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arXiv:2308.02381

Non-Ideal Measurement Heat Engines

Abhisek Panda, Felix C. Binder, Sai Vinjanampathy

Published Aug 4, 2023• 0 citations
arXivHTMLPDF

Abstract

We discuss the role of non-ideal measurements within the context of measurement engines by contrasting examples of measurement engines which have the same work output but with varying amounts of entanglement. Accounting for the cost of resetting, correlating the engine to a pointer state and also the cost of cooling the pointer state, we show that for a given work output, thermally correlated engines can outperform corresponding entanglement engines. We also show that the optimal efficiency of the thermally correlated measurement engine is achieved with a higher temperature pointer than the pointer temperature of the optimal entanglement engine.

DOI
10.48550/arxiv.2308.02381

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We discuss the role of non-ideal measurements within the context of measurement engines by contrasting examples of measurement engines which have the same work output but with varying amounts of entanglement. Accounting for the cost of resetting, correlating the engine to a pointer state and also the cost of cooling the pointer state, we show that for a given work output, thermally correlated engines can outperform corresponding entanglement engines. We also show that the optimal efficiency of the thermally correlated measurement engine is achieved with a higher temperature pointer than the pointer temperature of the optimal entanglement engine.
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Quantum measurements are known to affect the state of the measured system. Such a measurement backaction is due to the interaction of the quantum system with the measuring device. When the measured observable and the system's Hamiltonian do not commute, the backaction can lead to a mean energy change of the system. This energy change has been dubbed "quantum heat" and, in association with feedback processes and/or the interaction with thermal bath(s), proves to be a genuinely quantum resource to fuel new kinds quantum engines. We propose such a measurement powered engine exploiting the non-commutativity of local and non-local operations on a bipartite quantum system.We then investigate the origin of the quantum heat. Even if one cannot model the full dynamics of a measurement due to the collapse of the wavefunction, the energetic aspects can still be investigated by modeling the so-called pre-measurement. During this step, the system interacts and gets correlated with a quantum system which can be viewed as a small part of the measuring apparatus and called the quantum meter. Ideally, at the end of this process, the system's reduced state will be fully decohered in the measurement basis, thus corresponding to the averaged collapsed output states given by the measurement postulate. We find that the quantum heat received by the measured system corresponds to the energy necessary to turn off the coupling between the meter and the system. Using generalized definitions of heat and work, we moreover characterize the work and heat nature of these energy exchanges.Tracing the source of this energy one step further, we propose an autonomous description of a measurement. This is done by considering a flying qubit measured by the quantum field of the cavity it crosses. The interaction being position dependent, the kinetic degree of freedom is providing the required energy to switch on and off the interaction between the qubit and the meter field. A full quantum treatment allows us to evaluate the impact of the finite spatial and momentum extension of the qubit wavepacket. Since the kinetic degree of freedom can be affected by the interaction, it does not simply generate a time dependent Hamiltonian for the other degrees of freedom. We find the correction to this ideal dynamic and analyse its consequences on the nature of the energy fluxes. %spread/extension/broadnessTaking the opposite point of view, we compare the measurement cost of a qubit by a field propagating in a waveguide, depending on the initial state of the field. In the context of a circuit quantum electrodynamics setup, we find that thermal and coherent fields induce the same backaction on the qubit given the same energy constraints.The results presented and discussed in this thesis contribute to unravel the mysterious effects and mechanisms due to quantum measurements. Notably, they give an outlook to further analyse quantum measurement-based engines and to understand the energetic resource that measurements cost and constitute at the same time.
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Quantum measurement of a system can change its mean energy as well as entropy. A selective measurement (classical or quantum) can be used as a 'Maxwell's demon' to power a single-temperature heat engine by decreasing the entropy. Quantum mechanically, so can a non-selective measurement, despite increasing the entropy of a thermal state. The maximal amount of work extractable following the measurement is given by the change in free energy: W (non-)sel max = Δ E meas − T Bath Δ S (non-)sel meas . This follows from the 'generalized 2nd law for nonequilibrium initial state' (Hasegawa et al 2010 Phys. Lett. A 374 1001–4), an elementary reduction of which to the standard law is given here. It is shown that W sel max − W non-sel max is equal to the work required for resetting the memory of the measuring device and that no such resetting is needed in the non-selective case. Consequently, a single-bath engine powered by either kind of measurement works at a net loss of T Bath Δ S non-sel meas per cycle. By replacing the measurement by a reversible 'pre-measurement' and allowing a work source to couple to the system and memory , the cycle can be rendered completely reversible.
We study the impact of entangling measurements on the efficiency of quantum measurement-based engines. We first demonstrate that for engines comprising many subsystems the efficiency can be enhanced through the implementation of entangling measurements. Then, we show that when the collective measurement yields the same local state for the subsystems as individual local measurements, the improvement is directly proportional to the amount of correlations among the subsystems. Finally, we present examples for two-level systems where this type of engine can operate at perfect efficiency yielding a finite amount of work in the limit of a large number of subsystems; we also discuss how to generalize this idea to larger systems.