Check Codes in Continuous-Variable Quantum Key Distribution Systems,” Scientific Reports, vol. 10, no. 1, 1–11, 2020. [63] F. Grosshans, “Collective Attacks and Unconditional Security in Continuous Variable Quantum Key Distribution,” Physical Review Letters, vol. 94, 020504, 2005. [64] M. Navascu´es, F. Grosshans, and A. Acin, “Optimality of Gaussian Attacks in Continuous-Variable Quantum Cryptography,” Physical Review Letters, vol. 97, no. 19, 190502, 2006. [65] S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of Continuous-Variable Quantum Key Distribution Systems by Using Optical Preamplifiers,” Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 42, no. 11, 114014, 2009. [66] P. Jouguet, S. Kunz-Jacques, E. Diamanti, and A. Leverrier, “Analysis of Imperfections in Practical Continuous-Variable Quantum Key Distribution,” Physical Review A, vol. 86, no. 3, 032309, 2012.

Optimised Multithreaded CV-QKD Reconciliation for Global Quantum Networks: Conclusion & References

This paper is available on arxiv under CC 4.0 license. Authors: (1) Xiaoyu Ai, School of Electrical Engineering & Telecommunications, University of New South Wales, Sydney, NSW 2052, Australia; (2) Robert Malaney, School of Electrical Engineering & Telecommunications, University of New South Wales, Sydney, NSW 2052, Australia. Table of Links Abstract & Introduction System Overview Overcoming the limitation of key reconciliation Final Key Rate Experimental Results Discussion Conclusion & References Appendix Abstract Designing a practical Continuous Variable (CV) Quantum Key Distribution (QKD) system requires an estimation of the quantum channel characteristics and the extraction of secure key bits based on a large number of distributed quantum signals. Meeting this requirement in short timescales is difficult. On standard processors, it can take several hours to reconcile the required number of quantum signals. This problem is exacerbated in the context of Low Earth Orbit (LEO) satellite CV-QKD, in which the satellite flyover time is constrained to be less than a few minutes. A potential solution to this problem is massive parallelisation of the classical reconciliation process in which a large-code block is subdivided into many shorter blocks for individual decoding. However, the penalty of this procedure on the important final secured key rate is non-trivial to determine and hitherto has not been formally analysed. Ideally, a determination of the optimal reduced block size, maximising the final key rate, would be forthcoming in such an analysis. In this work, we fill this important knowledge gap via detailed analyses and experimental verification of a CV-QKD sliced reconciliation protocol that uses large block-length low-density parity-check decoders. Our new solution results in a significant increase in the final key rate relative to non-optimised reconciliation. In addition, it allows for the acquisition of quantum secured messages between terrestrial stations and LEO satellites within a flyover timescale even using off-the-shelf processors. Our work points the way to optimised global quantum networks secured via fundamental physics. I. INTRODUCTION Continuous Variable (CV) Quantum Key Distribution (QKD) has been intensively studied and significant breakthroughs have been achieved in both theory and experiment (see [1] for review). Compared to Discrete Variable (DV) QKD [2]–[5], CV-QKD can be implemented with well-developed technologies (e.g., homodyne detectors) in commercial fibreoptic networks [6], [7] and free-space optical communications [8], [9], providing it a potential advantage in practical deployments [10]–[14]. Considering the finite-key security of CV-QKD and DV-QKD, there are three critical parameters. These are, No, the number of original quantum signals sent by the transmitter (Alice) that are collected by the receiver (Bob); Ne, the number of quantum signals from which the protocol parameters are estimated;[1] and, ǫ, the probability that a QKD protocol fails to generate secret keys [15], [16]. To satisfy an upper limit on the failure probability of parameter estimation, Alice and Bob set Ne to a large value, which in turn implies a larger No. Despite the advantages in deployment, CV-QKD systems tend to demand a larger No to reach the same ǫ relative to DVQKD protocols. For example, to achieve a final key rate of 0.1 bits per pulse with ǫ = 10−9 , a CV-QKD protocol studied in [17] required No ≈ 109 signals. However, to achieve the same final key rate with ǫ = 10−14, the DV-QKD protocol in [18] required No ≈ 104 signals. This