Single-shot labeling of quantum observables

TL;DR

This paper investigates the problem of uniquely identifying quantum observables with permuted effects in a single measurement attempt, focusing on the labeling problem and characterizing which binary observables can be perfectly labeled.

Contribution

It introduces the labeling problem for quantum observables, analyzes its properties in the single-shot regime, and characterizes binary observables that can be perfectly labeled.

Findings

Identifies the class of observables with permuted effects involved in the labeling problem.

Characterizes binary observables that can be perfectly labeled in a single-shot measurement.

Provides theoretical insights into the distinguishability of quantum observables.

Abstract

We identify and study a particular class of distinguishability problems for quantum observables (POVMs), in which observables with permuted effects are involved, which we call as the labeling problem. Consequently, we identify the binary observables those can be "labeled" perfectly. In this work, we study these problems in the single-shot regime.