Intensive temperature and quantum correlations for refined quantum measurements

TL;DR

This paper investigates how the concept of temperature behaves in quantum systems under refined measurements, revealing conditions where temperature is not intensive and highlighting the role of entanglement in this context.

Contribution

It introduces a framework for understanding temperature in quantum systems with refined measurements and demonstrates when the classical notion of temperature as an intensive property breaks down.

Findings

Refined quantum measurements can distinguish block states from thermal states, challenging the notion of temperature as an intensive quantity.

Coarse-grained measurements restore the classical intensive temperature behavior.

Entanglement influences the applicability of the thermodynamic paradigm of temperature.

Abstract

We consider the concept of temperature in a setting beyond the standard thermodynamics prescriptions. Namely, rather than restricting to standard coarse-grained measurements, we consider observers able to master any possible quantum measurement--a scenario that might be relevant at nanoscopic scales. In this setting, we focus on quantum systems of coupled harmonic oscillators and study the question of whether the temperature is an intensive quantity, in the sense that a block of a thermal state can be approximated by an effective thermal state at the same temperature as the whole system. Using the quantum fidelity as figure of merit, we identify instances in which this approximation is not valid, as the block state and the reference thermal state are distinguishable for refined measurements. Actually, there are situation in which this distinguishability even increases with the block size. However, we also show that the two states do become less distinguishable with the block size for coarse-grained measurements--thus recovering the standard picture. We then go further and construct an effective thermal state which provides a good approximation of the block state for any observables and sizes. Finally, we point out the role entanglement plays in this scenario by showing that, in general, the thermodynamic paradigm of local intensive temperature applies whenever entanglement is not present in the system.