arXiv subjects

H. Wilming

Publications and source records attributed to H. Wilming.

11 recordsLinked to original sources

arXiv2019

Catalytic quantum randomness

Randomness is a defining element of mixing processes in nature and an essential ingredient to many protocols in quantum information. In this work, we investigate how much randomness is required to transform a given quantum state into another one. Specifically, we ask whether there is a gap between the power of a classical source of randomness compared to that of a quantum one. We provide a complete answer to these questions, by identifying provably optimal protocols for both classical and quantum sources of randomness, based on a dephasing construction. We find that in order to implement any noisy transition on a $d$-dimensional quantum system it is necessary and sufficient to have a quantum source of randomness of dimension $\sqrt{d}$ or a classical one of dimension $d$. Interestingly, coherences provided by quantum states in a source of randomness offer a quadratic advantage. The process we construct has the additional features to be robust and catalytic, i.e., the source of randomness can be re-used. Building upon this formal framework, we illustrate that this dephasing construction can serve as a useful primitive in both equilibration and quantum information theory: We discuss applications describing the smallest measurement device, capturing the smallest equilibrating environment allowed by quantum mechanics, or forming the basis for a cryptographic private quantum channel. We complement the exact analysis with a discussion of approximate protocols based on quantum expanders deriving from discrete Weyl systems. This gives rise to equilibrating environments of remarkably small dimension. Our results highlight the curious feature of randomness that residual correlations and dimension can be traded against each other.

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arXiv2018

Von Neumann entropy from unitarity

The von Neumann entropy is a key quantity in quantum information theory and, roughly speaking, quantifies the amount of quantum information contained in a state when many identical and independent i.i.d. copies of the state are available, in a regime that is often referred to as being asymptotic. In this work, we provide a new operational characterization of the von Neumann entropy which neither requires an i.i.d. limit nor any explicit randomness. We do so by showing that the von Neumann entropy fully characterizes single-shot state transitions in unitary quantum mechanics, as long as one has access to a catalyst - an ancillary system that can be re-used after the transition - and an environment which has the effect of dephasing in a preferred basis. Building upon these insights, we formulate and provide evidence for the catalytic entropy conjecture, which states that the above result holds true even in the absence of decoherence. If true, this would prove an intimate connection between single-shot state transitions in unitary quantum mechanics and the von Neumann entropy. Our results add significant support to recent insights that, contrary to common wisdom, the standard von Neumann entropy also characterizes single-shot situations and opens up the possibility for operational single-shot interpretations of other standard entropic quantities. We discuss implications of these insights to readings of the third law of quantum thermodynamics and hint at potentially profound implications to holography.

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arXiv2018

Equilibration times in closed quantum many-body systems

For a quantum system to be captured by a stationary statistical ensemble, as is common in thermodynamics and statistical mechanics, it is necessary that it reaches some apparently stationary state in the first place. In this book chapter, we discuss the problem of equilibration and specifically provide insights into how long it takes to reach equilibrium in closed quantum systems. We first briefly discuss the connection of this problem with recent experiments and forthcoming quantum simulators. Then we provide a comprehensive discussion of equilibration from a heuristic point of view, with a focus on providing an intuitive understanding and connecting the problem with general properties of interacting many-body systems. Finally, we provide a concise review of the rigorous results on equilibration times that are known in the literature.

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arXiv2017

What it takes to shun equilibration

Numerous works have shown that under mild assumptions unitary dynamics inevitably leads to equilibration of physical expectation values if many energy eigenstates contribute to the initial state. Here, we consider systems driven by arbitrary time-dependent Hamiltonians as a protocol to prepare systems that do not equilibrate. We introduce a measure of the resilience against equilibration of such states and show, under natural assumptions, that in order to increase the resilience against equilibration of a given system, one needs to possess a resource system which itself has a large resilience. In this way, we establish a new link between the theory of equilibration and resource theories by quantifying the resilience against equilibration and the resources that are needed to produce it. We connect these findings with insights into local quantum quenches and investigate the (im-)possibility of formulating a second law of equilibration, by studying how resilience can be either only redistributed among subsystems, if these remain completely uncorrelated, or in turn created in a catalytic process if subsystems are allowed to build up some correlations.

