Expanding the principle of local distinguishability

TL;DR

This paper explores the limits of the principle of local distinguishability in quantum systems, showing that for pure states, local measurements can sometimes distinguish all pure states without distinguishing all states, suggesting an expanded principle.

Contribution

It demonstrates that the principle of local distinguishability can be extended to pure states, challenging the traditional understanding of its scope.

Findings

Local measurements can distinguish all pure states but not all states in certain cases.

The principle of local distinguishability may be applicable beyond its usual scope.

Pure state distinguishability can be achieved with restricted local measurements.

Abstract

The principle of local distinguishability states that an arbitrary physical state of a bipartite system can be determined by the combined statistics of local measurements performed on the subsystems. A necessary and sufficient requirement for the local measurements is that each one must be able to distinguish between all pairs of states of the respective subsystems. We show that if the task is changed into the determination of an arbitrary bipartite pure state, then at least in certain cases it is possible to restrict to local measurements which can distintinguish all pure states but not all states. This surprising fact gives evidence that the principle of local distinguishability may be expanded beyond its usual applicability.