Precision Enhancement in Transient Quantum Thermometry:Cold-Probe Bias and Its Removal

TL;DR

This paper investigates the fundamental temperature bias in transient quantum thermometry, showing that initial colder probes are necessary for enhanced precision in Markovian and some non-Markovian regimes, but not in all non-Markovian models.

Contribution

It proves the cold-probe requirement for transient precision enhancement in Markovian dynamics and explores how different non-Markovian effects influence this bias.

Findings

Cold probes are necessary and sufficient for transient precision enhancement in Markovian environments.

Memory effects do not eliminate the cold-probe bias in certain non-Markovian scenarios.

Strong non-Markovianity can remove the transient enhancement, equalizing hot and cold probes.

Abstract

We unveil a fundamental temperature bias in transient quantum thermometry under Markovian dynamics. For qubit probes evolving in a thermal Markovian environment, we prove that transient precision beyond the steady-state benchmark can be achieved if and only if the probe is initially colder than the bath temperature to be estimated. Cold probes are therefore both necessary and sufficient for enhanced transient precision in the Markovian regime. We then investigate the fate of this bias in the presence of environmental memory. In particular, in a non-Markovian scenario generated by an auxiliary-mediated system-bath coupling, we find that the cold-probe requirement for enhanced transient precision persists, indicating that the temperature bias survives certain forms of memory effects. In contrast, for a non-Markovian collisional model with perfect swap interactions between bath ancillas, transient enhancement is entirely absent regardless of the probe's initial temperature. This indicates that strong non-Markovianity can lead to the complete disappearance of the enhancement effect, placing hot and cold probes on equal footing, with neither capable of achieving enhanced precision in this regime.