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Volumn 334, Issue 3, 2015, Pages 1617-1648

Quantum Hypothesis Testing and the Operational Interpretation of the Quantum Rényi Relative Entropies

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EID: 84923615213     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-014-2248-x     Document Type: Article
Times cited : (227)

References (51)
  • 1
    • 0000307085 scopus 로고
    • On an inequality of Lieb and Thirring
    • Araki H.: On an inequality of Lieb and Thirring. Lett. Math. Phys. 19(2), 167–170 (1990)
    • (1990) Lett. Math. Phys. , vol.19 , Issue.2 , pp. 167-170
    • Araki, H.1
  • 3
    • 58049202615 scopus 로고    scopus 로고
    • On the Araki–Lieb–Thirring inequality
    • Audenaert K.M.R.: On the Araki–Lieb–Thirring inequality. Int. J. Inf. Syst. Sci. 4, 78–83 (2008)
    • (2008) Int. J. Inf. Syst. Sci. , vol.4 , pp. 78-83
    • Audenaert, K.M.R.1
  • 4
    • 84891512930 scopus 로고    scopus 로고
    • Quantum Rényi divergence satisfies data processing inequality
    • Beigi S.: Quantum Rényi divergence satisfies data processing inequality. J. Math. Phys. 54, 122202 (2013)
    • (2013) J. Math. Phys. , vol.54 , pp. 122202
    • Beigi, S.1
  • 7
    • 0742323596 scopus 로고    scopus 로고
    • The Shannon–McMillan theorem for ergodic quantum lattice systems
    • Bjelakovic I., Krüger T., Siegmund-Schultze R., Szkoła A.: The Shannon–McMillan theorem for ergodic quantum lattice systems. Invent. Math. 155(1), 203–222 (2004)
    • (2004) Invent. Math. , vol.155 , Issue.1 , pp. 203-222
    • Bjelakovic, I.1    Krüger, T.2    Siegmund-Schultze, R.3    Szkoła, A.4
  • 8
    • 2942733388 scopus 로고    scopus 로고
    • An ergodic theorem for the quantum relative entropy
    • Bjelakovic I., Siegmund-Schultze R.: An ergodic theorem for the quantum relative entropy. Commun. Math. Phys. 247, 697–712 (2004)
    • (2004) Commun. Math. Phys. , vol.247 , pp. 697-712
    • Bjelakovic, I.1    Siegmund-Schultze, R.2
  • 10
    • 0029219702 scopus 로고
    • Generalized cutoff rates and Rényi’s information measures
    • Csiszár I.: Generalized cutoff rates and Rényi’s information measures. IEEE Trans. Inf. Theory 41, 26–34 (1995)
    • (1995) IEEE Trans. Inf. Theory , vol.41 , pp. 26-34
    • Csiszár, I.1
  • 11
    • 66949151794 scopus 로고    scopus 로고
    • Min- and max-relative entropies and a new entanglement monotone
    • Datta N.: Min- and max-relative entropies and a new entanglement monotone. IEEE Trans. Inf. Theory 55(6), 2816–2826 (2009)
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.6 , pp. 2816-2826
    • Datta, N.1
  • 13
    • 84891535488 scopus 로고    scopus 로고
    • Monotonicity of a relative Rényi entropy
    • Frank R.L., Lieb E.H.: Monotonicity of a relative Rényi entropy. J. Math. Phys 54, 122201 (2013)
    • (2013) J. Math. Phys , vol.54 , pp. 122201
    • Frank, R.L.1    Lieb, E.H.2
  • 14
    • 34250872362 scopus 로고
    • The strong converse theorem for hypothesis testing
    • Han T.S., Kobayashi K.: The strong converse theorem for hypothesis testing. IEEE Trans. Inf. Theory 35, 178–180 (1989)
    • (1989) IEEE Trans. Inf. Theory , vol.35 , pp. 178-180
    • Han, T.S.1    Kobayashi, K.2
  • 16
    • 0037147274 scopus 로고    scopus 로고
    • Optimal sequence of POVM’s in the sense of Stein’s lemma in quantum hypothesis testing
    • Hayashi M.: Optimal sequence of POVM’s in the sense of Stein’s lemma in quantum hypothesis testing. J. Phys. A Math. Gen. 35, 10759–10773 (2002)
    • (2002) J. Phys. A Math. Gen. , vol.35 , pp. 10759-10773
    • Hayashi, M.1
  • 18
    • 36849055722 scopus 로고    scopus 로고
    • Error exponent in asymmetric quantum hypothesis testing and its application to classical-quantum channel coding
