Efficient Quantum Measurement Engines

Work and efficiency fluctuations in a quantum Otto cycle with idle levels

We study the performance of a quantum Otto heat engine with two spins coupled by a Heisenberg interaction, taking into account not only the mean values of work and efficiency but also their fluctuations. We first show that, for this system, the output work and its fluctuations are directly related to the magnetization and magnetic susceptibility of the system at equilibrium with either heat bath. We analyze the regions where the work extraction can be done with low relative fluctuation for a given range of temperatures, while still achieving an efficiency higher than that of a single spin system heat engine. In particular, we find that, due to the presence of "idle" levels, an increase in the interspin coupling can either increase or decrease fluctuations, depending on the other parameters. In all cases, however, we find that the relative fluctuations in work or efficiency remain large, implying that this microscopic engine is not very reliable as a source of work.

Limits on quantum measurement engines

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.

Transport and Nonreciprocity in Monitored Quantum Devices: An Exact Study

We study noninteracting fermionic systems undergoing continuous monitoring and driven by biased reservoirs. Averaging over the measurement outcomes, we derive exact formulas for the particle and heat flows in the system. We show that these currents feature competing elastic and inelastic components, which depend nontrivially on the monitoring strength γ. We highlight that monitor-induced inelastic processes lead to nonreciprocal currents, allowing one to extract work from measurements without active feedback control. We illustrate our formalism with two distinct monitoring schemes providing measurement-induced power or cooling. Optimal performances are found for values of the monitoring strength γ, which are hard to address with perturbative approaches.

Monitored nonadiabatic and coherent-controlled quantum unital Otto heat engines: First four cumulants

Recently, measurement-based quantum thermal machines have drawn more attention in the field of quantum thermodynamics. However, the previous results on quantum Otto heat engines were either limited to special unital and nonunital channels in the bath stages, or a specific driving protocol at the work strokes and assuming the cycle being time-reversal symmetric, i.e., V^{†}=U (or V=U). In this paper, we consider a single spin-1/2 quantum Otto heat engine, by first replacing one of the heat baths by an arbitrary unital channel, and then we give the exact analytical expression of the characteristic function from which all the cumulants of heat and work emerge. We prove that under the effect of monitoring, ν_{2}>ν_{1} is a necessary condition for positive work, either for a symmetric or asymmetric-driven Otto cycle. Furthermore, going beyond the average we show that the ratio of the fluctuations of work and heat is lower and upper-bounded when the system is working as a heat engine. However, differently from the previous results in the literature, we consider the third and fourth cumulants as well. It is shown that the ratio of the third (fourth) cumulants of work and heat is not upper-bounded by unity nor lower-bounded by the third (fourth) power of the efficiency, as is the case for the ratio of fluctuations. Finally, we consider applying a specific unital map that plays the role of a heat bath in a coherently superposed manner, and we show the role of the initial coherence of the control qubit on efficiency, on the average work and its relative fluctuations.

Efficiency at Maximum Power of a Carnot Quantum Information Engine

Optimizing the performance of thermal machines is an essential task of thermodynamics. We here consider the optimization of information engines that convert information about the state of a system into work. We concretely introduce a generalized finite-time Carnot cycle for a quantum information engine and optimize its power output in the regime of low dissipation. We derive a general formula for its efficiency at maximum power valid for arbitrary working media. We further investigate the optimal performance of a qubit information engine subjected to weak energy measurements.

Quantum ergotropy and quantum feedback control

We study the energy extraction from and charging to a finite-dimensional quantum system by general quantum operations. We prove that the changes in energy induced by unital quantum operations are limited by the ergotropy and charging bounds for unitary quantum operations. This implies that, in order to break the ergotropy bound for unitary quantum operations, one needs to perform a quantum operation with feedback control. We also show that the ergotropy bound for unital quantum operations, applied to initial thermal equilibrium states, is tighter than the inequality representing the standard second law of thermodynamics without feedback control.

Energy dynamics, heat production and heat-work conversion with qubits: toward the development of quantum machines

We present an overview of recent advances in the study of energy dynamics and mechanisms for energy conversion in qubit systems with special focus on realizations in superconducting quantum circuits. We briefly introduce the relevant theoretical framework to analyze heat generation, energy transport and energy conversion in these systems with and without time-dependent driving considering the effect of equilibrium and non-equilibrium environments. We analyze specific problems and mechanisms under current investigation in the context of qubit systems. These include the problem of energy dissipation and possible routes for its control, energy pumping between driving sources and heat pumping between reservoirs, implementation of thermal machines and mechanisms for energy storage. We highlight the underlying fundamental phenomena related to geometrical and topological properties, as well as many-body correlations. We also present an overview of recent experimental activity in this field.

