M. Ohya and D. Petz: Quantum entropy and its use, (Springer 1993) Home/Search Document Not in Database Summary Related Articles Check |
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Quantum Information and Quantum Computing - These Are Lecture (Correct)
....in its Schmidt decomposition) is singled out as maximally entangled , because it is pure, but its restriction to a subsystem is as mixed as possible, namely the normalized trace. This reduces measures of entanglement to measures of mixedness, which are well studied in terms of entropy functionals [OP]. All measures of mixedness, which assign the same value to unitarily equivalent states, agree that the density matrix proportional to the identity is most mixed. The connection between entropy functionals and measures of entanglement will be pursued later on. 3.2] This identity can be ....
M. Ohya and D. Petz: Quantum entropy and its use, Springer Verlag, Heidelberg 1993.
Quantum Information Theory - an Invitation - Werner (2001) (2 citations) (Correct)
....#) # ; 6.27) Both quantities are positive, and may be infinite on an infinite dimensional space. The von Neumann entropy is concave, whereas the relative entropy is convex jointly in both arguments. For more precise definitions, and many further results, I recommend the book of Petz and Ohya [21]. The strongest coding theorem for quantum channels known so far is the following expression for the one shot classical capacity, proved by Holevo [23] C c,1 (T) max # S ## i p i T # [# i ] # # i p i S(T # [# i ] # (6.28) Whether or not this is equal to the classical capacity ....
M. Ohya and D. Petz: Quantum entropy and its use, (Springer 1993)
On Quantum Dynamical Entropy - Fannes, Tuyls (1994) (Correct)
....properties of the entropy generally don t extend to the non commutative situation. The last proposition gives a partial result. The proof uses the notion of relative entropy. We introduce it here very briefly and refer the reader to any standard work on entropy for a more detailed discussion [OP]. The relative entropy S(ae 1 ; ae 2 ) of two density matrices ae 1 and ae 2 on a Hilbert space H is given by: S(ae 1 ; ae 2 ) Tr ae 1 Gamma log ae 1 Gamma log ae 2 Delta : 20 Proposition 6.4 Let A be a C algebra and X , Y partitions of unity in A with X bistochastic. Then, for an ....
.... us denote by the normalized trace on the d dimensional subspace of H spanned by the vectors (Y) Omega and (Y ffi X ) Omega Gamma One easily verifies that S(ae; log d Gamma S(ae) Because Pi X is bistochastic: ffi Pi X = Uhlmann s monotonicity theorem for completely positive mappings [OP] gives then: S Gamma ae [Y ffi X ] Delta = S(j Omega ih Omega j ffi Pi YffiX ) GammaS(j Omega ih Omega j ffi Pi YffiX ; log d = GammaS(j Omega ih Omega j ffi Pi Y ffi Pi X ; log d GammaS(j Omega ih Omega j ffi Pi Y ; log d = S(ae [Y] Acknowledgements This ....
M. Ohya and D. Petz: Quantum Entropy and its Use, Texts and monographs in physics, Springer Verlag Heidelberg Berlin (1993)
Quantum Information Theory - an Invitation - Werner (2001) (2 citations) (Correct)
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M. Ohya and D. Petz: Quantum entropy and its use, (Springer 1993)
Optimal Cloning of Pure States - Werner (1998) (7 citations) (Correct)
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M. Ohya and D. Petz: Quantum entropy and its use, Springer Verlag, Heidelberg 1993.
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