The information-theoretic costs of simulating quantum measurements

Journal of Physics A: Mathematical and Theoretical

Volumn 45, Issue 45, 2012, Pages

  Wilde, Mark M ^a   Hayden, Patrick ^a   Buscemi, Francesco ^b   Hsieh, Min Hsiu ^c  

^a MCGILL UNIVERSITY   (Canada)

^b NAGOYA UNIVERSITY   (Japan)

^c UNIVERSITY OF TECHNOLOGY SYDNEY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84868283443     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/45/45/453001     Document Type: Review

References (68)

1. Abeyesinghe A, Devetak I, Hayden P and Winter A 2009 The mother of all protocols: restructuring quantum informations family tree Proc. R. Soc. A 465 2537-63 (arXiv:quant-ph/0606225)
2. Ahlswede R and Winter A J 2002 Strong converse for identification via quantum channels IEEE Trans. Inform. Theory 48 569-79 (arXiv:quant-ph/0012127) (Pubitemid 34239788)
3. Alicki R and Fannes M 2004 Continuity of quantum conditional information J. Phys. A: Math. Gen. 37 L55-7 (arXiv:quant-ph/0312081)
4. Audenaert K M R and Scheel S 2008 On random unitary channels New J. Phys. 10 023011
5. Bennett C H, Devetak I, Harrow A W, Shor P W and Winter A 2009 Quantum reverse Shannon theorem arXiv:0912.5537
6. Bennett C H, Shor P W, Smolin J A and Thapliyal A V 2002 Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem IEEE Trans. Inform. Theory 48 2637 (arXiv:quant-ph/0106052) (Pubitemid 35170324)
7. Berger T 1971 Rate Distortion Theory: A Mathematical Basis for Data Compression (Information and System Sciences) (Englewood Cliffs, NJ: Prentice Hall)
8. Berta M, Brandao F, Christandl M and Wehner S 2011 Entanglement cost of quantum channels arXiv:1108.5357
9. Berta M, Christandl M, Colbeck R, Renes J M and Renner R 2010 The uncertainty principle in the presence of quantum memory Nature Phys. 6 659-62 (arXiv:0909.0950)
10. Berta M, Christandl M and Renner R 2011 The quantum reverse Shannon theorem based on one-shot information theory Commun. Math. Phys. 306 579-615 (arXiv:0912.3805)
11. Buscemi F 2006 On the minimum number of unitaries needed to describe a random-unitary channel Phys. Lett. A 360 256-8 (Pubitemid 44660077)
12. Buscemi F, Hayashi M and Horodecki M 2008 Global information balance in quantum measurements Phys. Rev. Lett. 100 210504 (Pubitemid 351777213)
13. Buscemi F, Keyl M, DAriano G M, Perinotti P and Werner R F 2005 Clean positive operator valued measures J. Math. Phys. 46 082109 (Pubitemid 41247107)
14. Coles P J, Colbeck R, Li Y and Zwolak M 2012 Uncertainty relations from simple entropic properties Phys. Rev. Lett. 108 210405 (arXiv:1112.0543)
15. Cover T M and Thomas J A 1991 Elements of Information Theory (New York: Wiley)
16. Csiszár I and Korner J 1981 Information Theory: Coding Theorems for Discrete Memoryless Systems (Probability and Mathematical Statistics) (Budapest: Akademiai Kiado)
17. Cuff P 2008 Communication requirements for generating correlated random variables Proc. Int. Symp. on Information Theory pp 1393-7 (arXiv:0805.0065)
18. DAriano G M, Presti P Lo and Perinotti P 2005 Classical randomness in quantum measurements J. Phys. A: Math. Gen. 38 5979-91 (arXiv:quant-ph/0408115) (Pubitemid 40906234)
19. Datta N, Hsieh M-H and Wilde M M 2011 Quantum rate distortion, reverse Shannon theorems and source-channel separation IEEE Trans. Inform. Theory at press (doi:10.1109/TIT.2012.2215575) (arXiv:1108.4940)
