On the existence of LOCC-distinguishable bases in three-dimensional subspaces of bipartite 3 × n systems

Abstract

We present numerical evidence showing that any three-dimensional subspace of has an orthonormal basis which can be reliably distinguished using one-way LOCC (local operations and classical communication), where a measurement is made first on the three-dimensional part and the result used to select an optimal measurement on the n-dimensional part. We also show that the order of measurement is essential, by providing an example of a three-dimensional subspace of which does not have any basis that can be distinguished by measuring first on the five-dimensional factor.