메뉴 건너뛰기




Volumn 54, Issue 12, 2013, Pages

On quantum Rényi entropies: A new generalization and some properties

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84891551567     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4838856     Document Type: Article
Times cited : (834)

References (46)
  • 1
    • 0000307085 scopus 로고
    • On an inequality of Lieb and Thirring
    • 10.1007/BF01045887
    • Araki H. On an inequality of Lieb and Thirring. Lett. Math. Phys. 1990, 19(2):167-170. 10.1007/BF01045887
    • (1990) Lett. Math. Phys. , vol.19 , Issue.2 , pp. 167-170
    • Araki, H.1
  • 2
    • 33747650890 scopus 로고
    • Information measures and capacity of order alpha for discrete memoryless channels
    • I. Csiszar, P. Elias, ser. Colloq. Math. Soc. J. Bolyai, Eds., Amsterdam, North Holland
    • Arimoto S. Information measures and capacity of order alpha for discrete memoryless channels. Topics in Information Theory 1977, 16:41-52. I. Csiszar, P. Elias, in ser. Colloq. Math. Soc. J. BolyaiEds., Amsterdam, North Holland
    • (1977) Topics in Information Theory , vol.16 , pp. 41-52
    • Arimoto, S.1
  • 3
    • 84871858487 scopus 로고    scopus 로고
    • Quantum state discrimination bounds for finite sample size
    • 10.1063/1.4768252
    • Audenaert K.M. R. Mosonyi M. Verstraete F. Quantum state discrimination bounds for finite sample size. J. Math. Phys. 2012, 53(12):122205. 10.1063/1.4768252.
    • (2012) J. Math. Phys. , vol.53 , Issue.12 , pp. 122205
    • Audenaert, K.M.R.1    Mosonyi, M.2    Verstraete, F.3
  • 4
    • 84891512930 scopus 로고    scopus 로고
    • Sandwiched Rényi divergence satisfies data processing inequality
    • 10.1063/1.4838855
    • Beigi S. Sandwiched Rényi divergence satisfies data processing inequality. J. Math. Phys. 2013, 54:122202. 10.1063/1.4838855
    • (2013) J. Math. Phys. , vol.54 , pp. 122202
    • Beigi, S.1
  • 5
    • 77956305813 scopus 로고    scopus 로고
    • The uncertainty principle in the presence of quantum memory
    • 10.1038/nphys1734
    • Berta M. Christandl M. Colbeck R. Renes J.M. Renner R. The uncertainty principle in the presence of quantum memory. Nat. Phys. 2010, 6(9):659-662. 10.1038/nphys1734.
    • (2010) Nat. Phys. , vol.6 , Issue.9 , pp. 659-662
    • Berta, M.1    Christandl, M.2    Colbeck, R.3    Renes, J.M.4    Renner, R.5
  • 6
    • 0004151496 scopus 로고    scopus 로고
    • Graduate Texts in Mathematics, (Springer).
    • Bhatia R. Matrix Analysis 1997, 169. Graduate Texts in Mathematics Vol. (Springer).
    • (1997) Matrix Analysis , vol.169
    • Bhatia, R.1
  • 7
    • 84861644154 scopus 로고    scopus 로고
    • Uncertainty relations from simple entropic properties
    • 10.1103/PhysRevLett.108.210405
    • Coles P.J. Colbeck R. Yu L. Zwolak M. Uncertainty relations from simple entropic properties. Phys. Rev. Lett. 2012, 108(21):210405. 10.1103/PhysRevLett.108.210405.
    • (2012) Phys. Rev. Lett. , vol.108 , Issue.21 , pp. 210405
    • Coles, P.J.1    Colbeck, R.2    Yu, L.3    Zwolak, M.4
  • 8
    • 0029219702 scopus 로고
    • Generalized cutoff rates and Renyi's information measures
    • 10.1109/18.370121
    • Csiszar I. Generalized cutoff rates and Renyi's information measures. IEEE Trans. Inf. Theory 1995, 41(1):26-34. 10.1109/18.370121
    • (1995) IEEE Trans. Inf. Theory , vol.41 , Issue.1 , pp. 26-34
    • Csiszar, I.1
  • 9
    • 66949151794 scopus 로고    scopus 로고
    • Min- and max-relative entropies and a new entanglement monotone
    • 10.1109/TIT.2009.2018325
    • Datta N. Min- and max-relative entropies and a new entanglement monotone. IEEE Trans. Inf. Theory 2009, 55(6):2816-2826. 10.1109/TIT.2009.2018325
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.6 , pp. 2816-2826
    • Datta, N.1
  • 10
    • 84891513267 scopus 로고    scopus 로고
    • A limit of the quantum Rényi divergence
    • e-print arXiv:1308.5961.
