arXiv subjects

Cyril Elouard

Publications and source records attributed to Cyril Elouard.

At least 19 recordsLinked to original sources

arXiv2026

Quantum stochastic thermodynamics of macroscopic systems: an algebraic approach

We build a framework for the thermodynamics of macroscopic quantum systems. In contrast with approaches requiring access to the full density matrix, our framework relies on a coarse-grained description, based on measurement statistics of a few observables. When these observables commute, the outcomes define classical macrostates whose entropy is quantified by observational entropy, accounting for uncertainty about both the macrostate and the microstate within it. We extend this notion to non-commuting observables forming a subalgebra of the operator space, and use Jaynes' principle to define an algebra-dependent entropy interpolating between von Neumann and observational entropies. Given initial and final measurement sets, connected by internal and/or environment-induced dynamics, we derive a second law for the coarse-grained dynamics. Unlike formulations based on von Neumann entropy, our inequality captures irreversibility from both non-unitary environment-induced dynamics and internal equilibration. It takes the usual form of a positive entropy production when the system is initially at internal equilibrium, while correction terms capture nonequilibrium resources ignored by the coarse-graining. We also derive fluctuation theorems for coarse-grained thermodynamic quantities. Along a quasi-static path of measurement schemes, we identify quantum macroscopic notions of work and heat fulfilling the first and second laws, including an additional work contribution from manipulating the algebra to which the system is confined, through external constraints or quantum measurement backaction. Finally, we apply our framework to examples illustrating the impact of varying the coarse-graining scheme. Our approach unifies macroscopic and stochastic thermodynamics in a genuinely quantum framework, laying the basis for a versatile, experimentally friendly toolbox to analyze complex quantum dynamics.

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arXiv2026

Minimally invasive measurement of work in coherent quantum systems

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.

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arXiv2026

A refined thermodynamic analysis of nonsecular master equations

We present a systematic thermodynamic analysis of nonsecular master equations. We consider master equations resulting either from the partial secular and the geometric-arithmetic approximations, two approximations ensuring the positivity of the system's dynamics when some of its transition frequencies are too small to enable the full secular approximation. Both cause the system to relax towards a steady state which is not the Gibbs state of its bare Hamiltonian. Nonetheless, we build a unified, consistent thermodynamic framework for those dynamics. Starting from a microscopic expression of the second law based on system-environment correlations, we employ a systematic perturbation theory to preserve the positivity of the second law despite the approximations done on the dynamics. We show that, in spite of the weak system-bath coupling, the system-bath interaction energy participates to the energy balance, as well as the Lamb-shift. Those extra contributions give rise to work performed by the system on the bath when the former is out of equilibrium. We compare this microscopic entropy production with the definition based on the contractivity of the reduced system dynamics (Spohn inequality). We show that, unlike for secular master equations, the two entropy production rates differ because of the presence of non-vanishing stationary coherences in the energy eigenbasis. However, in the case of a single thermal bath, the difference is purely transient, and no work can be cyclically extracted from the steady-state despite its non-Gibbs form. Finally, we illustrate our results with a simple example, clarifying and completing the thermodynamic picture of Markovian dynamics in the quantum regime.

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arXiv2026

Revealing the fuel of a quantum continuous measurement-based refrigerator

While quantum measurements have been shown to constitute a resource for operating quantum thermal machines, the nature of the energy exchanges involved in the interaction between system and measurement apparatus is still under debate. In this work, we show that a microscopic model of the apparatus is necessary to unambiguously determine whether quantum measurements provide energy in the form of heat or work. We illustrate this result by considering a measurement-based refrigerator, made of a double quantum dot embedded in a two-terminal device, with the charge of one of the dots being continuously monitored. Tuning the parameters of the measurement device interpolates between a heat- and a work-fueled regimes with very different thermodynamic efficiency. Notably, we demonstrate a trade-off between a maximal thermodynamic efficiency when the measurement-based refrigerator is fueled by heat and a maximal measurement efficiency quantified by the signal-to-noise ratio in the work-fueled regime. Our analysis offers a new perspective on the nature of the energy exchanges occurring during a quantum measurement, paving the way for energy optimization in quantum protocols and quantum machines.

