Quantum Speed Limits for Observables

TL;DR

This paper establishes quantum speed limits for the evolution of observables in quantum systems, extending the concept beyond states to include operator dynamics, with broad implications for quantum control and many-body physics.

Contribution

It introduces quantum speed limits for observable evolution in both closed and open quantum systems, a novel extension of existing state-based bounds.

Findings

Derived bounds for observable evolution in various quantum systems

Applicable to quantum control, thermal machines, and many-body physics

Provides fundamental limits on operator and correlation growth

Abstract

In the Schr{\"o}dinger picture, the state of a quantum system evolves in time and the quantum speed limit describes how fast the state of a quantum system evolves from an initial state to a final state. However, in the Heisenberg picture the observable evolves in time instead of the state vector. Therefore, it is natural to ask how fast an observable evolves in time. This can impose a fundamental bound on the evolution time of the expectation value of quantum mechanical observables. We obtain the quantum speed limit time-bound for observable for closed systems, open quantum systems and arbitrary dynamics. Furthermore, we discuss various applications of these bounds. Our results can have several applications ranging from setting the speed limit for operator growth, correlation growth, quantum thermal machines, quantum control and many body physics.