Operational models of temperature superpositions

Abstract

When thermodynamical quantities are associated with quantum systems a question arises how to treat scenarios where the notion of temperature could exhibit some quantum features. It is known that the temperature of a gas in thermal equilibrium is not constant in a gravitational field, but it is not known how a delocalised quantum system would thermalise with such a bath. In this theoretical work we demonstrate two scenarios in which the notion of a 'superposition of temperatures' arises. First: a probe interacting with different baths dependent on the state of another quantum system (control). Second: the probe interacting with a bath in a superposition of purified states, each associated with a different temperature. We show that these 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 of the baths or purifications are equal. Furthermore, we show the final probe state depends on the specific realisation of the thermalising channels, being sensitive to the particular Kraus representations of the channels. This point appears to explain recent results obtained in the context of quantum interference of relativistic particle detectors thermalising with Unruh or Hawking radiation. Finally, we show that these results are reproduced in partial and pre-thermalisation processes, and thus our approach and conclusions also generally apply beyond the idealised scenarios, where thermalisation is not exact.

Quantum cooling activated by coherently-controlled thermalisation

“…Our results in this work focus on the ideal case of full thermalisation, and we notice that there is a recent paper [4] which models thermalisation as sequential collisions between the working system and the reservoirs, making the evaluation of the partial and pre-thermalisation processes possible. It is more realistic to analyse quantum working system which is far from equilibrium interacting with some reservoirs for a finite time.…”

“…At first we should consider the quantum-controlled interactions between the working qubit and the reservoir [4]. We consider a composite reservoir comprising N subsystems in a product state ρ R = N −1 i=0 ρ R i .The whole system including the control system is also in a product state initially ρ = ρ R ⊗ ρ C ⊗ ρ t .…”

“…The scheme of quantum-controlled thermalisation introduced in [4] is sensitive to the full process on the Kraus decomposition of the individual thermalizing channel, but we notice that the swapping operation decribed in [1] is a particular target-reservoir interaction leading to a specific Kraus representation of the thermalizing channel, and it obviously satisfies T r…”

“…Before the discussion about quantum-controlled thermalisation in [4], authors of [3] came up with scenarios where causal indefiniteness plays no role but similar advantages can be achieved in communication with noisy channels(although [11] suggests since in this scheme the target system only passes through one of the noisy channels instead of a sequence of them, so in a more fair comparison, the advantage provided by quantum switch is still the greatest in this kind of tasks). But different from the protocol with indefinite causal order, the new scheme of communication with superposing trajectories is implementationdependent(additional transformation matrices [3] or access to vacuum extension [24] with specific Kraus operators are needed).…”

“…Moreover, in the controlled-SWAP scheme first introduced in [1] where we have access to the reservoir qubits which are quantum correlated with the control-target system, the performance of the fridge can be greatly enhanced in general(tripled for all N 's and temperatures). Then inspired by [3,4], we show that coherently controls between thermalizing a working system with one of N identical thermalizing channels (where causal indefiniteness plays no role) show same advantages in controlled-SWAP scheme compared to the generalized N -SWITCH protocol for the thermodynamic task described in [1]. We also provide an experimental simulatable quantum cooling protocol with coherently-controlled thermalizing channels and notice that it can outperform ICO refrigerator with some specific implementations of the thermalizing channel in the case when we only have access to the control-target system.…”