    • Datta N. Leditzky F. A limit of the quantum Rényi divergence. and e-print arXiv:1308.5961.
    • Datta, N.1    Leditzky, F.2
  • 11
    • 84891498366 scopus 로고    scopus 로고
    • Entanglement sampling and applications
    • e-print arXiv:1305.1316.
    • Dupuis F. Fawzi O. Wehner S. Entanglement sampling and applications. and e-print arXiv:1305.1316.
    • Dupuis, F.1    Fawzi, O.2    Wehner, S.3
  • 12
    • 84891535488 scopus 로고    scopus 로고
    • Monotonicity of a relative Rényi entropy
    • 10.1063/1.4838835
    • Frank R.L. Lieb E.H. Monotonicity of a relative Rényi entropy. J. Math. Phys. 2013, 54:122201. 10.1063/1.4838835
    • (2013) J. Math. Phys. , vol.54 , pp. 122201
    • Frank, R.L.1    Lieb, E.H.2
  • 13
    • 41549146719 scopus 로고    scopus 로고
    • Error exponents in hypothesis testing for correlated states on a spin chain
    • 10.1063/1.2872276, e-print arXiv:0707.2020.
    • Hiai F. Mosonyi M. Ogawa T. Error exponents in hypothesis testing for correlated states on a spin chain. J. Math. Phys. 2008, 49:032112. 10.1063/1.2872276; e-print arXiv:0707.2020.
    • (2008) J. Math. Phys. , vol.49 , pp. 032112
    • Hiai, F.1    Mosonyi, M.2    Ogawa, T.3
  • 14
    • 34250918551 scopus 로고
    • Zur Quantenmechanischen Begründung des zweiten Hauptsatzes der Wärmelehre
    • 10.1007/BF01341997
    • Klein O. Zur Quantenmechanischen Begründung des zweiten Hauptsatzes der Wärmelehre. Z. Phys. 1931, 72(11-12):767-775. 10.1007/BF01341997
    • (1931) Z. Phys. , vol.72 , Issue.11-12 , pp. 767-775
    • Klein, O.1
  • 15
    • 69449101829 scopus 로고    scopus 로고
    • The operational meaning of min- and max-entropy
    • 10.1109/TIT.2009.2025545
    • König R. Renner R. Schaffner C. The operational meaning of min- and max-entropy. IEEE Trans. Inf. Theory 2009, 55(9):4337-4347. 10.1109/TIT.2009.2025545
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.9 , pp. 4337-4347
    • König, R.1    Renner, R.2    Schaffner, C.3
  • 16
    • 68949114247 scopus 로고    scopus 로고
    • A strong converse for classical channel coding using entangled inputs
    • 10.1103/PhysRevLett.103.070504
    • König R. Wehner S. A strong converse for classical channel coding using entangled inputs. Phys. Rev. Lett. 2009, 103(7):070504. 10.1103/PhysRevLett.103.070504
    • (2009) Phys. Rev. Lett. , vol.103 , Issue.7 , pp. 070504
    • König, R.1    Wehner, S.2
  • 18
    • 0004967775 scopus 로고
    • Proof of the strong subadditivity of quantum-mechanical entropy
    • 10.1063/1.1666274
    • Lieb E.H. Ruskai M.B. Proof of the strong subadditivity of quantum-mechanical entropy. J. Math. Phys. 1973, 14(12):1938. 10.1063/1.1666274
    • (1973) J. Math. Phys. , vol.14 , Issue.12 , pp. 1938
    • Lieb, E.H.1    Ruskai, M.B.2
  • 19
    • 0001335497 scopus 로고
    • Expectations and entropy inequalities for finite quantum systems
    • 10.1007/BF01608390
    • Lindblad G. Expectations and entropy inequalities for finite quantum systems. Commun. Math. Phys. 1974, 39:111-119. 10.1007/BF01608390
    • (1974) Commun. Math. Phys. , vol.39 , pp. 111-119
    • Lindblad, G.1
  • 20
    • 0001930151 scopus 로고
    • Completely positive maps and entropy inequalities
    • 10.1007/BF01609396
    • Lindblad G. Completely positive maps and entropy inequalities. Commun. Math. Phys. 1975, 40:147-151. 10.1007/BF01609396
    • (1975) Commun. Math. Phys. , vol.40 , pp. 147-151
    • Lindblad, G.1
  • 21
    • 0001287029 scopus 로고
    • Generalized entropic uncertainty relations
    • 10.1103/PhysRevLett.60.1103
    • Maassen H. Uffink J. Generalized entropic uncertainty relations. Phys. Rev. Lett. 1988, 60(12):1103-1106. 10.1103/PhysRevLett.60.1103
    • (1988) Phys. Rev. Lett. , vol.60 , Issue.12 , pp. 1103-1106
    • Maassen, H.1    Uffink, J.2
  • 22
    • 68749089914 scopus 로고    scopus 로고
    • Generalized relative entropies and the capacity of classical-quantum channels
    • 10.1063/1.3167288
    • Mosonyi M. Datta N. Generalized relative entropies and the capacity of classical-quantum channels. J. Math. Phys. 2009, 50:072104. 10.1063/1.3167288.