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arXiv2017

Strong coupling corrections in quantum thermodynamics

Quantum systems strongly coupled to many-body systems equilibrate to the reduced state of a global thermal state, deviating from the local thermal state of the system as it occurs in the weak-coupling limit. Taking this insight as a starting point, we study the thermodynamics of systems strongly coupled to thermal baths. First, we provide strong-coupling corrections to the second law applicable to general systems in three of its different readings: As a statement of maximal extractable work, on heat dissipation, and bound to the Carnot efficiency. These corrections become relevant for small quantum systems and always vanish in first order in the interaction strength. We then move to the question of power of heat engines, obtaining a bound on the power enhancement due to strong coupling. Our results are exemplified on the paradigmatic situation of non-Markovian quantum Brownian motion.

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arXiv2017

Towards local equilibration in closed interacting quantum many-body systems

One of the main questions of research on quantum many-body systems following unitary out of equilibrium dynamics is to find out how local expectation values equilibrate in time. For non-interacting models, this question is rather well understood. However, the best known bounds for general quantum systems are vastly crude, scaling unfavorable with the system size. Nevertheless, empirical and numerical evidence suggests that for generic interacting many-body systems, generic local observables, and sufficiently well-behaved states, the equilibration time does not depend strongly on the system size, but only the precision with which this occurs does. In this discussion paper, we aim at giving very simple and plausible arguments for why this happens. While our discussion does not yield rigorous results about equilibration time scales, we believe that it helps to clarify the essential underlying mechanisms, the intuition and important figure of merits behind equilibration. We then connect our arguments to common assumptions and numerical results in the field of equilibration and thermalization of closed quantum systems, such as the eigenstate thermalization hypothesis as well as rigorous results on interacting quantum many-body systems. Finally, we complement our discussions with numerical results - both in the case of examples and counter-examples of equilibrating systems.

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arXiv2016

Quantum thermodynamics with local control

We investigate the limitations that emerge in thermodynamic tasks as a result of having local control only over the components of a thermal machine. These limitations are particularly relevant for devices composed of interacting many-body systems. Specifically, we study protocols of work extraction that employ a many-body system as a working medium whose evolution can be driven by tuning the on-site Hamiltonian terms. This provides a restricted set of thermodynamic operations, giving rise to novel bounds for the performance of engines. Our findings show that those limitations in control render it in general impossible to reach Carnot efficiency; in its extreme ramification it can even forbid to reach a finite efficiency of work per particle. We focus on the 1D Ising model in the thermodynamic limit as a case study. We show that in the limit of strong interactions the ferromagnetic case becomes useless for work extraction, while the anti-ferromagnetic improves its performance with the strength of the couplings, reaching Carnot in the limit of arbitrary strong interactions. Our results provide a promising connection between the study of quantum control and thermodynamics and introduce a more realistic set of physical operations well suited to capture current experimental scenarios.

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arXiv2016

Work and entropy production in generalised Gibbs ensembles

Recent years have seen an enormously revived interest in the study of thermodynamic notions in the quantum regime. This applies both to the study of notions of work extraction in thermal machines in the quantum regime, as well as to questions of equilibration and thermalisation of interacting quantum many-body systems as such. In this work we bring together these two lines of research by studying work extraction in a closed system that undergoes a sequence of quenches and equilibration steps concomitant with free evolutions. In this way, we incorporate an important insight from the study of the dynamics of quantum many body systems: the evolution of closed systems is expected to be well described, for relevant observables and most times, by a suitable equilibrium state. We will consider three kinds of equilibration, namely to (i) the time averaged state, (ii) the Gibbs ensemble and (iii) the generalised Gibbs ensemble (GGE), reflecting further constants of motion in integrable models. For each effective description, we investigate notions of entropy production, the validity of the minimal work principle and properties of optimal work extraction protocols. While we keep the discussion general, much room is dedicated to the discussion of paradigmatic non-interacting fermionic quantum many-body systems, for which we identify significant differences with respect to the role of the minimal work principle. Our work not only has implications for experiments with cold atoms, but also can be viewed as suggesting a mindset for quantum thermodynamics where the role of the external heat baths is instead played by the system itself, with its internal degrees of freedom bringing coarse-grained observables to equilibrium.