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arXiv2026

Amplifying microwave pulses with a single qubit engine fueled by quantum measurements

Recent progress in manipulating individual quantum systems enables the exploration of engines exploiting non-classical resources. One of the most appealing is the energy provided by the inherent backaction of quantum measurements. While a handful of experiments have investigated the inner dynamics of engines fueled by measurement backaction, powering a task by such an engine is missing. Here we demonstrate the amplification of microwave signals by an engine fueled by repeated quantum measurements of a superconducting transmon qubit. Using feedback, the engine acts as a quantum Maxwell demon operating without a hot thermal source. Measuring the gain of this amplification constitutes a direct probing of the work output of the engine, in contrast with inferring the work by measuring the qubit state along its evolution. Observing a good agreement between both work estimation methods, our experiment validates the accuracy of the indirect method. We characterize the long-term stability of the engine as well as its robustness to transmon decoherence, loss and drifts. Our experiment exemplifies the use of energy brought by quantum measurement backaction.

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arXiv2026

Roadmap on Quantum Thermodynamics

The last two decades has seen quantum thermodynamics become a well established field of research in its own right. In that time, it has demonstrated a remarkably broad applicability, ranging from providing foundational advances in the understanding of how thermodynamic principles apply at the nano-scale and in the presence of quantum coherence, to providing a guiding framework for the development of efficient quantum devices. Exquisite levels of control have allowed state-of-the-art experimental platforms to explore energetics and thermodynamics at the smallest scales which has in turn helped to drive theoretical advances. This Roadmap provides an overview of the recent developments across many of the field's sub-disciplines, assessing the key challenges and future prospects, providing a guide for its near term progress.

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arXiv2025

The Jaynes Cummings model as an autonomous Maxwell demon

We revisit the Jaynes-Cummings model as an autonomous thermodynamic machine, where a qubit is driven by a cavity containing initially a large coherent field. Our analysis reveals a transition between the expected behavior of ideal-work source of the cavity at short times, and a long-time dynamics where the cavity autonomously measures the qubit and exerts a result-dependent drive. This autonomous feedback then purifies the qubit irrespective of its initial state. We show that the cavity functions thermodynamically as an autonomous Maxwell demon, trading mutual information for cooling power.

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arXiv2025

Confinement to deterministic manifolds and low-dimensional solution formulas for continuously measured quantum systems

Quantum systems subjected to a continuous weak measurement process evolve according to stochastic differential equations (SDE). Depending on the outcomes of these stochastic measurements, the quantum state may diffuse in various directions across the state space. This note points out that in many scenarios relevant to quantum engineering, this diffusion is effectively constrained to a low-dimensional space. Specifically, the quantum state remains confined to a low-dimensional, nonlinear manifold -- often time-dependent, yet independent of the specific measurement outcomes. This note derives the corresponding low-dimensional formulations for expressing the stochastically evolving state in several prototypical cases: quantum non-demolition measurements in arbitrary dimensions; quadrature measurements of a harmonic oscillator (linear quantum system); and measurements of subsystems within multipartite quantum systems. Additionally, it introduces an algebraic criterion to determine whether such low-dimensional manifolds exist or persist when additional dynamics are present.

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arXiv2025

Weak continuous measurements require more work than strong ones

Understanding the energy cost of quantum measurement process and its connection to the measurement performance faces the challenge of modeling the objectification process. The latter, turns the measurement result into an objective fact, available to independent observers, and is responsible for the measurement irreversibility. To address this issue, we propose and analyze a dynamical model of quantum measurement, able to capture nonideal (weak and inefficient) measurements. In this model, the objectification is induced by a contact with a macroscopic reservoir at equilibrium which is responsible for the redundant broadcast of the measurement outcome (producing a Spectrum Broadcast Structure (SBS) state) while inducing decoherence in the pointer basis, in the line of the theory of quantum Darwinism. We analyze the performance of the obtained measurement process by introducing figures of merit to quantify the strength of the measurement and its efficiency. We also derive and a lower bound on the measurement work cost that we can relate to the measurement quality. We take as an illustration the readout of a qubit via its coupling to a harmonic oscillator. We investigate the long sequences of extremely short and weak measurements (a.k.a continuous measurements), to find under which conditions they converge to an ideal (projective) measurement and analyze their work cost. Surprisingly, we find that a sequence converging to projective measurement has a much larger work cost than an equivalent strong measurement obtained from a single intense interaction with the apparatus. We extend this result to a large class of models owing to scaling arguments. Our analysis offers new insights into the trade-offs between measurement strength, energy consumption, and information extraction in quantum measurement protocols.

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arXiv2025

A thermodynamically consistent approach to the energy costs of quantum measurements

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.

