Fundamental speed limits on entanglement dynamics of bipartite quantum systems

TL;DR

This paper establishes fundamental speed limits on how quickly entanglement can be generated or degraded in bipartite quantum systems, applicable to various dynamics and providing bounds based on entanglement measures.

Contribution

It derives new bounds on entanglement speed limits for both unitary and non-unitary quantum processes, extending previous results to more general dynamics.

Findings

Derived bounds for entanglement speed limits using relative entropy and trace-distance measures.

Established a lower bound on the time needed to change a given amount of entanglement.

Demonstrated the tightness of the bounds with practical quantum processes.

Abstract

The speed limits on entanglement are defined as the maximal rate at which entanglement can be generated or degraded in a physical process. We derive the speed limits on entanglement, using the relative entropy of entanglement and trace-distance entanglement, for unitary as well as for arbitrary quantum dynamics, where we assume that the dynamics of the closest separable state can be approximately described by the closest separable dynamics of the actual dynamics of the system. For unitary dynamics of isolated bipartite systems which are described by pure states, the rate of entanglement production is bounded by the product of fluctuations of the system's driving Hamiltonian and the surprisal operator, with an additional term reflecting the time-dependent nature of the closest separable state. Removing restrictions on the purity of the input and on the unitarity of the evolution, the two terms in the bound get suitably altered. Furthermore, we find a lower bound on the time required to generate or degrade a certain amount of entanglement by arbitrary quantum dynamics. We demonstrate the tightness of our speed limits on entanglement by considering quantum processes of practical interest.