Conjectured strong complementary-correlations tradeoff

TL;DR

This paper introduces new, stronger uncertainty relations that limit correlations between measurement results of two separated quantum parties, with proofs for many cases and numerical evidence supporting their validity.

Contribution

It proposes novel conjectured uncertainty relations on mutual information bounds that are stronger than existing relations and provides proofs for broad classes of states and observables.

Findings

New uncertainty relations restrict correlations in quantum measurements.

Relations are stronger than previous Hall and Maassen-Uffink bounds.

Numerical evidence supports the validity of the conjectured relations.

Abstract

We conjecture new uncertainty relations which restrict correlations between results of measurements performed by two separated parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when one party measures a single observable and the other party measures one of two observables. The uncertainty relation does not follow from Maassen-Uffink uncertainty relation and is much stronger than Hall uncertainty relation derived from the latter. The second uncertainty relation bounds the sum of two mutual informations when each party measures one of two observables. We provide numerical evidence for validity of conjectured uncertainty relations and prove them for large classes of states and observables.