Online ISSN:1349-8606
Progress in Informatics  
No.8 March 2011  
Page 89-109  
 
Information geometric superactivation of classical zero-error capacity of quantum channels
Laszlo GYONGYOSI and Sandor IMRE

LINK [1] G. Smith and J. Yard, “Quantum Communication with Zero-capacity Channels,”Science vol.321, pp.1812-1815, 2008.

LINK [2] R. Duan, “Superactivation of zero-error capacity of noisy quantumchannels,” arXiv:0906.2527 [quant-ph], 2009.

LINK [3] T. Cubitt, J. X. Chen, and A. Harrow, arXiv: 0906.2547.

LINK [4] R. Duan, Y. Feng, Z. F. Ji, and M. S. Ying,Phys. Rev. Lett., vol.98, p.230502, 2007.

LINK [5] T. Cubitt, A. Montanaro, and A. Winter, arXiv: 0706.0705 [quant-ph], 2007.

LINK [6] T. Cubitt, A. Harrow, D. Leung, A. Montanaro, and A. Winter, Comm. Math. Phys., vol.284, no.1, p.281,2008.

LINK [7] R. C. Medeiros and F. M. de Assis, Int. J. Quant. Inf.,vol.3, p.135, 2005.

LINK [8] R. C. Medeiros, R. Alleaume, G. Cohen, and F. M. de Assis, quant-ph/0611042.

LINK [9] S. Beigi and P. W. Shor, arXiv:0709.2090 [quant-ph], 2007.

LINK [10] J. A. Cortese, “The Holevo-Schumacher-Westmoreland Channel Capacity for a Class of Qudit Unital Channels,” 2002, LANL ArXiV e-print quant-ph/0211093.

LINK [11] S. Imre and F. Balázs, Quantum Computing and CommunicationsAn Engineering Approach,John Wiley and Sons Ltd, 2005.

LINK [12] M. B. Ruskai, S. Szarek, and E. Werner, “An Analysis of Completely-Positive Trace-Preserving Maps on 2 by 2 Matrices,”2001, LANLArXiV e-print quant-ph/0101003.

LINK [13] J.-D. Boissonnat, C. Wormser, and M. Yvinec,Curved Voronoi diagrams, In J.-D. Boissonnat and M. Teillaud Eds, Effective Computational Geometry for Curves and Surfaces, pp.67-116,Springer-Verlag, Mathematics and Visualization, 2007.

LINK [14] F. Aurenhammer and R. Klein, Voronoi Diagrams,In J. Sack and G. Urrutia Eds, Handbook of Computational Geometry, Chapter V, pp.201-290, Elsevier Science Publishing, 2000.

LINK [15] M. Badoiu, S. Har-Peled, and P. Indyk, “Approximate clustering via core-sets,”In Proceedings 34th ACM Symposium on Theory of Computing,pp.250-257, 2002.

LINK [16] B. W. Schumacher and M. Westmoreland, “Relative Entropy in Quantum Information Theory” 2000, LANL ArXiV e-print quant-ph/0004045.

LINK [17] B. W. Schumacher and M. Westmoreland, “Optimal Signal Ensembles,”1999, LANLArXiV e-print quant-ph/9912122.

LINK [18] L. Gyongyosi and S. Imre, “Novel Geometrical Solution to Additivity Problem of Classical Quantum Channel Capacity,”The 33rd IEEE Sarnoff Symposium-2010, Princeton University,Apr. 2010, Princeton, New Jersey,USA.

LINK [19] M. R. Ackermann, J. Blömer, and C. Sohler, “Clustering for metric andnon-metric distance measures,”In Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '08), pp.799-808. Society for Industrial and Applied Mathematics, 2008.

LINK [20] K. Chen, “On k-median clustering in high dimensions,”In Proceedings of the17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '06),pp.1177-1185, 2006.

LINK [21] K. Chen, “On k-median and k-means clustering in metric and Euclidean spacesand their applications,”Manuscript, URL: http://ews.uiuc.edu/~kechen/, July 2007.

LINK [22] G. Frahling and C. Sohler, “Coresets in dynamic geometric data streams,”InProceedings of the 27th Annual ACM Symposium on Theory of Computing(STOC '05), pp.209-217, New York, NY, USA, 2005. ACM.

LINK [23] S. Har-Peled and A. Kushal, “Smaller coresets for k-median and k-meansclustering,” In Proceedings of the 21st Annual Symposium on Computational Geometry (SCG '05), pp.126-134, New York, NY, USA, 2005. ACM.

LINK [24] F. Nielsen, J.-D. Boissonnat, and R. Nock,“On Bregman Voronoi diagrams,” In Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '07),pp.746-755, Philadelphia, PA, USA, 2007. Society for Industrial and Applied Mathematics.

LINK [25] D. Feldman, M. Monemizadeh, and C. Sohler, “A PTAS for k-means clusteringbased on weak coresets,” In Proceedings of the 23rd ACM Symposium on Computational Geometry (SCG '07), pp.11-18, 2007.

