Distinguishability of maximally entangled states

Abstract

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.

Local copying and local discrimination as a study for nonlocality of a set of states

“…In the case of local discrimination, we can also prove that D is the maximum size of a locally distinguishable set of maximally entangled states. This statement was proved by the paper [27] only when the set of maximally entangled states {|Ψ j } N −1 j=0 consists of canonical form Bell states, where a canonical form Bell state |Ψ nm is defined as…”

“…In [3], they proposed a locally indistinguishable product basis and regarded its impossibility for perfect discrimination under LOCC as non-locality of it. After this work, there have been many results of the local discrimination problems [21,22,23,24,25,26,27]. Recently, as a similar problem to local discrimination, a new problem, "local copying", was also raised [9,10], as a problem to study a cloning of unknown entangled states under the LOCC restriction with only minimum entanglement resource.…”

Bipartite Subspaces Having No Bases Distinguishable by Local Operations and Classical Communication

“…In the two-party case, the two parties (Alice and Bob) share one of a known orthogonal collection of pure states, and their goal is to determine which of the states it is [1,2,3,4,6,5,9,10,13,14]. In some cases it is possible for Alice and Bob to perform this task without error and in some it is not.…”

Distillable entanglement ind ddimensions

“…However two orthogonal entangled states can be discriminated by LOCC if only one copy is provided. Recently, Ghosh et al [6] have generalized this result, by using the teleportation protocol of [7], and proved that …”