Quantum speed limits for Bell-diagonal states

TL;DR

This paper investigates quantum speed limits for Bell-diagonal states under decoherence, deriving exact formulas and revealing a sudden transition from classical to quantum decoherence at a critical time.

Contribution

It provides exact expressions for quantum speed limit times of Bell-diagonal states and uncovers a sudden transition in decoherence behavior.

Findings

Quantum speed limit time decreases over time with decoherence.

A critical time exists where the decay rate of the speed limit changes abruptly.

System dynamics transition from classical to quantum decoherence at this critical point.

Abstract

Bounds of the minimum evolution time between two distinguishable states of a system can help to assess the maximal speed of quantum computers and communication channels. We study the quantum speed limit time of a composite quantum states in the presence of nondissipative decoherence. For the initial states with maximally mixed marginals, we obtain the exactly expressions of quantum speed limit time which mainly depend on the parameters of the initial states and the decoherence channels. Furthermore, by calculating quantum speed limit time for the time-dependent states started from a class of initial states, we discover that the quantum speed limit time gradually decreases in time, and the decay rate of the quantum speed limit time would show a sudden change at a certain critical time. Interestingly, at the same critical time, the composite system dynamics would exhibit a sudden transition from classical to quantum decoherence.