# Symmetry constrained decoherence of conditional expectation values

## TL;DR

This paper investigates how conservation laws can eliminate the sensitivity of quantum conditional expectation values to decoherence, especially in systems with additive conserved quantities, with implications for quantum thermodynamics experiments.

## Contribution

It identifies conditions under which coherence does not affect conditional expectation values in systems constrained by conservation laws, using a Jaynes-Cummings model as a case study.

## Key findings

- Conservation laws can remove decoherence effects on conditional expectation values.
- Coherence plays no role in measurements when certain conditions are met.
- Results are relevant for quantum thermodynamics experiments with cavity QED systems.

## Abstract

Conditional expectation values of quantum mechanical observables reflect unique non-classical correlations, and are generally sensitive to decoherence. We consider the circumstances under which such sensitivity to decoherence is removed, namely, when the measurement process is subjected to conservation laws. Specifically, we address systems with additive conserved quantities and identify sufficient conditions for the system state such that its coherence plays no role in the conditional expectation values of observables that commute with the conserved quantity. We discuss our findings for a specific model where the system-detector coupling is given by the Jaynes-Cummings interaction, which is relevant to experiments tracking trajectories of qubits in cavities. Our results clarify, among others, the role of coherence in thermal measurements in current architectures for quantum thermodynamics experiments.