Measurement-Based Quantum Thermal Machines with Feedback Control

We investigated coupled-qubit-based thermal machines powered by quantum measurements and feedback. We considered two different versions of the machine: (1) a quantum Maxwell's demon, where the coupled-qubit system is connected to a detachable single shared bath, and (2) a measurement-assisted refrigerator, where the coupled-qubit system is in contact with a hot and cold bath. In the quantum Maxwell's demon case, we discuss both discrete and continuous measurements. We found that the power output from a single qubit-based device can be improved by coupling it to the second qubit. We further found that the simultaneous measurement of both qubits can produce higher net heat extraction compared to two setups operated in parallel where only single-qubit measurements are performed. In the refrigerator case, we used continuous measurement and unitary operations to power the coupled-qubit-based refrigerator. We found that the cooling power of a refrigerator operated with swap operations can be enhanced by performing suitable measurements.

Work extraction from single-mode thermal noise by measurements: How important is information?

Our goal in this article is to elucidate the rapport of work and information in the context of a minimal quantum-mechanical setup: a converter of heat input to work output, the input consisting of a single oscillator mode prepared in a hot thermal state along with a few much colder oscillator modes. The core issues we consider, taking account of the quantum nature of the setup, are as follows: (i) How and to what extent can information act as a work resource or, conversely, be redundant for work extraction? (ii) What is the optimal way of extracting work via information acquired by measurements? (iii) What is the bearing of information on the efficiency-power tradeoff achievable in such setups? We compare the efficiency of work extraction and the limitations of power in our minimal setup by different, generic, measurement strategies of the hot and cold modes. For each strategy, the rapport of work and information extraction is found and the cost of information erasure is allowed for. The possibilities of work extraction without information acquisition, via nonselective measurements, are also analyzed. Overall, we present, by generalizing a method based on optimized homodyning that we have recently proposed, the following insight: extraction of work by observation and feedforward that only measures a small fraction of the input is clearly advantageous to the conceivable alternatives. Our results may become the basis of a practical strategy of converting thermal noise to useful work in optical setups, such as coherent amplifiers of thermal light, as well as in their optomechanical and photovoltaic counterparts.

Energetics of a Single Qubit Gate

Qubits are physical, a quantum gate thus not only acts on the information carried by the qubit but also on its energy. What is then the corresponding flow of energy between the qubit and the controller that implements the gate? Here we exploit a superconducting platform to answer this question in the case of a quantum gate realized by a resonant drive field. During the gate, the superconducting qubit becomes entangled with the microwave drive pulse so that there is a quantum superposition between energy flows. We measure the energy change in the drive field conditioned on the outcome of a projective qubit measurement. We demonstrate that the drive's energy change associated with the measurement backaction can exceed by far the energy that can be extracted by the qubit. This can be understood by considering the qubit as a weak measurement apparatus of the driving field.

Heat engines with single-shot deterministic work extraction

We introduce heat engines working in the nanoregime that allow one to extract a finite amount of deterministic work. Using the resource theory approach to themodynamics, we show that the efficiency of these cycles is strictly smaller than Carnot's, and we associate this difference with a fundamental irreversibility that is present in single-shot transformations. When fluctuations in the extracted work are allowed there is a trade-off between their size and the efficiency. As the size of fluctuations increases so does the efficiency and optimal efficiency is attained for unbounded fluctuations, while a certain amount of deterministic work is drawn from the cycle. Finally, we show that when the working medium is composed of many particles, by creating an amount of correlations between the subsystems that scale logarithmically with their number, Carnot's efficiency can also be approached in the asymptotic limit along with deterministic work extraction.

Necessity of feedback control for the quantum Maxwell demon in a finite-time steady feedback cycle

We revisit quantum Maxwell demon in thermodynamic feedback cycle in the steady-state regime. We derive a generalized version of the Clausius inequality for a finite-time steady feedback cycle with a single heat bath. It is shown to be tighter than previously known ones, and allows us to clarify that feedback control is necessary to violate the standard Clausius inequality.