higher number of required signals in CV-QKD can render the classical post-processing (i.e. key reconciliation and privacy amplification[2] ) slow - possibly failing to meet target timescales for reconciliation. The end-users of a CV-QKD system expect the system to deliver two identical and secure keys under a limited time interval. For example, for satellite-based deployments, we would hope that the reconciliation is completed while maintaining a line-of-sight connection with the ground station. For a CV-QKD-enabled satellite with orbital parameters similar to Micius [20], this would mean the reconciliation should be completed in less than a few minutes. For the protocol we use in this work (see later), and for ǫ = 10−9 , this, in turn, would require the data rate of reconciliation to be at least 3.6 × 106 bits per second. For real-time reconciliation (say in subsecond timescales), two orders of magnitude increases in the reconciliation rates would be required. Demands for smaller ǫ will exacerbate the issue. Ideally, the rate of reconciliation should always be faster than the rate of quantum signalling. This all raises the question as to whether current CV-QKD reconciliation schemes are optimised for the highest possible key rates in bits per second. As we show here, this is not the case. Further optimisation is possible on all current schemes. To understand the issue better, we define reconciliation in the context of CV-QKD as a two-step scheme where the inputs to the reconciliation are non-identical N = 2No − 2Ne quadrature values[3] held by Alice and Bob (after parameter estimation), and the output is an identical bit string held by Alice and Bob [21]–[23]. Assuming a reverse reconciliation scheme, Bob first converts the quadrature values encoded by Alice in each signal to m bits. Alice, after converting each of her encoded real numbers also to m bits, then initiates some discrepancy-correction algorithms based on pre-defined errorcorrection codes to ensure her mN bits are identical to Bob’s. In this work, we will adopt Low-Density Parity-Check (LDPC) codes for the error correction. However, as alluded to above, reconciling mN bits within a limited time frame can be challenging. State-of-the-art LDPCbased reconciliation schemes for CV-QKD systems involve parallelised computation on a Graphics Processing Unit (GPU) [13], [24] or Field-Programmable Gate Arrays (FPGAs) [25], [26]. Reconciliation schemes implemented on FPGAs offer more programmable flexibility, but sometimes at the cost of reduced memory access relative to GPUs. For our purposes, both hardware architectures are useful - both offer massive parallelisation opportunities. These parallelisation solutions generally take the following two-step approach: 1) The mN bits are organised as m N-bit blocks to be reconciled. Each N-bit block is divided into multiple shorter blocks of size, say, NR. This is usually just set to a block size that can be processed within some timescale. 2) Then the m NR-bit blocks are reconciled in parallel (via independent processors) using optimally-designed LDPC decoders. However, what is missing in this approach is a proper optimisation analysis as to what the optimal value of NR is. As we show below, simply reducing NR at the cost of additional processing units is not an optimal solution. It transpires that in QKD the “penalty” cost of reducing the code rate (implicit in the use of small block lengths) significantly influences the bit per second final key rate. A more sophisticated analysis is required to determine the optimal reduced block length. Such an analysis is the key contribution of this work. Although we will adopt a specific CV-QKD protocol for our analysis, the key steps of our scheme will apply to any CV-QKD protocol. Our reconciliation scheme will deliver the highest reconciliation rate for a given processor speed - thus allowing for the optimal solution to CV-QKD reconciliation. [1] More precisely, in a CV-QKD protocol, Alice and Bob randomly select a Ne-signal subset from the No signals to estimate the parameters. [2] In this work, we focus on the key reconciliation step because it is the more time-consuming part in the post-processing steps while the privacy amplification involving only bit-wise operations can be easily implemented faster than the reconciliation [19]. [3] No and Ne are multiplied by 2 since Alice and Bob utilise both quadratures from heterodyne detection - the detection process we assume in this work.

Optimised Multithreaded CV-QKD Reconciliation for Global Quantum Networks: Abstract & Introduction

