# Squashed entanglement and approximate private states

Squashed entanglement and approximate private states The squashed entanglement is a fundamental entanglement measure in quantum information theory, finding application as an upper bound on the distillable secret key or distillable entanglement of a quantum state or a quantum channel. This paper simplifies proofs that the squashed entanglement is an upper bound on distillable key for finite-dimensional quantum systems and solidifies such proofs for infinite-dimensional quantum systems. More specifically, this paper establishes that the logarithm of the dimension of the key system (call it $$\log _{2}K$$ log 2 K ) in an $$\varepsilon$$ ε -approximate private state is bounded from above by the squashed entanglement of that state plus a term that depends only $$\varepsilon$$ ε and $$\log _{2}K$$ log 2 K . Importantly, the extra term does not depend on the dimension of the shield systems of the private state. The result holds for the bipartite squashed entanglement, and an extension of this result is established for two different flavors of the multipartite squashed entanglement. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Squashed entanglement and approximate private states

, Volume 15 (11) – Sep 1, 2016
18 pages

/lp/springer_journal/squashed-entanglement-and-approximate-private-states-xzvuCDnJwd
Publisher
Springer US
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-016-1432-7
Publisher site
See Article on Publisher Site

### Abstract

The squashed entanglement is a fundamental entanglement measure in quantum information theory, finding application as an upper bound on the distillable secret key or distillable entanglement of a quantum state or a quantum channel. This paper simplifies proofs that the squashed entanglement is an upper bound on distillable key for finite-dimensional quantum systems and solidifies such proofs for infinite-dimensional quantum systems. More specifically, this paper establishes that the logarithm of the dimension of the key system (call it $$\log _{2}K$$ log 2 K ) in an $$\varepsilon$$ ε -approximate private state is bounded from above by the squashed entanglement of that state plus a term that depends only $$\varepsilon$$ ε and $$\log _{2}K$$ log 2 K . Importantly, the extra term does not depend on the dimension of the shield systems of the private state. The result holds for the bipartite squashed entanglement, and an extension of this result is established for two different flavors of the multipartite squashed entanglement.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Sep 1, 2016

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