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arXiv2024

Complete positivity violation of the reduced dynamics in higher-order quantum adiabatic elimination

This paper discusses quantum adiabatic elimination, which is a model reduction technique for a composite Lindblad system consisting of a fast decaying sub-system coupled to another sub-system with a much slower timescale. Such a system features an invariant manifold that is close to the slow sub-system. This invariant manifold is reached subsequent to the decay of the fast degrees of freedom, after which the slow dynamics follow on it. By parametrizing invariant manifold, the slow dynamics can be simulated via a reduced model. To find the evolution of the reduced state, we perform the asymptotic expansion with respect to the timescale separation. So far, the second-order expansion has mostly been considered. It has then been revealed that the second-order expansion of the reduced dynamics is generally given by a Lindblad equation, which ensures complete positivity of the time evolution. In this paper, we present two examples where complete positivity of the reduced dynamics is violated with higher-order contributions. In the first example, the violation is detected for the evolution of the partial trace without truncation of the asymptotic expansion. The partial trace is not the only way to parametrize the slow dynamics. Concerning this non-uniqueness, it was conjectured in [R. Azouit, F. Chittaro, A. Sarlette, and P. Rouchon, Quantum Sci. Technol. 2, 044011 (2017)] that there exists a parameter choice ensuring complete positivity. With the second example, however, we refute this conjecture by showing that complete positivity cannot be restored in any choice of parametrization. We discuss these results in terms of unavoidable correlations, in the initial states on the invariant slow manifold, between the fast and the slow degrees of freedom.

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arXiv2024

Thermodynamics of autonomous optical Bloch equations

Optical Bloch Equations (OBEs) are canonical equations describing the dynamics of a classically driven atom coupled to a thermal bath. Their thermodynamics is highly relevant to establish fundamental energetic bounds of key quantum processes. A consistent framework is available in the regime where the drives and baths can be treated classically, i.e. remains insensitive to the coupling with the atom. This regime, however, is not adapted to explore minimal energy costs, nor to measure atom-induced energy variations inside drives and baths -- a key ability to directly measure and optimize work and heat exchanges. This calls for a new framework accounting for atomic back-actions on drives and baths. Here we build such a framework by describing the atom, the drive and the bath as a joint autonomous system, the drive and the bath being parts of the same electromagnetic field. Our approach captures atom-field correlations at fundamental timescales, as well as the atomic back-action on the field, allowing us to define work-like (heat-like) flows as energy flows stemming from effective unitary dynamics induced by one system on the other (non-unitary correlating dynamics). Time-integrated work-like and heat-like flows are directly measurable in the field, as changes of the mean field and fluctuations, respectively. Our approach differs from standard analyses by identifying an additional unitary contribution in the atom's dynamics, the self-drive, and its energetic counterpart, the self-work, yielding a tighter expression of the second law. We relate this tightening to the extra knowledge about the field state, as well as the potential of the interacted driving field to be recycled. Our autonomous framework deepens the current understanding of thermodynamics in the quantum regime and its potential for energy management at quantum scales.

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arXiv2023

Reply to "Comment on `Extending the laws of thermodynamics for arbitrary autonomous quantum systems'"

In his Comment [1], Philip Strasberg (PS) argues from the analysis of different examples that the framework we have presented in [2] does not recover known results of macroscopic textbook thermodynamics. Here, we show that such apparent contradictions disappear when the necessary assumptions the aforementioned known results pre-suppose are applied. Those assumptions concern the control ability of the observer, the nature of the described degree of freedom, or the scale of the systems. The ability to relax those assumptions is precisely a motivation of our framework, which can explore the capacity of quantum systems to exchange work and heat even at scales not captured by textbook thermodynamics. We take the opportunity of this reply to further expand on the use of our framework and its connections with traditional thermodynamics.

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arXiv2023

Extending the laws of thermodynamics for arbitrary autonomous quantum systems

Originally formulated for macroscopic machines, the laws of thermodynamics were recently shown to hold for quantum systems coupled to ideal sources of work (external classical fields) and heat (systems at equilibrium). Ongoing efforts have been focusing on extending the validity of thermodynamic laws to more realistic, non-ideal energy sources. Here, we go beyond these extensions and show that energy exchanges between arbitrary quantum systems are structured by the laws of thermodynamics. We first generalize the second law and identify the associated work and heat exchanges. After recovering known results from ideal work and heat sources, we analyze some consequences of hybrid work and heat sources. We illustrate our general laws with microscopic machines realizing thermodynamic tasks in which the roles of heat and work sources are simultaneously played by elementary quantum systems. Our results open perspectives to understand and optimize the energetic performances of realistic quantum devices, at any scale.

