Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy

Eric A. Carlen; Elliott H. Lieb

doi:10.1007/s11005-012-0565-6

Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy

Eric A. Carlen, Elliott H. Lieb

Mathematics

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

Let ρ ₁₂ be a bipartite density matrix. We prove lower bounds for the entanglement of formation E _f(ρ ₁₂) and the squashed entanglement E _sq(ρ ₁₂) in terms of the conditional entropy S ₁₂ - S ₁ and prove that these bounds are sharp by constructing a new class of states whose entanglements can be computed, and for which the bounds are saturated.

Original language	English (US)
Pages (from-to)	1-11
Number of pages	11
Journal	Letters in Mathematical Physics
Volume	101
Issue number	1
DOIs	https://doi.org/10.1007/s11005-012-0565-6
State	Published - Jul 2012

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

entanglement
entropy
strong subadditivity

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10.1007/s11005-012-0565-6

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title = "Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy",

abstract = "Let ρ 12 be a bipartite density matrix. We prove lower bounds for the entanglement of formation E f(ρ 12) and the squashed entanglement E sq(ρ 12) in terms of the conditional entropy S 12 - S 1 and prove that these bounds are sharp by constructing a new class of states whose entanglements can be computed, and for which the bounds are saturated.",

keywords = "entanglement, entropy, strong subadditivity",

author = "Carlen, {Eric A.} and Lieb, {Elliott H.}",

note = "Funding Information: E. A. Carlen{\textquoteright}s work partially supported by U.S. National Science Foundation grant DMS 0901632 and E. H. Lieb{\textquoteright}s work partially supported by U.S. National Science Foundati grant PHY 0965859. {\textcopyright}c 2012 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.",

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doi = "10.1007/s11005-012-0565-6",

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T1 - Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy

AU - Carlen, Eric A.

AU - Lieb, Elliott H.

N1 - Funding Information: E. A. Carlen’s work partially supported by U.S. National Science Foundation grant DMS 0901632 and E. H. Lieb’s work partially supported by U.S. National Science Foundati grant PHY 0965859. ©c 2012 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.

PY - 2012/7

Y1 - 2012/7

N2 - Let ρ 12 be a bipartite density matrix. We prove lower bounds for the entanglement of formation E f(ρ 12) and the squashed entanglement E sq(ρ 12) in terms of the conditional entropy S 12 - S 1 and prove that these bounds are sharp by constructing a new class of states whose entanglements can be computed, and for which the bounds are saturated.

AB - Let ρ 12 be a bipartite density matrix. We prove lower bounds for the entanglement of formation E f(ρ 12) and the squashed entanglement E sq(ρ 12) in terms of the conditional entropy S 12 - S 1 and prove that these bounds are sharp by constructing a new class of states whose entanglements can be computed, and for which the bounds are saturated.

KW - entanglement

KW - entropy

KW - strong subadditivity

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JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 1

ER -

Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy

Abstract

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