Simulating positive-operator-valued measures with projective measurements

TL;DR

This paper investigates which quantum measurements can be simulated by projective measurements combined with classical randomness, providing theoretical conditions, algorithms, and practical bounds relevant for quantum information processing.

Contribution

It introduces a framework to determine projective-simulability of measurements, including algorithms and bounds, advancing understanding of measurement simulation in quantum physics.

Findings

Every measurement can be realized by classical processing of projective measurements plus an ancilla.

Deciding projective-simulability in dimensions two and three can be formulated as semi-definite programming.

Conditions for measurement simulation using projective measurements are established for any dimension.

Abstract

Standard projective measurements represent a subset of all possible measurements in quantum physics, defined by positive-operator-valued measures. We study what quantum measurements are projective simulable, that is, can be simulated by using projective measurements and classical randomness. We first prove that every measurement on a given quantum system can be realised by classical processing of projective measurements on the system plus an ancilla of the same dimension. Then, given a general measurement in dimension two or three, we show that deciding whether it is projective-simulable can be solved by means of semi-definite programming. We also establish conditions for the simulation of measurements using projective ones valid for any dimension. As an application of our formalism, we improve the range of visibilities for which two-qubit Werner states do not violate any Bell inequality for all measurements. From an implementation point of view, our work provides bounds on the amount of noise a measurement tolerates before losing any advantage over projective ones.