    • Hayashi M.: Error exponent in asymmetric quantum hypothesis testing and its application to classical-quantum channel coding. Phys. Rev. A 76, 062301 (2007)
    • (2007) Phys. Rev. A , vol.76 , pp. 062301
    • Hayashi, M.1
  • 19
    • 84925474915 scopus 로고    scopus 로고
    • Hayashi, M.: Private communication (2014)
    • Hayashi, M.: Private communication (2014)
  • 22
    • 0002499298 scopus 로고
    • The proper formula for relative entropy and its asymptotics in quantum probability
    • Hiai F., Petz D.: The proper formula for relative entropy and its asymptotics in quantum probability. Commun. Math. Phys. 143, 99–114 (1991)
    • (1991) Commun. Math. Phys. , vol.143 , pp. 99-114
    • Hiai, F.1    Petz, D.2
  • 23
    • 0345784832 scopus 로고
    • Equality cases in matrix norm inequalities of Golden–Thompson type
    • Hiai F.: Equality cases in matrix norm inequalities of Golden–Thompson type. Linear Multilinear Algebra 36, 239–249 (1994)
    • (1994) Linear Multilinear Algebra , vol.36 , pp. 239-249
    • Hiai, F.1
  • 24
    • 41549146719 scopus 로고    scopus 로고
    • Error exponents in hypothesis testing for correlated states on a spin chain
    • Hiai F., Mosonyi M., Ogawa T.: Error exponents in hypothesis testing for correlated states on a spin chain. J. Math. Phys. 49, 032112 (2008)
    • (2008) J. Math. Phys. , vol.49 , pp. 032112
    • Hiai, F.1    Mosonyi, M.2    Ogawa, T.3
  • 25
    • 80052040382 scopus 로고    scopus 로고
    • Quantum f-divergences and error correction
    • Hiai F., Mosonyi M., Petz D., Bény C.: Quantum f-divergences and error correction. Rev. Math. Phys. 23(7), 691–747 (2011)
    • (2011) Rev. Math. Phys. , vol.23 , Issue.7 , pp. 691-747
    • Hiai, F.1    Mosonyi, M.2    Petz, D.3    Bény, C.4
  • 26
    • 32544435921 scopus 로고    scopus 로고
    • Sufficiency in quantum statistical inference
    • Jenčová A., Petz D.: Sufficiency in quantum statistical inference. Commun. Math. Phys. 263, 259–276 (2006)
    • (2006) Commun. Math. Phys. , vol.263 , pp. 259-276
    • Jenčová, A.1    Petz, D.2
  • 29
    • 36649022319 scopus 로고
    • Convex trace functions and the Wigner–Yanase–Dyson conjecture
    • Lieb E.H.: Convex trace functions and the Wigner–Yanase–Dyson conjecture. Adv. Math. 11, 267–288 (1973)
    • (1973) Adv. Math. , vol.11 , pp. 267-288
    • Lieb, E.H.1
  • 30
    • 84942233995 scopus 로고
    • Studies in Mathematical Physics
    • Princeton University Press, Princeton:
    • Lieb, E.H., Thirring, W.: Studies in Mathematical Physics, pp. 269–297. Princeton University Press, Princeton (1976)
    • (1976) pp , vol.269-297
    • Lieb, E.H.1    Thirring, W.2
  • 31
    • 79952824089 scopus 로고    scopus 로고
    • On the quantum Rényi relative entropies and related capacity formulas
    • Mosonyi M., Hiai F.: On the quantum Rényi relative entropies and related capacity formulas. IEEE Trans. Inf. Theory 57, 2474–2487 (2011)
    • (2011) IEEE Trans. Inf. Theory , vol.57 , pp. 2474-2487
    • Mosonyi, M.1    Hiai, F.2
  • 32
    • 84925474911 scopus 로고    scopus 로고
    • Mosonyi, M.: Inequalities for the quantum Rényi divergences with applications to compound coding problems (2013)
    • Mosonyi, M.: Inequalities for the quantum Rényi divergences with applications to compound coding problems (2013). arxiv:1310.7525
  • 33
    • 84925474910 scopus 로고    scopus 로고
    • Mosonyi, M., Ogawa, T.: The strong converse rate of quantum hypothesis testing for correlated quantum states
    • Mosonyi, M., Ogawa, T.: The strong converse rate of quantum hypothesis testing for correlated quantum states. arXiv:1407.3567
  • 36
    • 84925474908 scopus 로고    scopus 로고
    • Nagaoka, H.: The converse part of the theorem for quantum Hoeffding bound
    • Nagaoka, H.: The converse part of the theorem for quantum Hoeffding bound. quant-ph/0611289
