Quantum speed limits in arbitrary phase spaces

TL;DR

This paper derives a universal quantum speed limit bound applicable to any phase space, improving bounds in specific cases and enabling experimental testing in quantum information and optics.

Contribution

It introduces a universal QSL bound based on the Stratonovich-Weyl correspondence for arbitrary phase spaces, applicable to both continuous and discrete quantum systems.

Findings

The new QSL bound is tighter than previous bounds in certain phase spaces.

The bound is applicable to systems like single-mode fields and N-level systems.

Experimental methods to test the speed limit in phase spaces are proposed.

Abstract

Quantum speed limits (QSLs) provide an upper bound for the speed of evolution of quantum states in any physical process. Based on the Stratonovich-Weyl correspondence, we derive a universal QSL bound in arbitrary phase spaces that is applicable for both continuous variable systems and finite-dimensional discrete quantum systems. This QSL bound allows the determination of speed limit bounds in specific phase spaces that are tighter than those in Wigner phase space or Hilbert space under the same metric, as illustrated by several typical examples, e.g., a single-mode free field and $N$-level quantum systems in phase spaces. This QSL bound also provides an experimentally realizable way to examine the speed limit in phase spaces relevant to applications in quantum information and quantum optics.