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      Concurrence-based entanglement measure for Werner States

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          Abstract

          We give explicit expressions for entanglement measures of Werner states in arbitrary dimensions in terms of concurrence and tangle. We show that an optimal ensemble decomposition for a joint density matrix of a Werner state can achieve the minimum average concurrence and tangle simultaneously. Furthermore, the same decomposition also attains entanglement of formation for Werner states.

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          Entanglement of Formation of an Arbitrary State of Two Qubits

          William Wootters (1997)
          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 is defined as the minimum average entanglement of an ensemble of pure states that represents the given mixed state. An earlier paper [Phys. Rev. Lett. 78, 5022 (1997)] 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 to be true for a special class of mixed states. The present paper extends the proof to arbitrary states of this system and shows how to construct entanglement-minimizing pure-state decompositions.
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            Distributed Entanglement

            Valerie Coffman, Joydip Kundu, William Wootters (1999)
            Consider three qubits A, B, and C which may be entangled with each other. We show that there is a trade-off between A's entanglement with B and its entanglement with C. This relation is expressed in terms of a measure of entanglement called the "tangle," which is related to the entanglement of formation. Specifically, we show that the tangle between A and B, plus the tangle between A and C, cannot be greater than the tangle between A and the pair BC. This inequality is as strong as it could be, in the sense that for any values of the tangles satisfying the corresponding equality, one can find a quantum state consistent with those values. Further exploration of this result leads to a definition of the "three-way tangle" of the system, which is invariant under permutations of the qubits.
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              Entanglement Measures under Symmetry

              R. Werner, K. G. H. Vollbrecht (2000)
              We show how to simplify the computation of the entanglement of formation and the relative entropy of entanglement for states, which are invariant under a group of local symmetries. For several examples of groups we characterize the state spaces, which are invariant under these groups. For specific examples we calculate the entanglement measures. In particular, we derive an explicit formula for the entanglement of formation for UU-invariant states, and we find a counterexample to the additivity conjecture for the relative entropy of entanglement.
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                Author and article information

                Journal
                Publication date Created: 02 February 2007
                Article
                DOI: 10.1016/S0034-4877(07)00003-1
                ArXiV ID: quant-ph/0702017
                SO-VID: 55578bf8-62a9-4eb1-9e33-4352f183e0cb
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                Journal reference Rep. Math. Phys. 58, 325-334 (2006)
                Comments 5 pages, no figure
                Categories quant-ph

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