More nonlocality with less purity

TL;DR

This paper reveals that mixed quantum states can exhibit a form of nonlocality that pure states do not, as they can be indistinguishable by LOCC regardless of the number of copies, highlighting a fundamental difference.

Contribution

It demonstrates that orthogonal mixed states cannot be distinguished by LOCC even with many copies, unlike pure states, introducing a new perspective on quantum nonlocality.

Findings

Mixed states can be nonlocally indistinguishable regardless of copies.

Pure states are distinguishable with fewer copies than the total number of states.

Mixed states exhibit a new form of nonlocality absent in pure states.

Abstract

Quantum information is nonlocal in the sense that local measurements on a composite quantum system, prepared in one of many mutually orthogonal states, may not reveal in which state the system was prepared. It is shown that in the many copy limit this kind of nonlocality is fundamentally different for pure and mixed quantum states. In particular, orthogonal mixed states may not be distinguishable by local operations and classical communication (LOCC), no matter how many copies are supplied, whereas any set of N orthogonal pure states can be perfectly discriminated with m copies, where, m<N. Thus mixed quantum states can exhibit a new kind of nonlocality absent in pure states. We also argue that a set of orthogonal quantum states may be said to be maximally indistinguishable iff the set is not conclusively locally distinguishable with multiple copies.