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arXiv:2312.08148 · Physical review. E

Limits on quantum measurement engines

Guillermo Perna, Esteban Calzetta

Published Apr 1, 2024• 6 citations
arXivHTMLPDF

Abstract

A quantum measurement involves energy exchanges between the system to be measured and the measuring apparatus. Some of them involve energy losses, for example because energy is dissipated into the environment or is spent in recording the measurement outcome. Moreover, these processes take time. For this reason, these exchanges must be taken into account in the analysis of a quantum measurement engine, and set limits to its efficiency and power. We propose a quantum engine based on a spin 1/2 particle in a magnetic field and study its limitations due to the quantum nature of the evolution. The coupling with the electromagnetic vacuum is taken into account and plays the role of a measurement apparatus. We fully study its dynamics, work, power, and efficiency.

DOI
10.1103/physreve.109.044102

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A quantum measurement involves energy exchanges between the system to be measured and the measuring apparatus. Some of them involve energy losses, for example because energy is dissipated into the environment or is spent in recording the measurement outcome. Moreover, these processes take time. For this reason, these exchanges must be taken into account in the analysis of a quantum measurement engine, and set limits to its efficiency and power. We propose a quantum engine based on a spin 1/2 particle in a magnetic field and study its limitations due to the quantum nature of the evolution. The coupling with the electromagnetic vacuum is taken into account and plays the role of a measurement apparatus. We fully study its dynamics, work, power, and efficiency.
By considering the measurement of a quantum spin by two different models of the measuring apparatus, we try to throw some light on the nature of the apparatus that can perform quantum measurement. Our scheme is to consider a quantum spin in interaction with another quantum system playing the role of an apparatus, which in turn is dissipatively coupled to an environment. The coupling with the environment drives the density matrix of the apparatus to a diagonal form. However, measurement is performed only when the reduced density matrix of the apparatus contains correlations with the states of the spin. The two examples considered here show that this happens when the quantum apparatus has a well-defined classical limit. If the apparatus does not have a well-defined classical limit, the reduced density matrix of the apparatus is not correlated with the states of the measured system.
Energy exchanges under form of heat is neither the most natural or efficient way to operate an engine in the quantum realm. Recently there have been in the literature several proposals for "quantum measurement engines" where energy is fed into the machine by operations which otherwise would be conducive to quantum measurements on the working substance (henceforth "the system"). In the analysis of the working of these devices, oftentimes it is assumed that the only effect of measurement is to turn the state of the system from whatever prior state to an eigenstate of the measured property, and energy exchanges are determined therefrom. This ignores the intricacies of the quantum measurement process. We propose a simple model of a quantum measurement engine where the measurement process may be analyzed in detail, and therefore energy exchanges, and limitations on their duration, may be traced more fully.
Abstract In feedback controls, measurement is an essential step in designing protocols according to outcomes. For quantum mechanical systems, measurement has another effect; to supply energy to the measured system. We verify that in feedback-controlled quantum engines, measurement plays a dual role; not only as an auxiliary to perform feedback control but also as an energy supply to drive the engines. We consider a specific engine cycle exploiting feedback control followed by projective measurement and show that the maximum bound of the extractable work is set by both the efficacy of the feedback control and the energy change caused by projective measurement. We take a concrete example of an engine using an immobile spin-1/2 particle as a working substance and suggest two possible scenarios for work extraction.
Considering a general microscopic model for a quantum measuring apparatus comprising a quantum probe coupled to a thermal bath, we analyze the energetic resources necessary for the realization of a quantum measurement, which includes the creation of system-apparatus correlations, the irreversible transition to a statistical mixture of definite outcomes, and the apparatus resetting. Crucially, we do not resort to another quantum measurement to capture the emergence of objective measurement results, but rather exploit the properties of the thermal bath which redundantly records the measurement result in its degrees of freedom, naturally implementing the paradigm of quantum Darwinism. In practice, this model allows us to perform a quantitative thermodynamic analysis of the measurement process. From the expression of the second law, we show how the minimal required work depends on the energy variation of the system being measured plus information-theoretic quantities characterizing the performance of the measurement – efficiency and completeness. Additionally, we show that it is possible to perform a thermodynamically reversible measurement, thus reaching the minimal work expenditure, and provide the corresponding protocol. Finally, for finite-time measurement protocols, we illustrate the increasing work cost induced by rising entropy production inherent in finite-time thermodynamic processes. This highlights an emerging trade-off between velocity of the measurement and work cost, on top of a trade-off between efficiency of the measurement and work cost. We apply those findings to bring new insights in the thermodynamic balance of the measurement-powered quantum engines.
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.
Measurements take a singular role in quantum theory. While they are often idealized as an instantaneous process, this is in conflict with all other physical processes in nature. In this Letter, we adopt a standpoint where the interaction with an environment is a crucial ingredient for the occurrence of a measurement. Within this framework, we derive lower bounds on the time needed for a measurement to occur. Our bound scales proportionally to the change in entropy of the measured system, and decreases as the number of of possible measurement outcomes or the interaction strength driving the measurement increases. We evaluate our bound in two examples where the environment is modelled by bosonic modes and the measurement apparatus is modelled by spins or bosons.