20. Davies E B and Lewis J T 1970 An operational approach to quantum probability Commun. Math. Phys. 17 239-60
21. Davies E B 1976 Quantum Theory of Open Systems (New York: Academic)
22. Devetak I 2005 Distillation of local purity from quantum states Phys. Rev. A 71 062303 (arXiv:quant-ph/0406234) (Pubitemid 41481131)
23. Devetak I 2005 The private classical capacity and quantum capacity of a quantum channel IEEE Trans. Inform. Theory 51 44-55 (arXiv:quant-ph/0304127) (Pubitemid 40145986)
24. Devetak I 2006 Triangle of dualities between quantum communication protocols Phys. Rev. Lett. 97 140503 (arXiv:quant-ph/0505138) (Pubitemid 44522677)
25. Devetak I, Harrow A W and Winter A 2004 A family of quantum protocols Phys. Rev. Lett. 93 230504 (arXiv:quant-ph/0308044) (Pubitemid 40072708)
26. Devetak I, Harrow A W and Winter A 2008 A resource framework for quantum Shannon theory IEEE Trans. Inform. Theory 54 4587-618 (arXiv:quant-ph/0512015)
27. Devetak I and Winter A 2003 Classical data compression with quantum side information Phys. Rev. A 68 042301 (arXiv:quant-ph/0209029)
28. Devetak I and Winter A J 2004 Distilling common randomness from bipartite quantum states IEEE Trans. Inform. Theory 50 3183-96 (arXiv:quant-ph/0304196)
29. Devetak I and Yard J 2008 Exact cost of redistributing multipartite quantum states Phys. Rev. Lett. 100 230501
30. Gamal A El and Kim Y-H 2010 Lecture notes on network information theory arXiv:1001.3404v4
31. Frank R L and Lieb E H 2012 Extended quantum conditional entropy and quantum uncertainty inequalities arXiv:1204.0825
32. Giovannetti V, Lloyd S and Maccone L 2012 Achieving the Holevo bound via sequential measurements Phys. Rev. A 85 012302 (arXiv:1012.0386)
33. Groenewold H J 1971 A problem of information gain by quantal measurements Int. J. Theor. Phys. 4 327-38
34. Holevo A S 1982 Probabilistic and Statistical Aspects of Quantum Theory (Amsterdam: North-Holland)
35. Holevo A S 1998 The capacity of the quantum channel with general signal states IEEE Trans. Inform. Theory 44 269-73 (Pubitemid 128737894)
36. Horodecki M, Horodecki K, Horodecki P, Horodecki R, Oppenheim J, Sen(De) A and Sen U 2003 Local information as a resource in distributed quantum systems Phys. Rev. Lett. 90 100402 (arXiv:quant-ph/0207168)
37. Horodecki M, Horodecki P, Horodecki R, Oppenheim J, Sen(De) A, Sen U and Synak-Radtke B 2005 Local versus nonlocal information in quantum-information theory: formalism and phenomena Phys. Rev. A 71 062307 (arXiv:quant-ph/0410090) (Pubitemid 41481144)
38. Hsieh M-H and Wilde M M 2010 Trading classical communication, quantum communication and entanglement in quantum Shannon theory IEEE Trans. Inform. Theory 9 4705-30 (arXiv:0901.3038)
39. Hughston L P, Jozsa R and Wootters W K 1993 A complete classification of quantum ensembles having a given density matrix Phys. Lett. A 183 14-18
40. Kraus K 1983 States, Effects and Operations: Fundamental Notions of Quantum Theory (Berlin: Springer)
41. Krovi H and Devetak I 2007 Local purity distillation with bounded classical communication Phys. Rev. A 76 012321 (arXiv:0705.4089) (Pubitemid 47120495)
42. Lindblad G 1972 An entropy inequality for quantum measurements Commun. Math. Phys. 28 245-9
43. Luo Z 2009 Topics in quantum cryptography, quantum error correction and channel simulation PhD Thesis University of Southern California, CA, USA
