In $2\otimes 2$, more than two orthogonal Bell states with a single copy can never be discriminated with certainty if only local operations and classical communication (LOCC) are allowed. We show here that more than $d$ numbers of pairwise orthogonal maximally entangled states in $d\otimes d$, which are in canonical form, used by Bennett et al. [Phys. Rev. Lett. 70, 1895 (1993)], can never be discriminated with certainty by LOCC, when single copies of the states are provided. Interestingly we show here that all orthogonal maximally entangled states, which are in canonical form, can be discriminated with certainty by LOCC if and only if two copies of each of the states are provided. We provide here a conjecture regarding the highly nontrivial problem of local distinguishability of any $d$ or fewer numbers of pairwise orthogonal maximally entangled states in $d\otimes d$ (in the single copy case).

• Received 6 January 2004

DOI:https://doi.org/10.1103/PhysRevA.70.022304