Life happily carries on and we don’t even have to look at our own darkness. Perhaps the real problem with modern life is the benign micro-systems that foster the covert conspiracy- we agree to blame the world for things that are, in fact, within us all. Implicitly we agree to live in a superficial dystopia of masks and make-up, where the wounds of psyche and identity stay hidden below the surface. The very comforts that our system affords us, also engage us in a conspiracy of denial, where we avoid the discomfiting process of taking a deep look within, and consequently, we allow the demons free space in our psyche. That’s why the unacknowledged, negative parts of us don’t simply lay dormant; they affect our thinking and our behavior, both conscious and unconscious, in ways that can be insidious and even destructive. Recognizing our shadows is a positive expression of our autonomy, an alternative to the easy way of least resistance, it is a refusal to ignore parts of ourselves, and a positive act of contact with that essential but compromised figure we all carry around inside our heads in the form of ‘I’. Recognition, then, is neither masochism nor resigned submission to this feature of our psychology. It is a positive move towards genuine self-awareness, which – by integrating in this way the previously separate shadow, by bringing that shadow into the full light of consciousness – is then powerless to continue the task it set itself, i.e, to deceive us into projecting onto other people the pain or injustice it embodies. No longer can we be unsuspecting hosts for the behaviors that are put to use by the shadow with such vicious selectivity. It takes courage and defiance to engage in this process of recognition – both externally and inwardly – to challenge how confinement insulates us from the truth of our ambivalence, how confinement requires people to live in a suspended way, aware of only part of themselves. If we allow ourselves to acknowledge the full range of our humanity, we open ourselves to a greater capacity for change. There is power in the acknowledgment of our demons, which changes their ability to function in the dark; it will not make us immune to them, but it should let us manage them better. Knowing that we have a dark side expands our compassion towards ourselves and others. We all are fighting a battle within, and this makes us vulnerable to each other. But awareness can transform vulnerability into a source of solidarity. In fact, this recognition opens the door for a more equitable and empathetic society. In owning our inner conflict, we reduce the risk of projecting it onto others. This creates space for a culture of accountability and a compassionate conversation with our shadow as an integral part of the work of being in this world. It transforms the myth of ‘what was done’ to ‘what I’ve done’, and perhaps becomes a lifelong conversation with our courageous and compassionate inner voice: ‘This is what was done to me. Now, what can be done with it?’ To opt out of a system that not only permits but welcomes this denial of our demons is an act of profound individual and societal autonomy. It serves as an affirmation that we’re no longer willing to be accomplices to lying to ourselves and others; and, perhaps more vitally, that we decline to be complicit in the injustice of the status quo. Then, armed with this existential awareness of who we really are, we can begin to chart a course for a different kind of beings. We can let our actions become less reactive and more reflective, our behaviors less governed by dark assumptions, and conscious biases – and more the results of a holistic sense of self. In this emerging reality, autonomy and identity are no longer ideals we strive to achieve but realities we actively embody. They are a commitment to being human with grace, intentionality, and an intense dedication to becoming more fully human as individuals and a larger society. If we and create systems that nurture our deepest values, we unshackle ourselves from the painful inescapability of separate selves, and liberate ourselves to co-create a world in which human beings live their differences together in safety and dignity. pay attention to our demons,

Can Humanity's Systems Serve as Material Enablers for Evasion?

