Speed limits on correlations in bipartite quantum systems

TL;DR

This paper establishes fundamental speed limits on the evolution of quantum correlations like entanglement and Bell-CHSH correlations in bipartite quantum systems, providing bounds that are sometimes attainable in practical scenarios.

Contribution

It derives the first general speed limits on quantum correlations such as negativity and concurrence for bipartite systems under arbitrary processes.

Findings

Speed limits on negativity and concurrence are analytically and numerically computed.

Some derived speed limits are shown to be tight and attainable in practical examples.

The results apply to a wide range of bipartite quantum systems and processes.

Abstract

Quantum speed limit is bound on the minimum time a quantum system requires to evolve from an initial state to final state under a given dynamical process. It sheds light on how fast a desired state transformation can take place which is pertinent for design and control of quantum technologies. In this paper, we derive speed limits on correlations such as entanglement, Bell-CHSH correlation, and quantum mutual information of quantum systems evolving under dynamical processes. Our main result is speed limit on an entanglement monotone called negativity which holds for arbitrary dimensional bipartite quantum systems and processes. Another entanglement monotone which we consider is the concurrence. To illustrate efficacy of our speed limits, we analytically and numerically compute the speed limits on the negativity, concurrence, and Bell-CHSH correlation for various quantum processes of practical interest. We are able to show that for practical examples we have considered, some of the speed limits we derived are actually attainable and hence these bounds can be considered to be tight.