Werner state

A '''Werner state'''Werner:1989 is a d \times d dimensional bipartite quantum state that is invariant under the unitary U \otimes U for any unitary U. That is, a state \rho that satisfies :\rho = (U \otimes U) \rho (U^\dagger \otimes U^\dagger) for all U on the ''d''-dimensional subsystems. The Werner states are mixtures of projectors onto the symmetric- and anti-symmetric subspaces, with the relative weight p_{sym}being the only parameter that defines the state. :\rho = p_{sym} \frac{2}{d^2 + d} P_{sym} + (1-p_{sym}) \frac{2}{d^2 - d} P_{as}, where :P_{sym} = \frac{1}{2}(1+P), P_{as} = \frac{1}{2}(1-P), are the projectors and :P = \sum_{ij} |i\rangle \langle j| \otimes |j\rangle \langle i| is the permutation operator that exchanges the two subsystems. Werner states are separable for p_{sym} \geq 1/2 and entangled for p_{as} < 1/2. All entangled Werner states violate the PPT separability criterion, but for d \geq 3 no Werner states violate the weaker reduction criterion. Werner states can be parametrized in different ways. One way of writing them is :\rho = \frac{1}{d^2-d \alpha}(1 - \alpha P), where the new parameter \alpha varies between -1 and 1 and relates to the p_{sym} above as \alpha = ((1-2p_{sym})d+1)/(1-2p_{sym}+d). == Multipartite Werner states == Werner states can be generalized to the multipartite case Eggeling.etal:2008. An N-party Werner state is a state that is invariant under U⊗U⊗...⊗U for any unitary U on a single subsystem. The Werner state is no longer described by a single parameter, but by N!-1 parameters, and is a linear combination of the N! different permutations on N systems. == See also == * Isotropic state == References == Category:Quantum States

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Monday, October 26, 2015 - 17:56