This paper is available on arxiv under CC 4.0 license. Authors: (1) Terence Blésin, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (2) Wil Kao, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (3) Anat Siddharth, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (4) Alaina Attanasio, OxideMEMS lab, Purdue University; (5) Hao Tian, OxideMEMS lab, Purdue University; (6) Sunil A. Bhave, OxideMEMS lab, Purdue University; (7) Tobias J. Kippenberg, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL). Table of Links Introduction Results A. Physics and design B. Device characterization C. Bidirectional microwave-optical transduction D. Pulsed transduction Discussion Acknowledgments Appendix A: Theory Appendix B: Fabrication process flow Appendix C: Optical characterization Appendix D: Characterization of acoustic resonances Appendix E: Characterization of bidirectional transduction Appendix F: Optimization of optical extraction efficiency Coherent interconversion between microwave and optical frequencies can serve as both classical and quantum interfaces for computing, communication, and sensing. Here, we present a compact microwave-optical transducer based on monolithic integration of piezoelectric actuators atop silicon nitride photonic circuits. Such an actuator directly couples microwave signals to a high-overtone bulk acoustic resonator defined by the suspended silica cladding of the optical waveguide core, which leads to enhanced electromechanical and optomechanical couplings. At room temperature, this triply resonant piezo-optomechanical transducer achieves an off-chip photon number conversion efficiency of 1.6 × 10−5 over a bandwidth of 25 MHz at an input pump power of 21 dBm. The approach is scalable in manufacturing and, unlike existing electro-optic transducers, does not rely on superconducting resonators. As the transduction process is bidirectional, we further demonstrate synthesis of microwave pulses from a purely optical input. Combined with the capability of leveraging multiple acoustic modes for transduction, the present platform offers prospects for building frequency-multiplexed qubit interconnects and for microwave photonics at large. I. INTRODUCTION Modern data centers have seen rapidly increasing traffic that motivates an overhaul of existing network infrastructures. As optical fibers support nearly lossless transport and high bandwidths, twisted-pair copper deployment has shrunk in favor of optical interconnects. Energy-efficient optical transceivers [1] and optical network architectures [2] are being explored in parallel to accommodate emerging data- and resource-intensive applications. In an analogous fashion, processing quantum information in superconducting circuits and networking via photonic interconnects has been envisioned as an effective strategy to address the scalability challenges in advancing quantum technologies [3–5]. The scheme, featuring the full universal set of microwave quantum gates [6] with vanishing thermal occupancy and loss of the optical channels, calls for the development of microwaveoptical transducers to bridge the two energy scales that differ by more than four orders of magnitude. Aside from facilitating the networking of remote quantum processors, these transducers may enable fully optical control and readout of microwave qubits [7, 8]. The subsequent replacement of coaxial lines bridging room temperature and cryogenic environments by optical fibers is expected to significantly ease the space and heat load constraints in dilution refrigerators, opening up a path toward upscaling processor units housed in a single fridge. Efficient frequency conversion requires a nonlinear interaction stronger than the coupling to loss channels. The highest conversion efficiency to date has been achieved using an electro-optomechanical approach [9]. There, a silicon nitride membrane interacts with an optical mode of a free-space Fabry-Pérot cavity via radiation pressure and simultaneously serves as the top plate of a capacitor, parametrically coupling the mechanics to the microwave resonator. By virtue of the high resonator quality factors and pump power handling capability, 47% of input photons can be interconverted between optical and microwave domains [10], approaching the 50% efficiency required for attaining finite quantum capacity [11]. This highly efficient transducer has enabled optical dispersive qubit readout with negligible excess backaction [12]. The low-frequency (MHz) mechanical intermediary nevertheless limits the transduction bandwidth and leads to appreciable added noise even at dilution refrigerator temperature. To address these drawbacks, piezo-optomechanical transducers based on optomechanical crystals (OMC) have been developed [13–22], where a tightly confined high-frequency (GHz) mechanical mode and a co-localized optical mode can interact at a vacuum optomechanical coupling rate g0 ∼ 2π × 500 kHz. The trade-off lies instead in the sophistication required for microwave-phonon wave matching that significantly increases design complexity, as well as thermo-optic instability that constrains the intra-cavity photon number. An on-chip efficiency of 5% has recently been reported on such a platform [20]. However, low thermal conductance of these suspended quasi-one-dimensional structures hinders correlated microwave-optical photon pair generation at a practical rate. Cavity electro-optic modulators constitute a conceptually simpler approach where Pockels effect directly mediates microwave-optical interaction [23–25]. On-chip realizations employing planar superconducting microwave resonators, benefited from the deep sub-wavelength mode volume of the vacuum electric field, to reach single photon electro-optic coupling rates g0 ∼ 2π × 1 kHz [26– 29]. However, the material science of χ (2) crystals poses additional challenges. Photorefractive effects—observed, for instance, in LiNbO3 thin films [30]—hamper optical power handling, while piezoelectric loss and scattered optical photons degrade the quality factor of superconducting resonators [31, 32]. The difficulty of producing smooth sidewall surfaces in the workhorse Pockels material, LiNbO3 , through dry etching results in propagation losses an order of magnitude above the absorption limit [33]. As a result, the maximum on-chip efficiency achieved with integrated electro-optic transducers exceeds just 2% [26]. In the spirit of Ref. [9], a bulk transducer comprising a mm-size mechanically polished LiNbO3 whispering gallery mode (WGM) resonator coupled to a 3D superconducting microwave cavity has proved competitive, trading g0 for improved power handling and quality factors [34, 35]. Taking one step further with pulsed optical pumping, the system has demonstrated not only a hallmark 14.4% total efficiency but also electro-optic dynamical backaction [36, 37] and microwave-optical quadrature entanglement [38]. With the aforementioned design trade-offs in mind, we present a new piezo-optomechanical transducer based solely on wafer-scale, CMOS-compatible fabrication processes. We utilize a low-loss silicon nitride (Si3N4 ) photonic molecule, as well as multiple GHz high-overtone bulk acoustic resonances (HBAR) parametrically coupled to the optical modes. Endowed with power handling capabilities superior to existing integrated transducers, the device fits compactly within a 100 µm-by-50 µm footprint, in contrast to state-of-the-art bulk designs [10, 36]. In addition, the transduction HBAR modes are more readily coupled to the microwave signal, unlike OMC transducers. We demonstrate bidirectional microwave-optical transduction with a bandwidth of 25 MHz and total efficiency up to 1.6 × 10−5 by pumping with 21 dBm of off-chip optical power in continuous-wave (CW) operation. The device is also characterized with a pulsed optical pump, which constitutes the first step toward optical control and readout of qubits, as well as heralded microwave-optical photon pair generation. The simple design, ease of fabrication, robust operation, and compact form factor anticipate wide applicability in quantum technologies and microwave photonics at large.