  • 37
    • 33847667401 scopus 로고    scopus 로고
    • An information-spectrum approach to classical and quantum hypothesis testing for simple hypotheses
    • Nagaoka H., Hayashi M.: An information-spectrum approach to classical and quantum hypothesis testing for simple hypotheses. IEEE Trans. Inf. Theory 53, 534–549 (2007)
    • (2007) IEEE Trans. Inf. Theory , vol.53 , pp. 534-549
    • Nagaoka, H.1    Hayashi, M.2
  • 39
    • 0034316025 scopus 로고    scopus 로고
    • Strong converse and Stein’s lemma in quantum hypothesis testing
    • Ogawa T., Nagaoka H.: Strong converse and Stein’s lemma in quantum hypothesis testing. IEEE Trans. Inf. Theory 47, 2428–2433 (2000)
    • (2000) IEEE Trans. Inf. Theory , vol.47 , pp. 2428-2433
    • Ogawa, T.1    Nagaoka, H.2
  • 40
    • 0002988067 scopus 로고
    • Quasi-entropies for finite quantum systems
    • Petz D.: Quasi-entropies for finite quantum systems. Rep. Math. Phys. 23, 57–65 (1986)
    • (1986) Rep. Math. Phys. , vol.23 , pp. 57-65
    • Petz, D.1
  • 41
    • 0005156603 scopus 로고
    • Sufficient subalgebras and the relative entropy of states of a von Neumann algebra
    • Petz D.: Sufficient subalgebras and the relative entropy of states of a von Neumann algebra. Commun. Math. Phys. 105, 123–131 (1986)
    • (1986) Commun. Math. Phys. , vol.105 , pp. 123-131
    • Petz, D.1
  • 42
    • 77957179449 scopus 로고
    • Sufficiency of channels over von Neumann algebras
    • Petz D.: Sufficiency of channels over von Neumann algebras. Q. J. Math. Oxf. Ser. (2) 39(153), 97–108 (1988)
    • (1988) Q. J. Math. Oxf. Ser. (2) , vol.39 , Issue.153 , pp. 97-108
    • Petz, D.1
  • 43
    • 0037339343 scopus 로고    scopus 로고
    • Monotonicity of quantum relative entropy revisited
    • Petz D.: Monotonicity of quantum relative entropy revisited. Rev. Math. Phys. 15(1), 79–91 (2003)
    • (2003) Rev. Math. Phys. , vol.15 , Issue.1 , pp. 79-91
    • Petz, D.1
  • 44
    • 33846181385 scopus 로고    scopus 로고
    • Security of quantum key distribution. Ph.D. dissertation, Swiss Federal Institute of Technology Zurich, Diss
    • Renner, R.: Security of quantum key distribution. Ph.D. dissertation, Swiss Federal Institute of Technology Zurich, Diss. ETH No. 16242 (2005)
    • (2005) ETH No , pp. 16242
    • Renner, R.1
  • 46
    • 84876755252 scopus 로고    scopus 로고
    • A framework for non-asymptotic quantum information theory. Ph.D. thesis, Department of Physics
    • Tomamichel, M.: A framework for non-asymptotic quantum information theory. Ph.D. thesis, Department of Physics, ETH Zurich. arXiv:1203.2142
    • ETH Zurich. arXiv , pp. 1203
    • Tomamichel, M.1
  • 48
    • 0042030118 scopus 로고
    • Relative entropy and the Wigner–Yanase–Dyson–Lieb concavity in an interpolation theory
    • Uhlmann A.: Relative entropy and the Wigner–Yanase–Dyson–Lieb concavity in an interpolation theory. Commun. Math. Phys. 54, 21–32 (1977)
    • (1977) Commun. Math. Phys. , vol.54 , pp. 21-32
    • Uhlmann, A.1
  • 49
    • 11644261065 scopus 로고
    • Conditional expectation in an operator algebra
    • Umegaki H.: Conditional expectation in an operator algebra. Kodai Math. Sem. Rep. 14, 59–85 (1962)
    • (1962) Kodai Math. Sem. Rep. , vol.14 , pp. 59-85
    • Umegaki, H.1
  • 50
    • 84905085497 scopus 로고    scopus 로고
    • Strong converse for the classical capacity of entanglement-breaking and Hadamard channels
    • Wilde M.M., Winter A., Yang D.: Strong converse for the classical capacity of entanglement-breaking and Hadamard channels. Commun. Math. Phys. 331(2), 593–622 (2014)
    • (2014) Commun. Math. Phys. , vol.331 , Issue.2 , pp. 593-622
    • Wilde, M.M.1    Winter, A.2    Yang, D.3


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