Maximal gap between local and global distinguishability of bipartite quantum states

TL;DR

This paper establishes a nearly optimal lower bound on the ability of local quantum measurements to distinguish bipartite quantum states, showing the bound scales with the local dimensions and is tight up to a universal constant.

Contribution

It provides a tight lower bound on local measurement effectiveness for bipartite state discrimination, scaling optimally with local dimensions and improving understanding of quantum distinguishability.

Findings

Local measurements can discriminate orthogonal states with error probability bounded by a dimension-dependent term.

The distinguishability norm for local measurements is tightly bounded by the trace norm scaled by local dimensions.

The results are mathematically tight and scale optimally with the bipartite system dimensions.

Abstract

We prove a tight and close-to-optimal lower bound on the effectiveness of local quantum measurements (without classical communication) at discriminating any two bipartite quantum states. Our result implies, for example, that any two orthogonal quantum states of a $n_A\times n_B$ bipartite quantum system can be discriminated via local measurements with an error probability no larger than $\frac12 \left(1 - \frac{1}{c \min\{n_A, n_B\}} \right)$, where $1\leq c\leq 2\sqrt2$ is a universal constant, and our bound scales provably optimally with the local dimensions $n_A,n_B$. Mathematically, this is achieved by showing that the distinguishability norm $\|\cdot\|_{LO}$ associated with local measurements satisfies that $\|\cdot\|_1\leq 2\sqrt2 \min\{n_A,n_B\} \|\cdot\|_{LO}$, where $\|\cdot\|_1$ is the trace norm.