Classifying locally distinguishable sets: No activation across bipartitions

TL;DR

This paper investigates the conditions under which locally distinguishable quantum states can or cannot be converted into locally indistinguishable states using orthogonality-preserving LOCC, classifying sets into hierarchies and exploring multipartite complexities.

Contribution

It introduces a classification of locally distinguishable sets based on their convertibility to indistinguishable states and identifies structures that do not permit such conversion, especially in multipartite systems.

Findings

Identified structures of distinguishable states that cannot be converted to indistinguishable states.

Classified distinguishable sets into hierarchies based on conversion possibilities.

Discovered multipartite sets with no activation across bipartitions.

Abstract

A set of orthogonal quantum states is said to be locally indistinguishable if they cannot be perfectly distinguished by local operations and classical communication (LOCC). Otherwise, the states are locally distinguishable. Interestingly, locally indistinguishable states can have productive applications in quantum information processing protocols. In this sense, locally indistinguishable states are useful. On the other hand, it is usual to consider that locally distinguishable states are useless. Nevertheless, recent works suggest that locally distinguishable states should be given due consideration as in certain situations these states can be converted to locally indistinguishable states under orthogonality-preserving LOCC (OP-LOCC). Such a counterintuitive phenomenon motivates us to ask when the aforesaid conversion is possible and when it is not. In this work, we provide different structures of locally distinguishable product and entangled states which do not allow the aforesaid conversion. We also provide certain structures of locally distinguishable states which allow the aforesaid conversion. In this way, we classify the locally distinguishable sets by introducing hierarchies among them. In a multipartite system, this study becomes more involved as there exist multipartite locally distinguishable sets which cannot be converted to locally indistinguishable sets by OP-LOCC across any bipartition. We say this as ``no activation across bi-partitions".