arXiv subjects

M. Hamed Mohammady

Publications and source records attributed to M. Hamed Mohammady.

At least 19 recordsLinked to original sources

arXiv2026

Noether Symmetries Generate Deterministic Energy-Harvesting Protocols

We consider the general principles for when deterministic energy harvesting (DEH) is possible. DEH means absorbing energy from a fluctuating source without entropy being absorbed. We show that the symmetry structure of the source--harvester dynamics gives a general route beyond existing examples to identify DEH capable source states. Any continuous symmetry with a conserved Noether charge induces a source-side orbit of states that all implement the same deterministic harvester transition, provided the harvester boundary states are symmetry invariant. Consequently, one DEH capable source state with nonzero asymmetry between charge sectors can generate infinitely many simultaneously DEH capable source states. A Jaynes-Cummings model, a three-spin XX chain, and an SU(2) model illustrate the construction. We further extend Noether's theorem to generalised probabilistic theories and thereby generalise our main result. We further establish an asymmetry bound for harvesting, showing that source asymmetry cannot increase on average, while DEH saturates the bound exactly preserving asymmetry.

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arXiv2026

Thermodynamic closure of quantum measurements and the limits of the indirect measurement model

We investigate the consequences of requiring that a quantum measurement admit an adiabatic enclosure, so that it can be assigned a genuine thermodynamic description in which energy exchange is meaningfully resolved into work and heat. We identify two inequivalent levels at which such thermodynamic closure can be imposed: at the level of the measurement instrument acting on the system, or at the level of the indirect measurement process realising the instrument, namely the interaction between the system and a measuring apparatus, possibly including arbitrarily large environments. Although every instrument admits a unitary dilation, we show that such a construction does not generally provide an admissible thermodynamic closure. This distinction is especially dramatic for efficient measurements, i.e., measurements that are completely purity-preserving and described by a single Kraus operator, including von Neumann--Lüders and square-root state-update rules. While efficient measurements are compatible with the laws of thermodynamics when thermodynamic closure is imposed at the level of the instrument, they are categorically forbidden when closure is imposed at the level of the measurement process. Our results therefore reveal a fundamental tension between thermodynamics and the universal applicability of the unitary interaction-based indirect measurement model.

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arXiv2025

A hierarchy of thermodynamically consistent quantum operations

In order to determine what quantum operations and measurements are consistent with the laws of thermodynamics, one must start by allowing all processes allowed by the framework of quantum theory, and then impose the laws of thermodynamics as a set of constraints. Here, we consider a hierarchy of quantum operations and measurements that are consistent with ($I$) the weak third law, ($II$) the strong third law, and ($III$) both the second and the third laws of thermodynamics, i.e., operations and measurements that are fully consistent with thermodynamics. Such characterisation allows us to identify which particular thermodynamic principle is responsible for the (un)attainability of a given quantum operation or measurement. In the case of channels, i.e., trace-preserving operations, we show that a channel belongs to ($I$) and ($II$) if and only if it is strictly positive and rank non-decreasing, respectively, whereas a channel belongs to ($III$) only if it is rank non-decreasing and does not perturb a strictly positive state. On the other hand, while thermodynamics does not preclude the measurability of any POVM, the realisable state-update rules for measurements are increasingly restricted as we go from ($I$) to ($III$).

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arXiv2024

Universal validity of the second law of information thermodynamics

Adiabatic measurements, followed by feedback and erasure protocols, have often been considered as a model to embody Maxwell's Demon paradox and to study the interplay between thermodynamics and information processing. Such studies have led to the conclusion, now widely accepted in the community, that Maxwell's Demon and the second law of thermodynamics can peacefully coexist because any gain provided by the demon must be offset by the cost of performing the measurement and resetting the demon's memory to its initial state. Statements of this kind are collectively referred to as second laws of information thermodynamics and have recently been extended to include quantum theoretical scenarios. However, previous studies in this direction have made several assumptions, particularly about the feedback process and the demon's memory readout, and thus arrived at statements that are not universally applicable and whose range of validity is not clear. In this work, we fill this gap by precisely characterizing the full range of quantum feedback control and erasure protocols that are overall consistent with the second law of thermodynamics. This leads us to conclude that the second law of information thermodynamics is indeed universal: it must hold for any quantum feedback control and erasure protocol, regardless of the measurement process involved, as long as the protocol is overall compatible with thermodynamics. Our comprehensive analysis not only encompasses new scenarios but also retrieves previous ones, doing so with fewer assumptions. This simplification contributes to a clearer understanding of the theory.

