Contributions to single-shot energy exchanges in open quantum systems

TL;DR

This paper introduces an exact formula for energy exchange in open quantum systems, accounting for entanglement and strong coupling, enabling single-shot analysis beyond weakly coupled systems.

Contribution

It derives a novel, exact expression for energy flow in open quantum systems using the conditional wave function, applicable to arbitrary coupling and entanglement.

Findings

Identifies three contributions to energy flow: external, interaction, and entanglement.

Provides a framework for experimental studies of energy fluctuations in quantum systems.

Extends single-shot energy analysis to strongly coupled and entangled systems.

Abstract

The exchange of energy between a classical open system and its environment can be analysed for a single run of an experiment using the phase space trajectory of the system. By contrast, in the quantum regime such energy exchange processes must be defined for an {\it ensemble} of runs of the same experiment based on the reduced system density matrix. Single-shot approaches have been proposed for quantum systems that are weakly coupled to a heat bath. However, a single-shot analysis for a quantum system that is entangled or strongly interacting with external degrees of freedom has not been attempted because no system wave function exists for such a system within the standard formulation of quantum theory. Using the notion of the {\it conditional} wave function of a quantum system, we derive here an exact formula for the rate of total energy change in an open quantum system, valid for arbitrary coupling between the system and the environment. In particular, this allows us to identify three distinct contributions to the total energy flow: an external contribution coming from the explicit time dependence of the Hamiltonian, an interaction contribution associated with the interaction part of the Hamiltonian, and an entanglement contribution, directly related to the presence of entanglement between the system and its environment. Given the close connection between weak values and the conditional wave function, the approach presented here provides a new avenue for experimental studies of energy fluctuations in open quantum systems.