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arXiv:quant-ph/0203087 · Physical Review A

Entanglement measure for rank-2 mixed states

Tobias J. Osborne

Published Aug 12, 2005• 88 citations
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Abstract

We provide an easily computable formula for a bipartite mixed-state entanglement measure. Our formula can be applied to readily calculate the entanglement for any rank-2 mixed state of a bipartite system. We use this formula to provide a tight upper bound for the entanglement of formation for rank-2 states of a qubit and a qudit. We also outline situations where our formula could be applied to study the entanglement properties of complex quantum systems.

DOI
10.1103/physreva.72.022309

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We provide an easily computable formula for a bipartite mixed-state entanglement measure. Our formula can be applied to readily calculate the entanglement for any rank-2 mixed state of a bipartite system. We use this formula to provide a tight upper bound for the entanglement of formation for rank-2 states of a qubit and a qudit. We also outline situations where our formula could be applied to study the entanglement properties of complex quantum systems.
Wootters [Phys. Rev. Lett. 80,80,80, 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).d>~3).d> 3). The derivation of the lower bound is detailed for a system composed of a qubit and a qutrit (d=3);(d=3);(d=3); the generalization to d>3d>3d>3 then follows readily.