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Volumn 60, Issue 1, 2007, Pages 1-12

Another short and elementary proof of strong subadditivity of quantum entropy

Author keywords

Holevo bound; joint convexity of relative entropy; monotonicity of relative entropy; relative entropy; strong subadditivity; von Neumann entropy

Indexed keywords


EID: 35648990409     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0034-4877(07)00019-5     Document Type: Article
Times cited : (24)

References (27)
  • 1
    • 85008097854 scopus 로고
    • Relative entropy of state of von neumann algebras
    • Araki H. Relative entropy of state of von neumann algebras. Publ. RIMS Kyoto Univ. 9 (1976) 809-833
    • (1976) Publ. RIMS Kyoto Univ. , vol.9 , pp. 809-833
    • Araki, H.1
  • 3
    • 84972517904 scopus 로고
    • A Schwarz inequality for positive linear maps onC*-algebras
    • Choi M.-D. A Schwarz inequality for positive linear maps onC*-algebras. Illinois J. Math. 18 (1974) 565-574
    • (1974) Illinois J. Math. , vol.18 , pp. 565-574
    • Choi, M.-D.1
  • 4
    • 35649002887 scopus 로고    scopus 로고
    • A. S. Holevo: On complementary channels and the additivity problem, quant-ph/0509101.
  • 5
    • 0035089746 scopus 로고    scopus 로고
    • Minimal entropy of states emerging from noisy quantum channels
    • King C., and Ruskai M.B. Minimal entropy of states emerging from noisy quantum channels. 1EEE Trans. Info. Theory 47 (2001) 192-209
    • (2001) 1EEE Trans. Info. Theory , vol.47 , pp. 192-209
    • King, C.1    Ruskai, M.B.2
  • 6
    • 0035582576 scopus 로고    scopus 로고
    • Capacity of quantum channels using product measurements
    • King C., and Ruskai M.B. Capacity of quantum channels using product measurements. J. Math. Phys. 42 (2001) 87-98
    • (2001) J. Math. Phys. , vol.42 , pp. 87-98
    • King, C.1    Ruskai, M.B.2
  • 7
    • 35649010713 scopus 로고    scopus 로고
    • C. King, K. Matsumoto, M. Nathanson and M. B. Ruskai: Properties of conjugate channels with applications to additivity and multiplicativity, quant-ph/0509126.
  • 8
    • 35648999803 scopus 로고    scopus 로고
    • D. Kretschmann and R. F. Werner: Quantum channels with memory, quant-ph/0502106.
  • 9
    • 0033240088 scopus 로고    scopus 로고
    • Monotone Riemannian metrics and relative entropy on non-commutative probability spaces
    • Lesniewski A., and Ruskai M.B. Monotone Riemannian metrics and relative entropy on non-commutative probability spaces. J. Math. Phys. 40 (1999) 5702-5723
    • (1999) J. Math. Phys. , vol.40 , pp. 5702-5723
    • Lesniewski, A.1    Ruskai, M.B.2
  • 10
    • 0004967775 scopus 로고
    • Proof of the strong subadditivity of quantum mechanical entropy
    • Lieb E.H., and Ruskai M.B. Proof of the strong subadditivity of quantum mechanical entropy. J. Math. Phys. 14 (1973) 1938-1941
    • (1973) J. Math. Phys. , vol.14 , pp. 1938-1941
    • Lieb, E.H.1    Ruskai, M.B.2
  • 11
    • 0000411043 scopus 로고
    • Some operator inequalities of the Schwarz type
    • Lieb E.H., and Ruskai M.B. Some operator inequalities of the Schwarz type. Adv. Math 12 (1974) 269-273
    • (1974) Adv. Math , vol.12 , pp. 269-273
    • Lieb, E.H.1    Ruskai, M.B.2
  • 12
    • 26944431524 scopus 로고    scopus 로고
