TY - GEN
T1 - Degradable states and one-way entanglement distillation
AU - Leditzky, Felix
AU - Datta, Nilanjana
AU - Smith, Graeme
N1 - Funding Information:
Acknowledgements— We would like to thank Christian Ma-jenz and Andreas Winter (during the workshop “Beyond IID in Information Theory”, July 18-22, 2016 in Barcelona), as well as Will Matthews for helpful feedback. This material is based upon work supported by the National Science Foundation under Grant Number 1125844.
Publisher Copyright:
© 2017 IEEE.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017/8/9
Y1 - 2017/8/9
N2 - We derive an upper bound on the one-way distillable entanglement of bipartite quantum states. To this end, we revisit the notion of degradable, conjugate degradable, and antidegrad-able bipartite quantum states [1]. We prove that for degradable and conjugate degradable states the one-way distillable entanglement is equal to the coherent information, and thus given by a single-letter formula. Furthermore, it is well-known that the one-way distillable entanglement of antidegradable states is zero. We use these results to derive an upper bound for arbitrary bipartite quantum states, which is based on a convex decomposition of a bipartite state into degradable and antidegradable states. This upper bound is always at least as good an upper bound as the entanglement of formation. Applying our bound to the qubit depolarizing channel, we obtain an upper bound on its quantum capacity that is strictly better than previously known bounds in the high noise regime. We also transfer the concept of approximate degradability [2] to quantum states and show that this yields another easily computable upper bound on the one-way distillable entanglement. Moreover, both methods of obtaining upper bounds on the one-way distillable entanglement can be combined into a generalized one.
AB - We derive an upper bound on the one-way distillable entanglement of bipartite quantum states. To this end, we revisit the notion of degradable, conjugate degradable, and antidegrad-able bipartite quantum states [1]. We prove that for degradable and conjugate degradable states the one-way distillable entanglement is equal to the coherent information, and thus given by a single-letter formula. Furthermore, it is well-known that the one-way distillable entanglement of antidegradable states is zero. We use these results to derive an upper bound for arbitrary bipartite quantum states, which is based on a convex decomposition of a bipartite state into degradable and antidegradable states. This upper bound is always at least as good an upper bound as the entanglement of formation. Applying our bound to the qubit depolarizing channel, we obtain an upper bound on its quantum capacity that is strictly better than previously known bounds in the high noise regime. We also transfer the concept of approximate degradability [2] to quantum states and show that this yields another easily computable upper bound on the one-way distillable entanglement. Moreover, both methods of obtaining upper bounds on the one-way distillable entanglement can be combined into a generalized one.
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U2 - 10.1109/ISIT.2017.8006791
DO - 10.1109/ISIT.2017.8006791
M3 - Conference contribution
AN - SCOPUS:85034117538
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1559
EP - 1562
BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 IEEE International Symposium on Information Theory, ISIT 2017
Y2 - 25 June 2017 through 30 June 2017
ER -