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arXiv2024

Joint statistics of work and entropy production along quantum trajectories

In thermodynamics, entropy production and work quantify irreversibility and the consumption of useful energy, respectively, when a system is driven out of equilibrium. For quantum systems, these quantities can be identified at the stochastic level by unravelling the system's evolution in terms of quantum jump trajectories. We here derive a general formula for computing the joint statistics of work and entropy production in Markovian driven quantum systems, whose instantaneous steady-states are of Gibbs form. If the driven system remains close to the instantaneous Gibbs state at all times, we show that the corresponding two-variable cumulant generating function implies a joint detailed fluctuation theorem so long as detailed balance is satisfied. As a corollary, we derive a modified fluctuation-dissipation relation (FDR) for the entropy production alone, applicable to transitions between arbitrary steady-states, and for systems that violate detailed balance. This FDR contains a term arising from genuinely quantum fluctuations, and extends an analogous relation from classical thermodynamics to the quantum regime.

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arXiv2024

Thermodynamic uncertainty relation in slowly driven quantum heat engines

Thermodynamic Uncertainty Relations express a trade-off between precision, defined as the noise-to-signal ratio of a generic current, and the amount of associated entropy production. These results have deep consequences for autonomous heat engines operating at steady-state, imposing an upper bound for their efficiency in terms of the power yield and its fluctuations. In the present manuscript we analyse a different class of heat engines, namely those which are operating in the periodic slow-driving regime. We show that an alternative TUR is satisfied, which is less restrictive than that of steady-state engines: it allows for engines that produce finite power, with small power fluctuations, to operate close to the Carnot efficiency. The bound further incorporates the effect of quantum fluctuations, which reduces engine efficiency relative to the average power and reliability. We finally illustrate our findings in the experimentally relevant model of a single-ion heat engine.

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arXiv2023

Measurement disturbance and conservation laws in quantum mechanics

Measurement error and disturbance, in the presence of conservation laws, are analysed in general operational terms. We provide novel quantitative bounds demonstrating necessary conditions under which accurate or non-disturbing measurements can be achieved, highlighting an interesting interplay between incompatibility, unsharpness, and coherence. From here we obtain a substantial generalisation of the Wigner-Araki-Yanase (WAY) theorem. Our findings are further refined through the analysis of the fixed-point set of the measurement channel, some extra structure of which is characterised here for the first time.

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arXiv2023

Quantum measurements constrained by the third law of thermodynamics

In the quantum regime, the third law of thermodynamics implies the unattainability of pure states. As shown recently, such unattainability implies that a unitary interaction between the measured system and a measuring apparatus can never implement an ideal projective measurement. In this paper, we introduce an operational formulation of the third law for the most general class of physical transformations, the violation of which is both necessary and sufficient for the preparation of pure states. Subsequently, we investigate how such a law constrains measurements of general observables, or positive operator valued measures. We identify several desirable properties of measurements which are simultaneously enjoyed by ideal projective measurements -- and are hence all ruled out by the third law in such a case -- and determine if the third law allows for these properties to obtain for general measurements of general observables and, if so, under what conditions. It is shown that while the third law rules out some of these properties for all observables, others may be enjoyed by observables that are sufficiently "unsharp".

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arXiv2023

Thermodynamically free quantum measurements

Thermal channels -- the free processes allowed in the resource theory of quantum thermodynamics -- are generalised to thermal instruments, which we interpret as implementing thermodynamically free quantum measurements; a Maxwellian demon using such measurements never violates the second law of thermodynamics. Further properties of thermal instruments are investigated and, in particular, it is shown that they only measure observables commuting with the Hamiltonian, and they thermalise the measured system when performing a complete measurement, the latter of which indicates a thermodynamically induced information-disturbance trade-off. The demarcation of measurements that are not thermodynamically free paves the way for a resource-theoretic quantification of their thermodynamic cost.

