We review some results on analytical computations of the measures for quantum entanglement: entanglement of formation and concurrence. We introduce some estimations of the lower bounds for the entanglement of formation in bipartite mixed states, and of lower bounds for the concurrence in bipartite and tripartite systems. The results on lower bounds for the concurrence are also generalized to arbitrary multipartite systems.

Frontiers of Computer Science in ChinaJun 1, 200827 citations

Physics Letters A

A lower bound on entanglement of formation of 2⊗n system

Ping‐Xing Chen, Lin-Mei Liang, Cheng-Zu Li, Ming-Qiu Huang

Published Mar 1, 2002• 13 citations

Publisher

DOI: 10.1016/s0375-9601(02)00175-5

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Wootters [Phys. Rev. Lett.

80,

2245 (1998)] has derived a closed formula for the entanglement of formation (EOF) of an arbitrary mixed state in a system of two qubits. There is no known closed-form expression for the EOF of an arbitrary mixed state in any system more complicated than two qubits. This paper, via a relatively straightforward generalization of Wootters' original derivation, obtains a closed-form lower bound on the EOF of an arbitary mixed state of a system composed of a qubit and a qudit (a d-level quantum system, with

d>~3).

The derivation of the lower bound is detailed for a system composed of a qubit and a qutrit

(d=3);

the generalization to

d>3

then follows readily.