Adaptive strategy for joint measurements

TL;DR

This paper introduces a technique for determining the minimal noise required for joint measurability of incompatible quantum observables, with applications to symmetric measurement sets and the existence of 4-Specker sets in qubits.

Contribution

It presents a novel method to find simultaneous measurements for noisy quantum observables and establishes tight bounds for measurement compatibility.

Findings

Lower bounds for noise in joint measurements are tight for certain symmetric sets.

Existence of 4-Specker sets in the qubit case is proven.

The method advances understanding of measurement incompatibility in quantum information.

Abstract

We develop a technique to find simultaneous measurements for noisy quantum observables in finite-dimensional Hilbert spaces. We use the method to derive lower bounds for the noise needed to make incompatible measurements jointly measurable. Using our strategy together with recent devel- opments in the field of one-sided quantum information processing we show that the attained lower bounds are tight for various symmetric sets of quantum measurements. We use this characterisation to prove the existence of so called 4-Specker sets in the qubit case.