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

• URL: http://arxiv.org/abs/2604.17537v1
• Date: Sun, 19 Apr 2026 16:57:21 GMT
• Title: Surpassing thermal-state limit in thermometry via non-completely positive quantum encoding
• Abstract summary: Conventional quantum thermometry assumes completely positive (CP) encoding maps, where the probe is initially uncorrelated with the environment.<n>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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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