A Return to the Optimal Detection of Quantum Information

TL;DR

This paper revisits a classic quantum information problem, demonstrating that global operations outperform local ones in discriminating certain quantum states, revealing nonlocality without entanglement in two-qubit pure states.

Contribution

It proves the superiority of global over local operations in quantum state discrimination and identifies a finite gap between LOCC and separable operations, highlighting nonlocality without entanglement.

Findings

Global operations outperform LOCC in discriminating the double trine ensemble.

A finite gap exists between LOCC and separable operations.

Two-way adaptive LOCC strategies outperform one-way protocols.

Abstract

In 1991, Asher Peres and William Wootters wrote a seminal paper on the nonlocal processing of quantum information [\textit{Phys. Rev. Lett.} \textbf{66} 1119 (1991)]. We return to their classic problem and solve it in various contexts. Specifically, for discriminating the "double trine" ensemble with minimum error, we prove that global operations are more powerful than local operations with classical communication (LOCC). Even stronger, there exists a finite gap between the optimal LOCC probability and that obtainable by separable operations (SEP). Additionally we prove that a two-way, adaptive LOCC strategy can always beat a one-way protocol. Our results provide the first known instance of "nonlocality without entanglement" in two qubit pure states.