Necessary Condition for Local Distinguishability of Maximally Entangled States: Beyond Orthogonality Preservation

Abstract

The (im)possibility of local distinguishability of orthogonal multipartite quantum states still remains an intriguing question. Beyond ${\mathbb{C}}^3\otimes {\mathbb{C}}^3$, the problem remains unsolved even for maximally entangled states (MES). So far, the only known condition for the local distinguishability of states is the well-known orthogonality preservation (OP). Using an upper bound on the locally accessible information for bipartite states, we derive a very simple necessary condition for any set of pairwise orthogonal MES in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ to be perfectly locally distinguishable. This condition is seen to be stronger than the OP condition. This is particularly so for any set of $d$ number of pairwise orthogonal MES in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$. When testing this condition for the local distinguishability of all sets of four generalized Bell states in ${\mathbb{C}}^4\otimes {\mathbb{C}}^4$, we find that it is not only necessary but also sufficient to determine their local distinguishability. This demonstrates that the aforementioned upper-bound may play a significant role in the general scenario of local distinguishability of bipartite states.

11 pages. The content is essentially the same as the previous version, with the language having been simplified a bit. Also, the appendix has been shortened