More than two multipartite orthogonal states cannot always be discriminated if only local operations and classical communication (LOCC) are allowed. We show that four Bell states cannot be discriminated by LOCC, even probabilistically, using the separability properties of a four-party unlockable bound entangled state. Using an existing inequality among the measures of entanglement, we show that any three Bell states cannot be discriminated with certainty by LOCC. Exploiting the inequality, we calculate the distillable entanglement of a certain class of 4 multiply sign in circle 4 mixed states.

In 2 ⊗ 2, more than two orthogonal Bell states with single copy can never be discriminated with certainty if only local operations and classical communication (LOCC) are allowed. More than d orthogonal maximally entangled states in d ⊗ d, which are in canonical form, used by Bennett et al. [Phys. Rev. Lett. 70 (1993) 1895], can never be discriminated with certainty when a single copy of the states is provided. Interestingly we show that all orthogonal maximally entangled states , which are in canonical form, can be discriminated with certainty if and only if two copies of each of the states are provided. The highly nontrivial problem of local discrimination of any d or less no. of pairwise orthogonal maximally entangled states in d ⊗ d (in single copy case), which are in canonical form, is also discussed here.

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The necessary and sufficient amount of entanglement required for cloning of orthogonal Bell states by local operation and classical communication is derived, and using this result, we provide here some additional examples of reversible, as well as irreversible states.

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