Surpassing thermal-state limit in thermometry via non-completely positive quantum encoding

TL;DR

This paper demonstrates that non-completely positive quantum encodings, arising from initial probe-environment correlations, can surpass traditional thermal-state limits in quantum thermometry, offering enhanced temperature estimation precision.

Contribution

It introduces and analyzes non-completely positive encodings in quantum thermometry, showing they can outperform conventional methods constrained by the thermal-state limit.

Findings

NCP encoding can match the thermal-state bound with pure initial states.

General correlated initial states enable surpassing the thermal-state limit.

Results are illustrated with qubit probe-environment interactions.

Abstract

Conventional quantum thermometry assumes completely positive (CP) encoding maps, where the probe is initially uncorrelated with the environment. We consider realistic scenarios with initial probe-environment correlations leading to physically realizable non-completely positive (NCP) encoding, and show how such encodings can significantly impact temperature estimation of the environment. We first consider pure entangled probe-environment initial states (Type-I NCP encoding) and analytically show that for probes and environments of equal but arbitrary dimension, the maximum achievable precision matches the thermal-state bound, as in the CP case. However, upon relaxing the constraint of pure probe-environment states and considering general correlated initial states (Type-II NCP encoding), we demonstrate that the estimation precision can surpass the thermal-state limit. This establishes a clear advantage of NCP encoding in enhancing thermometric performance. We illustrate the results using qubit probes interacting with qubit environments via XY interactions.