LINK [26] K. Kato, M. Oto, H. Imai, and K. Imai, “Voronoi diagrams for pure 1-qubitquantum states,” quant-ph/0604101, 2006.

LINK [27] A. Banerjee, S. Merugu, I. S. Dhillon, and J. Ghosh,“Clustering with Bregman divergences,”Journal of Machine Learning Research, vol.6,pp.1705-1749, 2005.

LINK [28] R. Nock and F. Nielsen, “Fitting the Smallest Enclosing Bregman Ball,”ECML 2005,pp.649-656, ECML'05.

LINK [29] F. Nielsen and R. Nock, “On the smallest enclosing information disk.Inf. Process,” Lett. IPL '08, vol.105, no.3, pp.93-97, 2008.

LINK [30] F. Nielsen and R. Nock, “Quantum Voronoi Diagrams and Holevo Channel Capacityfor 1-Qubit Quantum States,” ISIT 2008.

LINK [31] F. Nielsen and R. Nock,“Bregman Sided and Symmetrized Centroids,” ICPR 2008,ICPR'08, arXiv:0711.3242.

LINK [32] F. Nielsen and R. Nock, “Approximating Smallest Enclosing Balls with Applicationto Machine Learning,” International Journal on Computational Geometry and Applications (IJCGA '09), 2009.

LINK [33] M. B. Hastings, “A Counterexample to Additivity of Minimum Output Entropy”Nature Physics, vol.5, p.255, 2009. arXiv:0809.3972.

LINK [34] F. Brandao and M. Horodecki, “On Hastings' counterexamples to the minimumoutput entropy additivity conjecture,” arXiv:0907.3210.

LINK [35] C. King, “Additivity for unital qubit channels,”J. Math. Phys., vol.43, pp.4641-4653, 2002.

LINK [36] M. Fukuda, C. King, and D. K. Moser, “Comments on Hastings'Additivity Counterexamples,”Communications in Mathematical Physics,2010, DOI 10.1007/s00220-010-0996-9.

LINK [37] N. Datta, A. S. Holevo, and Y. Suhov, “A quantum channel with additiveminimum output entropy,” 2004,URL: http://arxiv.org/abs/quant-ph/0403072.

LINK [38] K. Matsumoto and F. Yura, “Entanglement cost of antisymmetric states andadditivity of capacity of some quantum channels,”Journal of Phys. A, vol.37, pp.L167-L171, 2004.

LINK [39] P. Shor, “Additivity of the classical capacity of entanglementbreakingquantum channels,” J. Math. Phys., vol.246, no.3, pp.453-472,2004, URL:http://arxiv.org/abs/quant-ph/0305035.

LINK [40] M. M. Wolf and J. Eisert, “Classical information capacity of a class ofquantum channels,” New Journal of Physics, vol.7, no.93, 2005.

LINK [41] M. Hayashi and H. Nagaoka, “General formulas for capacity ofclassical-quantum channels,”IEEE Transactions on Information Theory,vol.49, no.7, pp.1753-1768, 2003.

LINK [42] M. Hayashi, H. Imai, K. Matsumoto, M. B. Ruskai and T. Shimono, “Qubitchannels which require four inputs to achieve capacity: Implications foradditivity conjectures,” Quantum Information and Computation,vol.5, pp.032-040, 2005.

LINK [43] L. Gyongyosi and S. Imre, “Computational Geometric Analysis of Physically Allowed Quantum Cloning Transformations for Quantum Cryptography,”InProceedings of the 4th WSEAS International Conference on Computer Engineering and Applications (CEA '10),pp.121-126,Harvard University, Cambridge, USA, 2010.

LINK [44] L. Gyongyosi and S. Imre, “Information Geometrical Solution to Additivity of Non-Unital Quantum Channels,”QCMC 2010, 10th Quantum Communication, Measurement & Computing Conference, July 2010, University of Queensland, Brisbane, Queensland, Australia.

LINK [45] L. Gyongyosi and S. Imre, “Computational Information Geometric Analysis of Quantum Channel Additivity,”Photon10 Conference, Quantum Electronics Group (QEP-19), 2010,Southampton, UK.

LINK [46] L. Gyongyosi and S. Imre, “Information Geometrical Analysis of Additivity of Optical Quantum Channels,”IEEE/OSA Journal of Optical Communications and Networking (JOCN), IEEE Photonics Society & Optical Society of America, ISSN: 1943-0620, 2010.

LINK [47] C. Shannon, “The zero-error capacity of a noisy channel,” IEEE Trans. Information Theory, pp.8-19,1956.

LINK [48] B. Bollobas, Modern graph theory,Springer-Verlag New York, Inc., New York, 1998.

LINK [49] J. Koner and A. Orlitsky, “Zero-error information theory,”IEEE Trans. Info.Theory, vol.44, no.6, pp.2207-2229, 1998.

LINK [50] L. Gyongyosi and S. Imre, “Capacity Recovery of Useless Photonic Quantum Communication Channels,”ALS Conference, Lawrence Berkeley National Laboratory (Berkeley Lab), University of California, Berkeley (California), USA, 2010.