    • (2009) J. Math. Phys. , vol.50 , pp. 072104
    • Mosonyi, M.1    Datta, N.2
  • 23
    • 79952824089 scopus 로고    scopus 로고
    • On the quantum Renyi relative entropies and related capacity formulas
    • 10.1109/TIT.2011.2110050
    • Mosonyi M. Hiai F. On the quantum Renyi relative entropies and related capacity formulas. IEEE Trans. Inf. Theory 2011, 57:2474-2487. 10.1109/TIT.2011.2110050
    • (2011) IEEE Trans. Inf. Theory , vol.57 , pp. 2474-2487
    • Mosonyi, M.1    Hiai, F.2
  • 24
    • 84923615213 scopus 로고    scopus 로고
    • Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
    • e-print arXiv:1309.3228.
    • Mosonyi M. Ogawa T. Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies. and e-print arXiv:1309.3228.
    • Mosonyi, M.1    Ogawa, T.2
  • 25
    • 84891545793 scopus 로고    scopus 로고
    • Quantum relative Rényi entropies
    • Master thesis, ETH Zurich.
    • Müller-Lennert M. Quantum relative Rényi entropies. 2013, Master thesis, ETH Zurich.
    • (2013)
    • Müller-Lennert, M.1
  • 26
    • 84891529492 scopus 로고    scopus 로고
    • On quantum Rényi entropies: A new definition, some properties and several conjectures
    • e-print arXiv:1306.3142v1.
    • Müller-Lennert M. Dupuis F. Szehr O. Fehr S. Tomamichel M. On quantum Rényi entropies: A new definition, some properties and several conjectures. and e-print arXiv:1306.3142v1.
    • Müller-Lennert, M.1    Dupuis, F.2    Szehr, O.3    Fehr, S.4    Tomamichel, M.5
  • 27
    • 0034316025 scopus 로고    scopus 로고
    • Strong converse and Stein's lemma in quantum hypothesis testing
    • 10.1109/18.887855
    • Ogawa T. Nagaoka H. Strong converse and Stein's lemma in quantum hypothesis testing. IEEE Trans. Inf. Theory 2000, 46(7):2428-2433. 10.1109/18.887855
    • (2000) IEEE Trans. Inf. Theory , vol.46 , Issue.7 , pp. 2428-2433
    • Ogawa, T.1    Nagaoka, H.2
  • 28
    • 2942640136 scopus 로고    scopus 로고
    • On error exponents in quantum hypothesis testing
    • 10.1109/TIT.2004.828155
    • Ogawa T. Hayashi M. On error exponents in quantum hypothesis testing. IEEE Trans. Inf. Theory 2004, 50(6):1368-1372. 10.1109/TIT.2004.828155
    • (2004) IEEE Trans. Inf. Theory , vol.50 , Issue.6 , pp. 1368-1372
    • Ogawa, T.1    Hayashi, M.2
  • 29
    • 0033540129 scopus 로고    scopus 로고
    • Hypercontractivity in noncommutative Lp spaces
    • 10.1006/jfan.1998.3342
    • Olkiewicz R. Zegarlinski B. Hypercontractivity in noncommutative Lp spaces. J. Funct. Anal. 1999, 161(1):246-285. 10.1006/jfan.1998.3342
    • (1999) J. Funct. Anal. , vol.161 , Issue.1 , pp. 246-285
    • Olkiewicz, R.1    Zegarlinski, B.2
  • 30
    • 0002988067 scopus 로고
    • Quasi-entropies for finite quantum systems
    • 10.1016/0034-4877(86)90067-4
    • Petz D. Quasi-entropies for finite quantum systems. Rep. Math. Phys. 1986, 23:57-65. 10.1016/0034-4877(86)90067-4
    • (1986) Rep. Math. Phys. , vol.23 , pp. 57-65
    • Petz, D.1
  • 31
    • 33846181385 scopus 로고    scopus 로고
    • Security of quantum key distribution
    • Ph.D. thesis, ETH Zurich.
