Determining the work statistics of quantum engines is challenging due to measurement backaction. We here show that a dynamic Bayesian network-based measurement scheme, which preserves quantum coherence within an engine cycle, is minimally invasive, in the sense that the averaged measured state over one cycle exactly coincides with the unmeasured state. It therefore provides a general framework to investigate energy exchange statistics in quantum machines. This stands in contrast to the standard two-point measurement protocol, whose backaction can be so strong that it generally fails to reproduce the average work output of a coherent motor. It may even alter its mode of operation, causing it to cease functioning as an engine under observation. We further demonstrate that recently proposed universal fluctuation bounds do not necessarily apply to coherent machines.
Determining the work statistics of quantum engines is challenging due to measurement backaction. We here show that a dynamic Bayesian network-based measurement scheme, which preserves quantum coherence within an engine cycle, is minimally invasive, in the sense that the averaged measured state over one cycle exactly coincides with the unmeasured state. It therefore provides a general framework to investigate energy exchange statistics in quantum machines. This stands in contrast to the standard two-point measurement protocol, whose backaction can be so strong that it generally fails to reproduce the average work output of a coherent motor. It may even alter its mode of operation, causing it to cease functioning as an engine under observation. We further demonstrate that recently proposed universal fluctuation bounds do not necessarily apply to coherent machines.
A central challenge in quantum thermodynamics is to access work fluctuations in coherent processes without distorting the energetics of the unmeasured evolution. In standard two-point schemes, the initial energy measurement dephases coherent inputs, causing the measured average work to differ from that of the unmeasured evolution. Here, we develop an operational scheme for accessing work statistics for closed quantum systems based on the abstract notion of variation in the Heisenberg picture Hamiltonian. This scheme preserves energetically relevant coherences, thereby faithfully reproducing unmeasured work, while still producing positive probabilities. We derive modified Jarzynski and Crooks relations, as well as a thermodynamic uncertainty relation, identifying coherence-induced correction terms. Furthermore, we show that this scheme can reliably quantify the performance of a coherent engine in situations where the two-point energy measurement would suppress work output. In addition, the scheme requires only a single measurement and can predict the work associated with a subsequent unitary transformation. We exploit this feature to construct a Maxwell-demon protocol that can outperform energy-based feedback engines for coherent work extraction. Our results establish this scheme as a framework for accessing coherent work fluctuations without erasing the coherence that drives quantum thermodynamic performance.
Finite-time quantum thermal machines require diagnostics beyond average work and efficiency, because microscopic engines operate in regimes where fluctuations, incomplete thermalization, and coherence are equally important. Here we develop a measurement-backaction-free (coherence-preserving) fluctuation diagnostic for an engineered qubit Otto engine coupled to an actively maintained population-inverted hot channel. The engine is analyzed using a dynamic Bayesian network (DBN) reconstruction of the unmeasured coherent cycle, yielding work, heat, power, and normalized efficiency-proxy fluctuations without imposing the projective dephasing inherent in two-point energy measurements. The inverted channel is treated as an active reduced-model resource; accordingly, all reported power and efficiency enhancements represent gross working-medium advantages, not net device efficiencies. In the full-thermalization limit, population inversion enhances extracted work and output power while opening a stability sector with markedly reduced relative power fluctuations. When finite-duration isochores are implemented, this gross enhancement reorganizes into a structured operating landscape with distinct high-power, high-efficiency, and low-relative-noise sectors, whose boundaries are governed by the competing timescales of nonadiabatic driving and thermalization rates. A direct comparison reveals that DBN and conventional two-point measurement predictions diverge precisely in coherence-rich regimes, identifying where a backaction-free reconstruction is essential. A coherence-sensitive analysis further shows that the positive-temperature reference operates optimally in an almost decohered region, whereas the inverted high-efficiency branch remains aligned with the dominant post-hot-bath coherence ridge. These results provide a reduced-model benchmarking framework for engineered qubit thermal machines.
When an observable is measured on an evolving coherent quantum system twice, the first measurement generally alters the statistics of the second one, which is known as measurement backaction. We introduce, and push to its theoretical and experimental limits, a novel method of backaction evasion, whereby entangled collective measurements are performed on several copies of the system. This method is inspired by a similar idea designed for the problem of measuring quantum work [Perarnau-Llobet et al., Phys. Rev. Lett. 118, 070601 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.070601]. By using entanglement as a resource, we show that the backaction can be extremely suppressed compared to all previous schemes. Importantly, the backaction can be eliminated in highly coherent processes.
We propose and analyze the theoretical model for a two-stroke quantum heat engine with one of the heat baths replaced by a non-selective quantum measurement. We show that the engine's invariant reference state depends on whether the cycle is monitored or unmonitored via diagnostic measurements to determine the engine's work output. We explore in detail the average work output and fluctuations of the proposed heat engine for the monitored and unmonitored cases. We also identify unitary work strokes for which the invariant states can support coherences in the energy basis leading to differing predictions for the average energy change during the unitary work strokes and the average work from the standard two-projective measurement approach.
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.
In this Letter we investigate the concept of quantum work and its measurability from the viewpoint of quantum measurement theory. Very often, quantum work and fluctuation theorems are discussed in the framework of projective two-point measurement (TPM) schemes. According to a well-known no-go theorem, there is no work observable which satisfies both (i) an average work condition and (ii) the TPM statistics for diagonal input states. Such projective measurements represent a restrictive class among all possible measurements. It is desirable, both from a theoretical and experimental point of view, to extend the scheme to the general case including suitably designed unsharp measurements. This shifts the focus to the question of what information about work and its fluctuations one is able to extract from such generalized measurements. We show that the no-go theorem no longer holds if the observables in a TPM scheme are jointly measurable for any intermediate unitary evolution. We explicitly construct a model with unsharp energy measurements and derive bounds for the visibility that ensure joint measurability. In such an unsharp scenario a single work measurement apparatus can be constructed that allows us to determine the correct average work and to obtain free energy differences with the help of a Jarzynski equality.