Energy-limited quantum dynamics

TL;DR

This paper studies quantum systems with energy constraints, introducing the concept of energy-limited channels and dynamics, and derives new inequalities and bounds related to energy-constrained quantum processes.

Contribution

It systematically characterizes energy-limited quantum channels and dynamics, establishing operator inequalities and continuity bounds for quantum speed limits.

Findings

Energy-limitedness is equivalent to a single operator inequality in the Markovian case.

New submultiplicativity inequalities for energy-constrained norms are established.

State-dependent continuity bounds for quantum speed limits are derived.

Abstract

We consider quantum systems with energy constraints relative to a reference Hamiltonian. In general, quantum channels and continuous-time dynamics need not satisfy energy conservation. Physically meaningful channels, however, only introduce a finite amount of energy to the system, and continuous-time dynamics only increase the energy gradually over time. We systematically study such "energy-limited" channels and dynamics. For Markovian dynamics, energy-limitedness is equivalent to a single operator inequality in the Heisenberg picture. We observe new submultiplicativity inequalities for the energy-constrained diamond and operator norms and use them to derive new state-dependent continuity bounds for quantum speed limits.