Efficiently fueling a quantum engine with incompatible measurements

We propose a quantum harmonic oscillator measurement engine fueled by simultaneous quantum measurements of the noncommuting position and momentum quadratures of the quantum oscillator. The engine extracts work by moving the harmonic trap suddenly, conditioned on the measurement outcomes. We present two protocols for work extraction, respectively based on single-shot and time-continuous quantum measurements. In the single-shot limit, the oscillator is measured in a coherent state basis; the measurement adds an average of one quantum of energy to the oscillator, which is then extracted in the feedback step. In the time-continuous limit, continuous weak quantum measurements of both position and momentum of the quantum oscillator result in a coherent state, whose coordinates diffuse in time. We relate the extractable work to the noise added by quadrature measurements, and present exact results for the work distribution at arbitrary finite time. Both protocols can achieve unit work conversion efficiency in principle.

Efficiency gain and bidirectional operation of quantum engines with decoupled internal levels

We present a mechanism for efficiency increase in quantum heat engines containing internal energy levels that do not couple to the external work sink. The gain is achieved by using these levels to channel heat in a direction opposite to the one dictated by the second law. No quantum coherence, quantum correlations or ergotropy are required. A similar mechanism allows the engine to run "in reverse" and still produce useful work. We illustrate these ideas using a simple quantum Otto cycle in a coupled-spin system. We find this engine also exhibits other counterintuitive phenomenology. For example, its efficiency may increase as the temperature difference between the heat baths decreases. Conversely, it may cease to operate if the hotter bath becomes too hot or the colder bath too cold.

Channels, measurements, and postselection in quantum thermodynamics

We analyze the benefit, in terms of extracting work, of having a single use of a quantum channel or measurement in quantum thermodynamics. This highlights a connection between unital and catalytic channels, and some subtleties concerning the conditional work cost of implementing a measurement given that a certain result was obtained. We also consider postselected measurements and show that any nontrivial postselection leads to an unbounded work benefit.

Work Generation from Thermal Noise by Quantum Phase-Sensitive Observation

We put forward the concept of work extraction from thermal noise by phase-sensitive (homodyne) measurements of the noisy input followed by (outcome-dependent) unitary manipulations of the postmeasured state. For optimized measurements, noise input with more than one quantum on average is shown to yield heat-to-work conversion with efficiency and power that grow with the mean number of input quanta, the efficiency and the inverse temperature of the detector. This protocol is shown to be advantageous compared to common models of information and heat engines.

Coherences and the thermodynamic uncertainty relation: Insights from quantum absorption refrigerators

The thermodynamic uncertainty relation, originally derived for classical Markov-jump processes, provides a tradeoff relation between precision and dissipation, deepening our understanding of the performance of quantum thermal machines. Here, we examine the interplay of quantum system coherences and heat current fluctuations on the validity of the thermodynamics uncertainty relation in the quantum regime. To achieve the current statistics, we perform a full counting statistics simulation of the Redfield quantum master equation. We focus on steady-state quantum absorption refrigerators where nonzero coherence between eigenstates can either suppress or enhance the cooling power, compared with the incoherent limit. In either scenario, we find enhanced relative noise of the cooling power (standard deviation of the power over the mean) in the presence of system coherence, thereby corroborating the thermodynamic uncertainty relation. Our results indicate that fluctuations necessitate consideration when assessing the performance of quantum coherent thermal machines.

Two-Qubit Engine Fueled by Entanglement and Local Measurements

We introduce a two-qubit engine that is powered by entanglement and local measurements. Energy is extracted from the detuned qubits coherently exchanging a single excitation. Generalizing to an N-qubit chain, we show that the low energy of the first qubit can be up-converted to an arbitrarily high energy at the last qubit by successive neighbor swap operations and local measurements. We finally model the local measurement as the entanglement of a qubit with a meter, and we identify the fuel as the energetic cost to erase the correlations between the qubits. Our findings extend measurement-powered engines to composite working substances and provide a microscopic interpretation of the fueling mechanism.

Finite-time performance of a single-ion quantum Otto engine

We study how a quantum heat engine based on a single trapped ion performs in finite time. The always-on thermal environment acts like the hot bath, while the motional degree of freedom of the ion plays the role of the effective cold bath. The hot isochoric stroke is implemented via the interaction of the ion with its hot environment, while a projective measurement of the internal state of the ion is performed as an equivalent to the cold isochoric stroke. The expansion and compression strokes are implemented via suitable change in applied magnetic field. We study in detail how the finite duration of each stroke affects the engine performance. We show that partial thermalization can in fact enhance the efficiency of the engine, due to the residual coherence, whereas faster expansion and compression strokes increase the inner friction and therefore reduce the efficiency.

