Operational models of temperature superpositions

Abstract

A quantum system and a thermal bath can reach thermal equilibrium through an interaction, whereupon the system acquires the same temperature as the bath. But how does a delocalised quantum system thermalise with a bath whose local temperature varies, as, for example, in the Tolman effect? Here we formulate two scenarios in which the notion of a ``superposition of temperatures'' may arise. First: a probe interacting with two different baths dependent on the state of another quantum system (control). Second: a probe interacting with a single bath whose purified state is a superposition of states corresponding to different temperatures. We show that the two scenarios are fundamentally different and can be operationally distinguished. Moreover, we show that the probe does not in general thermalise even when the involved temperatures are equal, and that the final probe state is sensitive to the specific realisation of the thermalising channels. Our models may be applied to scenarios involving joint quantum, gravitational, and thermodynamic phenomena, and explain some recent results found in quantum intereference of relativistic probes thermalising with Unruh or Hawking radiation. Finally, we show that our results are reproduced in partial and pre-thermalisation processes, and thus our approach and conclusions hold beyond the idealised scenarios, where thermalisation is incomplete.

13 pages, including references and appendix, 5 figures. Significant rewording of arguments in several sections, updated references

References in corpus (27)

• The Unruh effect and its applications
• Quantum Thermodynamics
• Quantum computations without definite causal structure
• Thermalizing Quantum Machines: Dissipation and Entanglement
• Thermometry in the quantum regime: Recent theoretical progress
• Quantum Limits of Thermometry
• Single-qubit thermometry
• Quantum Refrigeration with Indefinite Causal Order
• Quantum circuits cannot control unknown operations
• Quantum Shannon theory with superpositions of trajectories
• Communication through coherent control of quantum channels
• Communication through quantum-controlled noise
• Interference of Quantum Channels
• Narrow Bounds for the Quantum Capacity of Thermal Attenuators
• Work extraction from coherently activated maps via quantum switch
• Unruh-deWitt detectors in quantum superpositions of trajectories
• Thermodynamic advancement in the causally inseparable occurrence of thermal maps
• Unruh effect for detectors in superposition of accelerations
• Quantum superpositions and entanglement of thermal states at high temperatures and their applications to quantum information processing
• Subspace local quantum channels
• Subspace preserving completely positive maps
• Gluing of completely positive maps
• Thermality, causality and the quantum-controlled Unruh-deWitt detector
• Quantum conditional operations
• Reassessing thermodynamic advantage from indefinite causal order
• Temperature as a quantum observable
• Local Quantum Thermometry using Unruh-De Witt detectors