A smallest computable entanglement monotone
Eisert J, Wilde MM (2022)
Publication Type: Conference contribution
Publication year: 2022
Publisher: Institute of Electrical and Electronics Engineers Inc.
Book Volume: 2022-June
Pages Range: 2439-2444
Conference Proceedings Title: IEEE International Symposium on Information Theory - Proceedings
Event location: Espoo, FIN
ISBN: 9781665421591
DOI: 10.1109/ISIT50566.2022.9834375
Abstract
The Rains relative entropy of a bipartite quantum state is the tightest known upper bound on its distillable entanglement - which has a crisp physical interpretation of entanglement as a resource - and it is efficiently computable by convex programming. It has not been known to be a selective entanglement monotone in its own right. In this work, we strengthen the interpretation of the Rains relative entropy by showing that it is monotone under the action of selective operations that completely preserve the positivity of the partial transpose, reasonably quantifying entanglement. That is, we prove that Rains relative entropy of an ensemble generated by such an operation does not exceed the Rains relative entropy of the initial state in expectation, giving rise to the smallest, most conservative known computable selective entanglement monotone. Additionally, we show that this is true not only for the original Rains relative entropy, but also for Rains relative entropies derived from various Rényi relative entropies. As an application of these findings, we prove, in both the non-asymptotic and asymptotic settings, that the probabilistic approximate distillable entanglement of a state is bounded from above by various Rains relative entropies.Full version available at https://arxiv.org/abs/2201.00835
Involved external institutions
United States (USA) (US)
Germany (DE)How to cite
APA:
Eisert, J., & Wilde, M.M. (2022). A smallest computable entanglement monotone. In IEEE International Symposium on Information Theory - Proceedings (pp. 2439-2444). Espoo, FIN: Institute of Electrical and Electronics Engineers Inc..
MLA:
Eisert, Jens, and Mark M. Wilde. "A smallest computable entanglement monotone." Proceedings of the 2022 IEEE International Symposium on Information Theory, ISIT 2022, Espoo, FIN Institute of Electrical and Electronics Engineers Inc., 2022. 2439-2444.
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