Quantum speed limits for observables

In the Schrodinger 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.

Automated summary

We investigate the limits on the evolution speed of quantum systems in both the Schrödinger and Heisenberg pictures. We derive time bounds for the evolution of observables in closed systems, open quantum systems, and systems with arbitrary dynamics. Additionally, we discuss various applications of these bounds, including operator growth, correlation growth, quantum thermal machines, quantum control, and many-body physics.