    • A stronger subadditivity of entropy
    • math-ph/0412009, 062329
    • Lieb E.H., and Seiringer R. A stronger subadditivity of entropy. Phys. Rev. A71 (2005) math-ph/0412009, 062329
    • (2005) Phys. Rev. , vol.A71
    • Lieb, E.H.1    Seiringer, R.2
  • 13
    • 0001930151 scopus 로고
    • Completely positive maps and entropy inequalities
    • Lindblad G. Completely positive maps and entropy inequalities. Commun. Math. Phys. 40 (1975) 147-151
    • (1975) Commun. Math. Phys. , vol.40 , pp. 147-151
    • Lindblad, G.1
  • 15
    • 35648971382 scopus 로고    scopus 로고
    • M. A. Nielsen and D. Petz: A simple proof of the strong subadditivity inequality, QIC quant-ph/0408130
  • 18
    • 0002988067 scopus 로고
    • Quasi-entropies for finite quantum systems
    • Petz D. Quasi-entropies for finite quantum systems. Rep. Math. Phys. 23 (1986) 57-65
    • (1986) Rep. Math. Phys. , vol.23 , pp. 57-65
    • Petz, D.1
  • 19
    • 0030501619 scopus 로고    scopus 로고
    • Monotone metrics on matrix spaces
    • Petz D. Monotone metrics on matrix spaces. Lin. AIg. Appl. 244 (1996) 81-96
    • (1996) Lin. AIg. Appl. , vol.244 , pp. 81-96
    • Petz, D.1
  • 20
    • 0035981724 scopus 로고    scopus 로고
    • Inequalities for quantum entropy: A review with conditions for equality
    • erratum 46 (2005), 4358-4375, 019901
    • Ruskai M.B. Inequalities for quantum entropy: A review with conditions for equality. J. Math. Phys. 43 (2002) erratum 46 (2005), 4358-4375, 019901
    • (2002) J. Math. Phys. , vol.43
    • Ruskai, M.B.1
  • 21
    • 35648971383 scopus 로고    scopus 로고
    • pK† B(1-p)K and remarks on related inequalities, quant-ph/0404 126
  • 22
    • 84968466834 scopus 로고
    • Positive functions on C*-algebras
    • E Stinespring W. Positive functions on C*-algebras. Proc. Amer. Math. Soc. 6 (1955) 211-216
    • (1955) Proc. Amer. Math. Soc. , vol.6 , pp. 211-216
    • E Stinespring, W.1
  • 23
    • 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 (1977) 21-32
    • (1977) Commun. Math. Phys. , vol.54 , pp. 21-32
    • Uhlmann, A.1
  • 24
    • 0000557238 scopus 로고
    • Thermodynamik quantenmechanischer Gesamheiten
    • von Neumann J. Thermodynamik quantenmechanischer Gesamheiten. Grtt. Nach. 1 (1927) 273-291
    • (1927) Grtt. Nach. , vol.1 , pp. 273-291
    • von Neumann, J.1
  • 25
    • 35648981369 scopus 로고
    • Berlin English translation by R. T. Beyer, Mathematical Foundations of Quantum Mechanics, Princeton, 1955
    • von Neumann J. Thermodynamik (1932), Berlin English translation by R. T. Beyer, Mathematical Foundations of Quantum Mechanics, Princeton, 1955
    • (1932) Thermodynamik
    • von Neumann, J.1
  • 26
    • 5844266551 scopus 로고
    • General properties of entropy
    • Wehrl A. General properties of entropy. Rev. Mod. Phys. 50 (1978) 221-260
    • (1978) Rev. Mod. Phys. , vol.50 , pp. 221-260
    • Wehrl, A.1
  • 27
    • 12044250345 scopus 로고
    • Ultimate information carrying limit of quantum systems
    • Yuen H.P., and Ozawa M. Ultimate information carrying limit of quantum systems. Phys. Rev. Lett. 70 (1993) 363-366
    • (1993) Phys. Rev. Lett. , vol.70 , pp. 363-366
    • Yuen, H.P.1    Ozawa, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.