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arXiv2021

Classicality of the heat produced by quantum measurements

Quantum measurement is ultimately a physical process, resulting from an interaction between the measured system and a measuring apparatus. Considering the physical process of measurement within a thermodynamic context naturally raises the following question: How can the work and heat be interpreted? In the present paper we model the measurement process for an arbitrary discrete observable as a measurement scheme. Here the system to be measured is first unitarily coupled with an apparatus and subsequently the compound system is objectified with respect to a pointer observable, thus producing definite measurement outcomes. The work can therefore be interpreted as the change in internal energy of the compound system due to the unitary coupling. By the first law of thermodynamics, the heat is the subsequent change in internal energy of this compound due to pointer objectification. We argue that the apparatus serves as a stable record for the measurement outcomes only if the pointer observable commutes with the Hamiltonian and show that such commutativity implies that the uncertainty of heat will necessarily be classical.

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arXiv2021

Self-consistency of the two-point energy measurement protocol

A thermally isolated quantum system undergoes unitary evolution by interacting with an external work source. The two-point energy measurement (TPM) protocol defines the work exchanged between the system and the work source by performing ideal energy measurements on the system before, and after, the unitary evolution. However, the ideal energy measurements used in the TPM protocol ultimately result from a unitary coupling with a measurement apparatus, which requires an interaction with an external work source. For the TPM protocol to be self-consistent, we must be able to perform the TPM protocol on the compound of system plus apparatus, thus revealing the total work distribution, such that when ignoring the apparatus degrees of freedom, we recover the original TPM work distribution for the system of interest. In the present manuscript, we show that such self-consistency is satisfied so long as the apparatus is initially prepared in an energy eigenstate. Moreover, we demonstrate that if the apparatus Hamiltonian is equivalent to the "pointer observable", then: (i) the total work distribution will satisfy the "unmeasured" first law of thermodynamics for all system states and system-only unitary processes; and (ii) the total work distribution will be identical to the system-only work distribution, for all system states and system-only unitary processes, if and only if the unmeasured work due to the unitary coupling between system and apparatus is zero for all system states.

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arXiv2020

Fluctuating quantum heat

The increase in average energy of a quantum system undergoing projective energy measurements is referred to as "quantum heat", which is always zero. In the framework of quantum stochastic thermodynamics, this is constructed as the average over the fluctuating quantum heat (FQH), defined as the increase in expected value of the Hamiltonian along two-point eigenstate trajectories. However, such a definition has two drawbacks: (i) if the initial state does not commute with the Hamiltonian and has degeneracies, the higher moments of the FQH will not be uniquely defined, and therefore it is arguable whether such a quantity is physically meaningful; (ii) the definition is operationally demanding as it requires full knowledge of the initial state. In the present manuscript we show that the FQH is an instance of conditional increase in energy given sequential measurements, the first of which is with respect to the eigen-decomposition of the initial state. By coarse-graining this initial measurement, first by only distinguishing between degenerate subspaces of the state, and finally by not distinguishing between any subspace at all, we provide two alternative definitions for the FQH, which we call the partially coarse-grained FQH and fully coarse-grained FQH, respectively. The partially coarse-grained FQH resolves issue (i), whereas the fully coarse-grained FQH resolves both (i) and (ii).

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arXiv2019

Conditional work statistics of quantum measurements

In this paper we introduce a definition for conditional energy changes due to general quantum measurements, as the change in the conditional energy evaluated before, and after, the measurement process. By imposing minimal physical requirements on these conditional energies, we show that the most general expression for the conditional energy after the measurement is simply the expected value of the Hamiltonian given the post-measurement state. Conversely, the conditional energy before the measurement process is shown to be given by the real component of the weak value of the Hamiltonian. Our definition generalises well-known notions of distributions of internal energy change, such as that given by stochastic thermodynamics. By determining the conditional energy change of both system and measurement apparatus, we obtain the full conditional work statistics of quantum measurements, and show that this vanishes for all measurement outcomes if the measurement process conserves the total energy. Additionally, by incorporating the measurement process within a cyclic heat engine, we quantify the non-recoverable work due to measurements. This is shown to always be non-negative, thus satisfying the second law, and will be independent of the apparatus specifics for two classes of projective measurements.

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arXiv2019

Efficiency of a cyclic quantum heat engine with finite-size baths

In this paper we investigate the relationship between the efficiency of a cyclic quantum heat engine with the Hilbert space dimension of the thermal baths. By means of a general inequality, we show that the Carnot efficiency can be obtained only when both the hot and cold baths are infinitely large. By further introducing a specific model where the baths are constituted of ensembles of finite-dimensional particles, we further demonstrate the relationship between the engine's power and efficiency, with the dimension of the working substance and the bath particles.