    • Renner R. Security of quantum key distribution. 2005, Ph.D. thesis, ETH Zurich.
    • (2005)
    • Renner, R.1
  • 33
    • 0035981724 scopus 로고    scopus 로고
    • Inequalities for quantum entropy: A review with conditions for equality
    • 10.1063/1.1497701
    • Ruskai M.-B. Inequalities for quantum entropy: A review with conditions for equality. J. Math. Phys. 2002, 43(9):4358. 10.1063/1.1497701
    • (2002) J. Math. Phys. , vol.43 , Issue.9 , pp. 4358
    • Ruskai, M.-B.1
  • 34
    • 84856043672 scopus 로고
    • A mathematical theory of communication
    • 10.1002/j.1538-7305.1948.tb01338.x
    • Shannon C. A mathematical theory of communication. Bell Syst. Tech. J. 1948, 27:379-423. 10.1002/j.1538-7305.1948.tb01338.x
    • (1948) Bell Syst. Tech. J. , vol.27 , pp. 379-423
    • Shannon, C.1
  • 35
    • 84972513554 scopus 로고
    • On general minimax theorems
    • 10.2140/pjm.1958.8.171
    • Sion M. On general minimax theorems. Pac. J. Math. 1958, 8:171-176. 10.2140/pjm.1958.8.171
    • (1958) Pac. J. Math. , vol.8 , pp. 171-176
    • Sion, M.1
  • 36
    • 84968466834 scopus 로고
    • Positive functions on C*-algebras
    • 10.1090/S0002-9939-1955-0069403-4
    • Stinespring W.F. Positive functions on C*-algebras. Proc. Am. Math. Soc. 1955, 6:211-216. 10.1090/S0002-9939-1955-0069403-4
    • (1955) Proc. Am. Math. Soc. , vol.6 , pp. 211-216
    • Stinespring, W.F.1
  • 37
    • 84876755252 scopus 로고    scopus 로고
    • A framework for non-asymptotic quantum information theory
    • Ph.D. thesis, ETH Zurich.
    • Tomamichel M. A framework for non-asymptotic quantum information theory. 2012, Ph.D. thesis, ETH Zurich.
    • (2012)
    • Tomamichel, M.1
  • 38
    • 84891531122 scopus 로고    scopus 로고
    • Focus Tutorial: Smooth min/max-entropies
    • QCrypt 2012, Slides available online at.
    • Tomamichel M. Focus Tutorial: Smooth min/max-entropies. QCrypt 2012, Slides available online at.
    • Tomamichel, M.1
  • 39
    • 77949536061 scopus 로고    scopus 로고
    • A fully quantum asymptotic equipartition property
    • 10.1109/TIT.2009.2032797
    • Tomamichel M. Colbeck R. Renner R. A fully quantum asymptotic equipartition property. IEEE Trans. Inf. Theory 2009, 55(12):5840-5847. 10.1109/TIT.2009.2032797.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.12 , pp. 5840-5847
    • Tomamichel, M.1    Colbeck, R.2    Renner, R.3
  • 40
    • 79952714639 scopus 로고    scopus 로고
    • Uncertainty relation for smooth entropies
    • 10.1103/PhysRevLett.106.110506
    • Tomamichel M. Renner R. Uncertainty relation for smooth entropies. Phys. Rev. Lett. 2011, 106(11):110506. 10.1103/PhysRevLett.106.110506.
    • (2011) Phys. Rev. Lett. , vol.106 , Issue.11 , pp. 110506
    • Tomamichel, M.1    Renner, R.2
  • 42
    • 0042030118 scopus 로고
    • Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory
    • 10.1007/BF01609834
    • Uhlmann A. Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory. Commun. Math. Phys. 1977, 54:21-32. 10.1007/BF01609834
    • (1977) Commun. Math. Phys. , vol.54 , pp. 21-32
    • Uhlmann, A.1
  • 43
    • 84891501226 scopus 로고    scopus 로고
    • Strong converse for the classical capacity of entanglement-breaking channels
    • e-print arXiv:1306.1586.
    • Wilde M.M. Winter A. Yang D. Strong converse for the classical capacity of entanglement-breaking channels. and e-print arXiv:1306.1586.
    • Wilde, M.M.1    Winter, A.2    Yang, D.3
  • 45
    • 84891506339 scopus 로고    scopus 로고
    • In contrast, the mean H(ρ⊕σ)=max{H(ρ),H(σ)} would lead to a quantity that is not continuous.
    • In contrast, the mean H(ρ⊕σ)=max{H(ρ),H(σ)} would lead to a quantity that is not continuous.
  • 46
    • 84891525186 scopus 로고    scopus 로고
    • 2)
    • 2).


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.