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arXiv2022

Probing many-body correlations using quantum-cascade correlation spectroscopy

The radiative quantum cascade, i.e. the consecutive emission of photons from a ladder of energy levels, is of fundamental importance in quantum optics. For example, the two-photon cascaded emission from calcium atoms was used in pioneering experiments to test Bell inequalities. In solid-state quantum optics, the radiative biexciton-exciton cascade has proven useful to generate entangled-photon pairs. More recently, correlations and entanglement of microwave photons emitted from a two-photon cascaded process were measured using superconducting circuits. All these experiments rely on the highly non-linear nature of the underlying energy ladder, enabling direct excitation and probing of specific single-photon transitions. Here, we use exciton polaritons to explore the cascaded emission of photons in the regime where individual transitions of the ladder are not resolved, a regime that has not been addressed so far. We excite a polariton quantum cascade by off-resonant laser excitation and probe the emitted luminescence using a combination of spectral filtering and correlation spectroscopy. Remarkably, the measured photon-photon correlations exhibit a strong dependence on the polariton energy, and therefore on the underlying polaritonic interaction strength, with clear signatures from two- and three-body Feshbach resonances. Our experiment establishes photon-cascade correlation spectroscopy as a highly sensitive tool to provide valuable information about the underlying quantum properties of novel semiconductor materials and we predict its usefulness in view of studying many-body quantum phenomena.

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arXiv2022

A topologically protected quantum dynamo effect in a driven spin-boson model

We describe a quantum dynamo effect in a driven system coupled to a harmonic oscillator describing a cavity mode or to a collection of modes forming an Ohmic bosonic bath. When the system Hamiltonian changes in time, this induces a dynamical field in the bosonic modes having resonant frequencies with the driving velocity. This field opposes the change of the external driving field in a way reminiscent of Faraday's law of induction, justifying the term 'quantum dynamo effect'. For the specific situation of a periodically driven spin-$\frac{1}{2}$ on the Bloch sphere, we show that the work done by rolling the spin from north to south pole can efficiently be converted into a coherent displacement of the resonant bosonic modes, the effect thus corresponds to a work-to-work conversion and allows to interpret this transmitted energy into the bath as work. We study this effect, its performance and limitations in detail for a driven spin-$\frac{1}{2}$ in the presence of a radial magnetic field addressing a relation with topological systems through the formation of an effective charge in the core of the sphere. We show that the dynamo effect is directly related to the dynamically measured topology of this spin-$\frac{1}{2}$ and thus in the adiabatic limit provides a topologically protected method to convert driving work into a coherent field in the reservoir. The quantum dynamo model is realizable in mesoscopic and atomic systems.

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arXiv2022

Complete Positivity Violation in Higher-order Quantum Adiabatic Elimination

When a composite Lindblad system consists of weakly coupled sub-systems with fast and slow timescales, the description of slow dynamics can be simplified by discarding fast degrees of freedom. This model reduction technique is called adiabatic elimination. While second-order perturbative expansion with respect to the timescale separation has revealed that the evolution of a reduced state is completely positive, this paper presents an example exhibiting complete positivity violation in the fourth-order expansion. Despite the non-uniqueness of slow dynamics parametrization, we prove that complete positivity cannot be ensured in any parametrization. The violation stems from correlation in the initial state.

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arXiv2022

Anomalous energy exchanges and Wigner function negativities in a single qubit gate

Anomalous weak values and Wigner function's negativity are well known witnesses of quantum contextuality. We show that these effects occur when analyzing the energetics of a single qubit gate generated by a resonant coherent field traveling in a waveguide. The buildup of correlations between the qubit and the field is responsible for bounds on the gate fidelity, but also for a nontrivial energy balance recently observed in a superconducting setup. In the experimental scheme, the field is continuously monitored through heterodyne detection and then post-selected over the outcomes of a final qubit's measurement. The post-selected data can be interpreted as field's weak values and can show anomalous values in the variation of the field's energy. We model the joint system dynamics with a collision model, gaining access to the qubit-field entangled state at any time. We find an analytical expression of the quasi-probability distribution of the post-selected heterodyne signal, i.e. the conditional Husimi-Q function. The latter grants access to all the field's weak values: we use it to obtain that of the field's energy change and display its anomalous behaviour. Finally, we derive the field's conditional Wigner function and show that anomalous weak values and Wigner function's negativities arise for the same values of the gate's angle.

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