Quantum speed limits in open system dynamics

TL;DR

This paper derives a new quantum speed limit bound for open quantum systems, extending fundamental limits on evolution speed to non-unitary dynamics and demonstrating its applications in quantum metrology and dynamics.

Contribution

It introduces a time-energy uncertainty relation for open quantum systems with CPT evolution, generalizing the Mandelstam-Tamm relation to non-unitary processes.

Findings

Derived a bound for open quantum system evolution speed.

Applied the bound to quantum metrology under dephasing noise.

Demonstrated the bound's utility in estimating passage times.

Abstract

Bounds to the speed of evolution of a quantum system are of fundamental interest in quantum metrology, quantum chemical dynamics and quantum computation. We derive a time-energy uncertainty relation for open quantum systems undergoing a general, completely positive and trace preserving (CPT) evolution which provides a bound to the quantum speed limit. When the evolution is of the Lindblad form, the bound is analogous to the Mandelstam-Tamm relation which applies in the unitary case, with the role of the Hamiltonian being played by the adjoint of the generator of the dynamical semigroup. The utility of the new bound is exemplified in different scenarios, ranging from the estimation of the passage time to the determination of precision limits for quantum metrology in the presence of dephasing noise.