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Maximal p-norms of entanglement breaking channels

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Quantum Information & Computation, Volume 3, Issue 2

Pages 186 - 190

Published: 01 March 2003 Publication History

Abstract

It shown that when one of the components of a product channel is entanglement breaking, the output state with maximal p-norm is always a product state. This result complements Shor's theorem that both minimal entropy and Holevo capacity are additive for entanglement breaking channels. It is also shown how Shor's results can be recovered from the p-norm results by considering their behavior for p close to one.

References

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A. S. Holevo, "Quantum coding theorems", Russian Math. Surveys, 53, 1295-1331 (1999).

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P. Shor, "Additivity of the classical capacity of entanglement-breaking channels", Journal of Mathematical Physics, 43, no. 9, 4334-4340 (2002).

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G. G. Amosov, A. S. Holevo, and R. F. Werner, "On Some Additivity Problems in Quantum Information Theory", Problems in Information Transmission, 36, 305-313 (2000).

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E. Lieb and W. Thirring, "Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and Their Relation to Sobolev Inequalities", in Studies in Mathematical Physics, E. Lieb, B. Simon, A. Wightman eds., pp. 269-303 (Princeton University Press, 1976).

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K. Matsumoto, T. Shimono and A. Winter, "Remarks on additivity of the Holevo channel capacity and of the entanglement of formation", preprint lanl:quant-ph/0206148.

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Published In

Quantum Information & Computation Volume 3, Issue 2

March 2003

96 pages

ISSN:1533-7146

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Rinton Press, Incorporated

Paramus, NJ

Publication History

Published: 01 March 2003

Received: 18 December 2002

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https://dl.acm.org/doi/10.1109/TIT.2022.3218540
Ding DWilde M(2018)Strong Converse for the Feedback-Assisted Classical Capacity of Entanglement-Breaking ChannelsProblems of Information Transmission10.1134/S003294601801001554:1(1-19)Online publication date: 1-Jan-2018
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Fukuda MNechita I(2018)On the Minimum Output Entropy of Random Orthogonal Quantum ChannelsIEEE Transactions on Information Theory10.1109/TIT.2017.277483364:2(1374-1384)Online publication date: 1-Feb-2018
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Fukuda MGour G(2017)Additive Bounds of Minimum Output Entropies for Unital Channels and an Exact Qubit FormulaIEEE Transactions on Information Theory10.1109/TIT.2016.264145563:3(1818-1828)Online publication date: 1-Mar-2017
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King C(2014)Multiplicativity of superoperator norms for some entanglement breaking channelsQuantum Information & Computation10.5555/2685164.268517414:13-14(1203-1212)Online publication date: 1-Oct-2014
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Watrous J(2005)Notes on super-operator norms induced by schatten normsQuantum Information & Computation10.5555/2011608.20116145:1(58-68)Online publication date: 1-Jan-2005
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King CRuskai M(2004)Comments on multiplicativity of maximalp-norms whenp=2Quantum Information & Computation10.5555/2011593.20116024:6(500-512)Online publication date: 1-Dec-2004
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Audenaert KFuchs CKing CWinter A(2004)Multiplicativity of accessible fidelity and quantumness for sets of quantum statesQuantum Information & Computation10.5555/2011572.20115734:1(1-11)Online publication date: 1-Jan-2004
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Multiplicativity of superoperator norms for some entanglement breaking channels

Entanglement-breaking of quantum dynamical channels

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