Bidirectional Microwave-optical Transduction Based on Integration: Introduction

Discussing the Impact of Our Exoplanet Study: How This Impacts Everything

This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Flor Ortiz, University of Luxembour; (2) Juan A. Vasquez-Peralvo, University of Luxembour; (3) Jorge Querol, University of Luxembour; (4) Eva Lagunas, University of Luxembour; (5) Jorge L. Gonzalez Rios, University of Luxembour; (6) Marcele O. K. Mendonc¸a, University of Luxembour; (7) Luis Garces, University of Luxembour; (8) Victor Monzon Baeza, University of Luxembour; (9) Symeon Chatzinotas, University of Luxembou. Table of Links Abstract & Introduction System Model and Problem Statement Antenna Design and Training Data Generation Supervised Learning for Adaptive Beamforming Numerical Results Conclusions, Acknowledgment, and References III. ANTENNA DESIGN AND TRAINING DATA GENERATION A. Antenna Design For GEO missions, efficient antenna design is crucial due to substantial free space losses and stringent constraints on permissible losses. To address these challenges, we have developed an open-ended waveguide antenna as the unit cell antenna for this scenario, as explained in [8]. This antenna design offers significantly lower losses than alternative solutions like patch antennas or dielectric-based antennas. The antenna consists of three main components: the open-ended waveguide itself, the groove polarizer responsible for circular polarization, and the rectangular-to-circular transition for connecting to the distribution network. Simulation results, confirm that the antenna meets the requirements. It radiates within the required frequency band, emitting Left-Hand Circular Polarized (LHCP) waves with minimal cross-polarization. This is evident from the S11 parameter, below -10 dB, and the axial ratio measuring less than 3 dB within the intended frequency range [8] We consider the coverage area over the Earth’s surface to determine the number of elements required for the array antenna. In the context of Very High Throughput satellite missions, where small areas need to be covered to avoid channel link saturation, we set a minimum beam diameter of 260 km or a coverage area Ac = 53093 km2 when the satellite is at nadir. It’s worth noting that the coverage area can be adjusted based on specific beam requirements We then calculate the 3 dB antenna beamwidth θ−3dB required to illuminate this area. Using geometric relations and the satellite’s location, we estimate θ−3dB, which in this case is found to be 0.41◦ . However, this number of elements is impractical regarding space, cost, and power requirements, as each element requires an RF chain. To address this, subarrays are introduced. The number of subarray elements is determined to avoid grating lobes intersecting the antenna’s Field of View (FoV) over the Earth’s surface resulting in an element spacing of d = 3.5λ0. With this spacing, subarrays of 4×4 elements are employed, resulting in 36×36 RF chains B. Training Data Generation The approach chosen in this study is array thinning, which consists of selectively activating and deactivating elements to form the desired antenna beam, as illustrated in Figure 1. Array thinning allows precise control of the beamwidth, uniform power distribution among the elements in multi-beam scenarios and orientation of the radiation pattern in the desired direction by progressive phase shifting. To create the training data for this antenna array, a Genetic Algorithm (GA) was employed. The goal of the GA was to find the optimal set of active antenna elements while respecting specific constraints, such as beamwidth, SLL and EIRP. The GA optimization process iteratively refines the antenna element configurations, starting from an initial configuration and continuing until convergence or until a predefined maximum iteration limit is reached. It considers several performance parameters simultaneously, such as beamwidth, SLL and EIRP, making it particularly suitable for optimizing complex antenna systems such as the distributed reflector antenna. The resulting training dataset consists of 174,203 samples, each representing different antenna element configurations that meet the defined constraints. This dataset serves as a reference for evaluating antenna performance and training machine learning models in the later sections of this paper. The main purpose of this database is to establish correlations between beamforming array weights and critical system parameters, including beamwidth, SLL, and EIRP. For more detailed information on the generated database, including access to the dataset itself, see [9], where it is openly available.