44. Luo Z and Devetak I 2009 Channel simulation with quantum side information IEEE Trans. Inform. Theory 55 1331-42 (arXiv:quant-ph/0611008)
45. Martens H and de Muynck W M 1990 Nonideal quantum measurements Found. Phys. 20 255-81
46. Massar S and Popescu S 2000 Amount of information obtained by a quantum measurement Phys. Rev. A 61 062303
47. Ogawa T and Nagaoka H 2007 Making good codes for classical-quantum channel coding via quantum hypothesis testing IEEE Trans. Inform. Theory 53 2261-6 (Pubitemid 46852033)
48. Ozawa M 1984 Quantum measuring processes of continuous observables J. Math. Phys. 25 79-87
49. Ozawa M 1986 On information gain by quantum measurements of continuous observables J. Math. Phys. 27 759-63
50. Renes J M 2011 Duality of privacy amplification against quantum adversaries and data compression with quantum side information Proc. R. Soc. A 467 1604-23 (arXiv:1003.0703)
51. Renes J M and Boileau J-C 2008 Physical underpinnings of privacy Phys. Rev. A 78 032335 (arXiv:0803.3096)
52. Renes J M and Boileau J-C 2009 Conjectured strong complementary information tradeoff Phys. Rev. Lett. 103 020402 (arXiv:0806.3984)
53. Renes J M and Renner R 2011 Noisy channel coding via privacy amplification and information reconciliation IEEE Trans. Inform. Theory 57 7377-85 (arXiv:1012.4814)
54. Renes J M and Renner R 2012 One-shot classical data compression with quantum side information and the distillation of common randomness or secret keys IEEE Trans. Inform. Theory 58 1985-91 (arXiv:1008.0452)
55. Schumacher B and Westmoreland M D 1997 Sending classical information via noisy quantum channels Phys. Rev. A 56 131-8 (Pubitemid 127605032)
56. Sen P 2011 Achieving the Han-Kobayashi inner bound for the quantum interference channel by sequential decoding arXiv:1109.0802
57. Shannon C E 1948 A mathematical theory of communication Bell Syst. Tech. J. 27 379-423
58. Slepian D and Wolf J K 1973 Noiseless coding of correlated information sources IEEE Trans. Inform. Theory 19 471-80
59. Tomamichel M and Renner R 2011 Uncertainty relation for smooth entropies Phys. Rev. Lett. 106 110506 (arXiv:1009.2015)
60. Wilde M M 2011 From classical to quantum Shannon theory arXiv:1106.1445
61. Wilde M M, Guha S, Tan S-H and Lloyd S 2012 Explicit capacity-achieving receivers for optical communication and quantum reading Proc. Int. Symp. on Information Theory pp 551-5 (arXiv:1202.0518)
62. Wilde M M and Renes J M 2012 Quantum polar codes for arbitrary channels Proc. Int. Symp. on Information Theory pp 334-8 (arXiv:1201.2906)
63. Winter A 1999 Coding theorem and strong converse for quantum channels IEEE Trans. Inform. Theory 45 2481-5 (Pubitemid 30514205)
64. Winter A J 2002 Compression of sources of probability distributions and density operators arXiv:quant-ph/0208131
65. Winter A J 2004 Extrinsic and intrinsic data in quantum measurements: asymptotic convex decomposition of positive operator valued measures Commun. Math. Phys. 244 157-85 (arXiv:quant-ph/0109050) (Pubitemid 38148876)
66. Winter A J and Massar S 2001 Compression of quantum-measurement operations Phys. Rev. A 64 012311 (arXiv:quant-ph/0012128)
67. Wyner A 1975 The common information of two dependent random variables IEEE Trans. Inform. Theory 21 163-79
68. Yard J and Devetak I 2009 Optimal quantum source coding with quantum side information at the encoder and decoder IEEE Trans. Inform. Theory 55 5339-51 (arXiv:0706.2907)