Nonequilibrium Many-Body Quantum Engine Driven by Time-Translation Symmetry Breaking

Quantum many-body systems out of equilibrium can host intriguing phenomena such as transitions to exotic dynamical states. Although this emergent behaviour can be observed in experiments, its potential for technological applications is largely unexplored. Here, we investigate the impact of collective effects on quantum engines that extract mechanical work from a many-body system. Using an optomechanical cavity setup with an interacting atomic gas as a working fluid, we demonstrate theoretically that such engines produce work under periodic driving. The stationary cycle of the working fluid features nonequilibrium phase transitions, resulting in abrupt changes of the work output. Remarkably, we find that our many-body quantum engine operates even without periodic driving. This phenomenon occurs when its working fluid enters a phase that breaks continuous time-translation symmetry: The emergent time-crystalline phase can sustain the motion of a load generating mechanical work. Our findings pave the way for designing novel nonequilibrium quantum machines.

Quantum Finite-Time Thermodynamics: Insight from a Single Qubit Engine

Incorporating time into thermodynamics allows for addressing the tradeoff between efficiency and power. A qubit engine serves as a toy model in order to study this tradeoff from first principles, based on the quantum theory of open systems. We study the quantum origin of irreversibility, originating from heat transport, quantum friction, and thermalization in the presence of external driving. We construct various finite-time engine cycles that are based on the Otto and Carnot templates. Our analysis highlights the role of coherence and the quantum origin of entropy production.

Nonequilibrium Quantum Many-Body Rydberg Atom Engine

The standard approach to quantum engines is based on equilibrium systems and on thermodynamic transformations between Gibbs states. However, nonequilibrium quantum systems offer enhanced experimental flexibility in the control of their parameters and, if used as engines, a more direct interpretation of the type of work they deliver. Here we introduce an out-of-equilibrium quantum engine inspired by recent experiments with cold atoms. Our system is connected to a single environment and produces mechanical work from many-body interparticle interactions arising between atoms in highly excited Rydberg states. As such, it is not a heat engine but an isothermal one. We perform many-body simulations to show that this system can produce work. The setup we introduce and investigate represents a promising platform for devising new types of microscopic machines and for exploring quantum effects in thermodynamic processes.

Maxwell's Lesser Demon: A Quantum Engine Driven by Pointer Measurements

We discuss a self-contained spin-boson model for a measurement-driven engine, in which a demon generates work from thermal excitations of a quantum spin via measurement and feedback control. Instead of granting it full direct access to the spin state and to Landauer's erasure strokes for optimal performance, we restrict this demon's action to pointer measurements, i.e., random or continuous interrogations of a damped mechanical oscillator that assumes macroscopically distinct positions depending on the spin state. The engine can reach simultaneously the power and efficiency benchmarks and operate in temperature regimes where quantum Otto engines would fail.

Measurement Induced Synthesis of Coherent Quantum Batteries

Quantum coherence represented by a superposition of energy eigenstates is, together with energy, an important resource for quantum technology and thermodynamics. Energy and quantum coherence however, can be complementary. The increase of energy can reduce quantum coherence and vice versa. Recently, it was realized that steady-state quantum coherence could be autonomously harnessed from a cold environment. We propose a conditional synthesis of N independent two-level systems (TLS) with partial quantum coherence obtained from an environment to one coherent system using a measurement able to increase both energy and coherence simultaneously. The measurement process acts here as a Maxwell demon synthesizing the coherent energy of individual TLS to one large coherent quantum battery. The measurement process described by POVM elements is diagonal in energy representation and, therefore, it does not project on states with quantum coherence at all. We discuss various strategies and their efficiency to reach large coherent energy of the battery. After numerical optimization and proof-of-principle tests, it opens way to feasible repeat-until-success synthesis of coherent quantum batteries from steady-state autonomous coherence.