Supervised Learning Based Real-Time Adaptive Beamforming On-board: Antenna Design and Training Data

File with code #!/usr/bin/env python3

import shutil

def check_disk_usage(disk, min_absolute, min_percent):
    """Returns True if there is enough free disk space, false otherwise."""
    du = shutil.disk_usage(disk)
    # Calculate the percentage of free space
    percent_free = 100 * du.free / du.total
    # Calculate how many free gigabytes
    gigabytes_free = du.free / 2**30
    if percent_free < min_percent or gigabytes_free < min_absolute:
        return False
    return True

# Check for at least 2 GB and 10% free
if not check_disk_usage("/", 2*2**30, 10):
    print("ERROR: Not enough disk space")
    return 1

print("Everything ok")
return 0 Command: $ cp disk_usage.py disk_usage_original.py 
$ cp disk_usage.py disk_usage_fixed.py 
# this throws an error
$ ./disk_usage_fixed.py Code output: File "./disk_usage_fixed.py", line 19

    return 1

    ^

SyntaxError: 'return' outside function File with code Adds at the beginning, then change to and to . import sys return 1 sys.exit(1) return 0 sys.exit(0) #!/usr/bin/env python3

import shutil
import sys

def check_disk_usage(disk, min_absolute, min_percent):
    """Returns True if there is enough free disk space, false otherwise."""
    du = shutil.disk_usage(disk)
    # Calculate the percentage of free space
    percent_free = 100 * du.free / du.total
    # Calculate how many free gigabytes
    gigabytes_free = du.free / 2**30
    if percent_free < min_percent or gigabytes_free < min_absolute:
        return False
    return True

# Check for at least 2 GB and 10% free
if not check_disk_usage("/", 2*2**30, 10):
    print("ERROR: Not enough disk space")
    sys.exit(1)

print("Everything ok")
sys.exit(0) Command: $ ./disk_usage_fixed.py Code output: ERROR: Not enough disk space File with code Change in previous file to .Because the code changes the value to gigabytes, so don't need to multiply by . check_disk_usage("/", 2*2**30, 10) check_disk_usage("/", 2, 10) gigabytes_free = du.free / 2**30 2**30 #!/usr/bin/env python3

import shutil
import sys

def check_disk_usage(disk, min_absolute, min_percent):
    """Returns True if there is enough free disk space, false otherwise."""
    du = shutil.disk_usage(disk)
    # Calculate the percentage of free space
    percent_free = 100 * du.free / du.total
    # Calculate how many free gigabytes
    gigabytes_free = du.free / 2**30
    if percent_free < min_percent or gigabytes_free < min_absolute:
        return False
    return True

# Check for at least 2 GB and 10% free
if not check_disk_usage("/", 2, 10):
    print("ERROR: Not enough disk space")
    sys.exit(1)

print("Everything ok")
sys.exit(0) Command: $ ./disk_usage_fixed.py Code output: Everything ok Command: $ diff -u disk_usage_original.py disk_usage_fixed.py > disk_usage.diff
$ cat disk_usage.diff Code output: --- disk_usage_original.py	2023-06-22 15:13:38.591579963 -0700

+++ disk_usage_fixed.py	2023-06-22 15:41:35.013023839 -0700

@@ -1,6 +1,7 @@

 #!/usr/bin/env python3

 

 import shutil

+import sys

 

 def check_disk_usage(disk, min_absolute, min_percent):

     """Returns True if there is enough free disk space, false otherwise."""

@@ -14,9 +15,9 @@

     return True

 

 # Check for at least 2 GB and 10% free

-if not check_disk_usage("/", 2*2**30, 10):

+if not check_disk_usage("/", 2, 10):

     print("ERROR: Not enough disk space")

-    return 1

+    sys.exit(1)

 

 print("Everything ok")

-return 0

+sys.exit(0) Command: $ patch disk_usage.py < disk_usage.diff Code output: patching file disk_usage.py Command: $ ./disk_usage.py Code output: Everything ok

FREESPACE

afreespace.com

-- employees

Since n.d.

COMPANY RANKING

FREESPACE

EVERGREEN INDEX #4471

Representing this company? Click here to claim and customize this page!

Freespace WIKI

Apply to get your Tech Company News Page live on HackerNoon.com today!

FREESPACE

afreespace.com

-- employees

Since n.d.

COMPANY RANKING

FREESPACE

EVERGREEN INDEX #4471

RELATED COMPANIESRANK

STORIES ABOUT FREESPACE

Representing this company? Click here to claim and customize this page!

Freespace WIKI

Apply to get your Tech Company News Page live on HackerNoon.com today!