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arXiv2016

Second laws under control restrictions

The second law of thermodynamics, formulated as an ultimate bound on the maximum extractable work, has been rigorously derived in multiple scenarios. However, the unavoidable limitations that emerge due to the lack of control on small systems are often disregarded when deriving such bounds, which is specifically important in the context of quantum thermodynamics. Here, we study the maximum extractable work with limited control over the working system and its interaction with the heat bath. We derive a general second law when the set of accessible Hamiltonians of the working-system is arbitrarily restricted. We then apply our bound to particular scenarios that are important in realistic implementations: limitations on the maximum energy gap and local control over many-body systems. We hence demonstrate in what precise way the lack of control affects the second law. In particular, contrary to the unrestricted case, we show that the optimal work extraction is not achieved by simple thermal contacts. Our results do not only generalize the second law to scenarios of practical relevance, but also take first steps in the direction of local thermodynamics.

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arXiv2016

Emergence of spontaneous symmetry breaking in dissipative lattice systems

A cornerstone of the theory of phase transitions is the observation that many-body systems exhibiting a spontaneous symmetry breaking in the thermodynamic limit generally show extensive fluctuations of an order parameter in large but finite systems. In this work, we introduce the dynamical analogue of such a theory. Specifically, we consider local dissipative dynamics preparing a steady-state of quantum spins on a lattice exhibiting a discrete or continuous symmetry but with extensive fluctuations in a local order parameter. We show that for all such processes satisfying detailed balance, there exist metastable symmetry-breaking states, i.e., states that become stationary in the thermodynamic limit and give a finite value to the order parameter. We give results both for discrete and continuous symmetries and explicitly show how to construct the symmetry-breaking states. Our results show in a simple way that, in large systems, local dissipative dynamics satisfying detailed balance cannot uniquely and efficiently prepare states with extensive fluctuations with respect to local operators. We discuss the implications of our results for quantum simulators and dissipative state preparation.

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arXiv2015

Thermodynamic work from operational principles

In recent years we have witnessed a concentrated effort to make sense of thermodynamics for small-scale systems. One of the main difficulties is to capture a suitable notion of work that models realistically the purpose of quantum machines, in an analogous way to the role played, for macroscopic machines, by the energy stored in the idealisation of a lifted weight. Despite of several attempts to resolve this issue by putting forward specific models, these are far from capturing realistically the transitions that a quantum machine is expected to perform. In this work, we adopt a novel strategy by considering arbitrary kinds of systems that one can attach to a quantum thermal machine and seeking for work quantifiers. These are functions that measure the value of a transition and generalise the concept of work beyond the model of a lifted weight. We do so by imposing simple operational axioms that any reasonable work quantifier must fulfil and by deriving from them stringent mathematical condition with a clear physical interpretation. Our approach allows us to derive much of the structure of the theory of thermodynamics without taking as a primitive the definition of work. We can derive, for any work quantifier, a quantitative second law in the sense of bounding the work that can be performed using some non-equilibrium resource by the work that is needed to create it. We also discuss in detail the role of reversibility and correlations in connection with the second law. Furthermore, we recover the usual identification of work with energy in degrees of freedom with vanishing entropy as a particular case of our formalism. Our mathematical results can be formulated abstractly and are general enough to carry over to other resource theories than quantum thermodynamics.

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