Multi-copy adaptive local discrimination: Strongest possible two-qubit nonlocal bases

TL;DR

This paper investigates the limits of adaptive local discrimination of orthogonal two-qubit states, revealing ensembles that require more copies than previously known and exploring the nonlocal strength and super-additivity in quantum information tasks.

Contribution

It provides new examples of two-qubit bases requiring three copies for adaptive discrimination and analyzes the varying nonlocal strength of ensembles in this context.

Findings

Some orthonormal bases need 3 copies for adaptive discrimination.

Discrimination requirements vary among different ensembles.

Super-additivity phenomena are observed in locally accessible information.

Abstract

Ensembles of composite quantum states can exhibit nonlocal behaviour in the sense that their optimal discrimination may require global operations. Such an ensemble containing N pairwise orthogonal pure states, however, can always be perfectly distinguished under adaptive local scheme if (N-1) copies of the state are available. In this letter, we provide examples of orthonormal bases in two-qubit Hilbert space whose adaptive discrimination require 3 copies of the state. For this composite system we analyze multi-copy adaptive local distinguishability of orthogonal ensembles in full generality which in turn assigns varying nonlocal strength to different such ensembles. We also come up with ensembles whose discrimination under adaptive separable scheme require less number of copies than adaptive local schemes. Our construction finds important application in multipartite secret sharing tasks and indicates towards an intriguing super-additivity phenomenon for locally accessible information.