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Phys. Rev. Lett. 80, 2245–2248 (1998)

Entanglement of Formation of an Arbitrary State of Two Qubits

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William K. Wootters
Department of Physics, Williams College, Williamstown, Massachusetts 01267

Received 12 September 1997; published in the issue dated 9 March 1998

The entanglement of a pure state of a pair of quantum systems is defined as the entropy of either member of the pair. The entanglement of formation of a mixed state ρ is the minimum average entanglement of an ensemble of pure states that represents ρ. An earlier paper conjectured an explicit formula for the entanglement of formation of a pair of binary quantum objects (qubits) as a function of their density matrix, and proved the formula for special states. The present paper extends the proof to arbitrary states of this system and shows how to construct entanglement-minimizing decompositions.

© 1998 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.80.2245
DOI:
10.1103/PhysRevLett.80.2245
PACS:
03.67.-a, 03.65.Bz, 89.70.+c