Distinguishability and indistinguishability by LOCC

Abstract

We show that a set of linearly independent quantum states $\{(U_{m,n}\otimes I){\rho }^{AB}(U_{m,n}^{†}\otimes I){\}}_{m,n=0}^{d-1}$, where $U_{m,n}$ are generalized Pauli matrices, cannot be discriminated deterministically or probabilistically by local operations and classical communications (LOCC). On the other hand, any $l$ maximally entangled states from this set are locally distinguishable if $l(l-1)\le 2d$. The explicit projecting measurements are obtained to locally discriminate these states. As an example, we show that four Werner states are locally indistinguishable.

5 pages

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