Measurement Based Quantum Heat Engine with Coupled Working Medium

We consider measurement based single temperature quantum heat engine without feedback control, introduced recently by Yi, Talkner and Kim [Phys. Rev. E96, 022108 (2017)]. Taking the working medium of the engine to be a one-dimensional Heisenberg model of two spins, we calculate the efficiency of the engine undergoing a cyclic process. Starting with two spin-1/2 particles, we investigate the scenario of higher spins also. We show that, for this model of coupled working medium, efficiency can be higher than that of an uncoupled one. However, the relationship between the coupling constant and the efficiency of the engine is rather involved. We find that in the higher spin scenario efficiency can sometimes be negative (this means work has to be done to run the engine cycle) for certain range of coupling constants, in contrast to the aforesaid work of Yi, Talkner and Kim, where they showed that the extracted work is always positive in the absence of coupling. We provide arguments for this negative efficiency in higher spin scenarios. Interestingly, this happens only in the asymmetric scenarios, where the two spins are different. Given these facts, for judiciously chosen conditions, an engine with coupled working medium gives advantage for the efficiency over the uncoupled one.

Power and efficiency of a thermal engine with a coherent bath

We consider a quantum engine driven by repeated weak interactions with a heat bath of identical three-level atoms. This model was first introduced by Scully et al. [Science 299, 862 (2003)SCIEAS0036-807510.1126/science.1078955], who showed that coherence between the energy-degenerate ground states serves as a thermodynamic resource that allows operation of a thermal cycle with a coherence-dependent thermalization temperature. We consider a similar engine out of the quasistatic limit and find that the ground-state coherence also determines the rate of thermalization, therefore increasing the output power and the engine efficiency only when the thermalization temperature is reduced; revealing a more nuanced perspective of coherence as a resource. This allows us to optimize the output power by adjusting the coherence and relative stroke durations.

Daemonic Ergotropy: Generalised Measurements and Multipartite Settings

Recently, the concept of daemonic ergotropy has been introduced to quantify the maximum energy that can be obtained from a quantum system through an ancilla-assisted work extraction protocol based on information gain via projective measurements [G. Francica et al., npj Quant. Inf. 3, 12 (2018)]. We prove that quantum correlations are not advantageous over classical correlations if projective measurements are considered. We go beyond the limitations of the original definition to include generalised measurements and provide an example in which this allows for a higher daemonic ergotropy. Moreover, we propose a see-saw algorithm to find a measurement that attains the maximum work extraction. Finally, we provide a multipartite generalisation of daemonic ergotropy that pinpoints the influence of multipartite quantum correlations, and study it for multipartite entangled and classical states.

Characterizing a Statistical Arrow of Time in Quantum Measurement Dynamics

In both thermodynamics and quantum mechanics, the arrow of time is characterized by the statistical likelihood of physical processes. We characterize this arrow of time for the continuous quantum measurement dynamics of a superconducting qubit. By experimentally tracking individual weak measurement trajectories, we compare the path probabilities of forward and backward-in-time evolution to develop an arrow of time statistic associated with measurement dynamics. We compare the statistics of individual trajectories to ensemble properties showing that the measurement dynamics obeys both detailed and integral fluctuation theorems, thus establishing the consistency between microscopic and macroscopic measurement dynamics.

Nonequilibrium dynamics with finite-time repeated interactions

We study quantum dynamics in the framework of repeated interactions between a system and a stream of identical probes. We present a coarse-grained master equation that captures the system's dynamics in the natural regime where interactions with different probes do not overlap, but it is otherwise valid for arbitrary values of the interaction strength and mean interaction time. We then apply it to some specific examples. For probes prepared in Gibbs states, such channels have been used to describe thermalization: while this is the case for many choices of parameters, for others one finds out-of-equilibrium states including inverted Gibbs and maximally mixed states. Gapless probes can be interpreted as performing an indirect measurement, and we study the energy transfer associated with this measurement.

Quantum Measurement Cooling

Invasiveness of quantum measurements is a genuinely quantum mechanical feature that is not necessarily detrimental: Here we show how quantum measurements can be used to fuel a cooling engine. We illustrate quantum measurement cooling (QMC) by means of a prototypical two-stroke two-qubit engine which interacts with a measurement apparatus and two heat reservoirs at different temperatures. We show that feedback control is not necessary for operation while entanglement must be present in the measurement projectors. We quantify the probability that QMC occurs when the measurement basis is chosen randomly, and find that it can be very large as compared to the probability of extracting energy (heat engine operation), while remaining always smaller than the most useless operation, namely, dumping heat in both baths. These results show that QMC can be very robust to experimental noise. A possible low-temperature solid-state implementation that integrates circuit QED technology with circuit quantum thermodynamics technology is presented.