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arXiv2019

Symmetry constrained decoherence of conditional expectation values

Conditional expectation values of quantum mechanical observables reflect unique non-classical correlations, and are generally sensitive to decoherence. We consider the circumstances under which such sensitivity to decoherence is removed, namely, when the measurement process is subjected to conservation laws. Specifically, we address systems with additive conserved quantities and identify sufficient conditions for the system state such that its coherence plays no role in the conditional expectation values of observables that commute with the conserved quantity. We discuss our findings for a specific model where the system-detector coupling is given by the Jaynes-Cummings interaction, which is relevant to experiments tracking trajectories of qubits in cavities. Our results clarify, among others, the role of coherence in thermal measurements in current architectures for quantum thermodynamics experiments.

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arXiv2018

Low-control and robust quantum refrigerator and applications with electronic spins in diamond

We propose a general protocol for low-control refrigeration and thermometry of thermal qubits, which can be implemented using electronic spins in diamond. The refrigeration is implemented by a probe, consisting of a network of interacting spins. The protocol involves two operations: (i) free evolution of the probe; and (ii) a swap gate between one spin in the probe and the thermal qubit we wish to cool. We show that if the initial state of the probe falls within a suitable range, and the free evolution of the probe is both unital and conserves the excitation in the $z$-direction, then the cooling protocol will always succeed, with an efficiency that depends on the rate of spin dephasing and the swap gate fidelity. Furthermore, measuring the probe after it has cooled many qubits provides an estimate of their temperature. We provide a specific example where the probe is a Heisenberg spin chain, and suggest a physical implementation using electronic spins in diamond. Here the probe is constituted of nitrogen vacancy (NV) centers, while the thermal qubits are dark spins. By using a novel pulse sequence, a chain of NV centers can be made to evolve according to a Heisenberg Hamiltonian. This proposal allows for a range of applications, such as NV-based nuclear magnetic resonance of photosensitive molecules kept in a dark spot on a sample, and it opens up possibilities for the study of quantum thermodynamics, environment-assisted sensing, and many-body physics.

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arXiv2017

A quantum Szilard engine without heat from a thermal reservoir

We study a quantum Szilard engine that is not powered by heat drawn from a thermal reservoir, but rather by projective measurements. The engine is constituted of a system $\mathcal{S}$, a weight $\mathcal{W}$, and a Maxwell demon $\mathcal{D}$, and extracts work via measurement-assisted feedback control. By imposing natural constraints on the measurement and feedback processes, such as energy conservation and leaving the memory of the demon intact, we show that while the engine can function without heat from a thermal reservoir, it must give up at least one of the following features that are satisfied by a standard Szilard engine: (i) repeatability of measurements; (ii) invariant weight entropy; or (iii) positive work extraction for all measurement outcomes. This result is shown to be a consequence of the Wigner-Araki-Yanase (WAY) theorem, which imposes restrictions on the observables that can be measured under additive conservation laws. This observation is a first-step towards developing "second-law-like" relations for measurement-assisted feedback control beyond thermality.

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arXiv2016

Minimising the heat dissipation of quantum information erasure

Quantum state engineering and quantum computation rely on information erasure procedures that, up to some fidelity, prepare a quantum object in a pure state. Such processes occur within Landauer's framework if they rely on an interaction between the object and a thermal reservoir. Landauer's principle dictates that this must dissipate a minimum quantity of heat, proportional to the entropy reduction that is incurred by the object, to the thermal reservoir. However, this lower bound is only reachable for some specific physical situations, and it is not necessarily achievable for any given reservoir. The main task of our work can be stated as the minimisation of heat dissipation given probabilistic information erasure, i.e., minimising the amount of energy transferred to the thermal reservoir as heat if we require that the probability of preparing the object in a specific pure state $|φ_1\rangle$ be no smaller than $p_{φ_1}^{\max}-δ$. Here $p_{φ_1}^{\max}$ is the maximum probability of information erasure that is permissible by the physical context, and $δ\geqslant 0$ the error. To determine the achievable minimal heat dissipation of quantum information erasure within a given physical context, we explicitly optimise over all possible unitary operators that act on the composite system of object and reservoir. Specifically, we characterise the equivalence class of such optimal unitary operators, using tools from majorisation theory, when we are restricted to finite-dimensional Hilbert spaces. Furthermore, we discuss how pure state preparation processes could be achieved with a smaller heat cost than Landauer's limit, by operating outside of Landauer's framework.

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