Quantum Fisher information as a probe for Unruh thermality

TL;DR

This paper uses quantum Fisher information to analyze the thermal nature of the Unruh effect, revealing how it encodes both global and local thermal properties and how mass and dimensionality influence estimation precision.

Contribution

It introduces QFI as a novel probe for Unruh thermality, demonstrating its time evolution, dependence on background field properties, and robustness against decoherence.

Findings

QFI asymptotically depends only on Unruh temperature, confirming global thermality.

QFI exhibits monotonic or non-monotonic behavior depending on spacetime dimension.

Massive fields enhance QFI robustness and prolong estimation precision.

Abstract

A long-standing debate on Unruh effect is about its obscure thermal nature. In this Letter, we use quantum Fisher information (QFI) as an effective probe to explore the thermal nature of Unruh effect from both local and global perspectives. By resolving the full dynamics of UDW detector, we find that the QFI is a time-evolving function of detector's energy gap, Unruh temperature $T_U$ and particularities of background field, e.g., mass and spacetime dimensionality. We show that the asymptotic QFI whence detector arrives its equilibrium is solely determined by $T_U$, demonstrating the global side of Unruh thermality alluded by the KMS condition. We also show that the local side of Unruh effect, i.e., the different ways for the detector to approach the same thermal equilibrium, is encoded in the corresponding time-evolution of the QFI. In particular, we find that with massless scalar background the QFI has unique monotonicity in $n=3$ dimensional spacetime, and becomes non-monotonous for $n\neq3$ models where a local peak value exists at early time and for finite acceleration, indicating an enhanced precision of estimation on Unruh temperature at a relative low acceleration can be achieved. Once the field acquiring mass, the related QFI becomes significantly robust against the Unruh decoherence in the sense that its local peak sustains for a very long time. While coupling to a more massive background, the persistence can even be strengthened and the QFI possesses a larger maximal value. Such robustness of QFI can surely facilitate any practical quantum estimation task.