Trade-Off Between Work and Correlations in Quantum Thermodynamics

Vitagliano, Giuseppe; Klöckl, Claude; Huber, Marcus; Friis, Nicolai

doi:10.1007/978-3-319-99046-0_30

Cited by 15 publications

(24 citation statements)

References 58 publications

(96 reference statements)

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“…Several works address the influence of coherence [12,14,15,27,28] and correlations [7,19,[29][30][31][32][33][34][35][36][37][38] in thermodynamic transformations in different scenarios. In * cerisola@df.uba.ar † augusto@df.uba.ar general, the creation of correlations is associated to some energetic cost and strategies to optimally extract work from them have been put forward [33][34][35][36][37][38]. On the other hand, it has been demonstrated that in the single-shot regime, by allowing auxiliary correlated catalytic systems [7] or correlations with catalytic systems [19], it is possible to enlarge the set of achievable transformations.…”

Section: Introductionmentioning

confidence: 99%

Correlations as a resource in quantum thermodynamics

2019

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The presence of correlations in physical systems can be a valuable resource for many quantum information tasks. They are also relevant in thermodynamic transformations, and their creation is usually associated to some energetic cost. In this work, we study the role of correlations in the thermodynamic process of state formation in the single-shot regime, and find that correlations can also be viewed as a resource. First, we show that the energetic cost of creating multiple copies of a given state can be reduced by allowing correlations in the final state. We obtain the minimum cost for every finite number of subsystems, and then we show that this feature is not restricted to the case of copies. More generally, we demonstrate that in the asymptotic limit, by allowing a logarithmic amount of correlations, we can recover standard results where the free energy quantifies this minimum cost.

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Section: Introductionmentioning

confidence: 99%

Correlations as a resource in quantum thermodynamics

2019

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“…To formulate our ideas we adopt a commonplace view in quantum thermodynamics, namely, that work is a central resource that is required to move systems away from freely available thermal equilibrium states [24]-an approach that has staged a diverse range of investigations within the broader field [25][26][27]. In this paradigm, previous research has investigated the work-cost (or gain) of quantum processes [28][29][30][31][32], refrigeration [33,34], or for establishing correlations [35][36][37][38].…”

Section: Tpm Schemementioning

confidence: 99%

Work estimation and work fluctuations in the presence of non-ideal measurements

et al. 2019

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From the perspective of quantum thermodynamics, realisable measurements cost work and result in measurement devices that are not perfectly correlated with the measured systems. We investigate the consequences for the estimation of work in non-equilibrium processes and for the fundamental structure of the work fluctuations when one assumes that the measurements are non-ideal. We show that obtaining work estimates and their statistical moments at finite work cost implies an imperfection of the estimates themselves: more accurate estimates incur higher costs. Our results provide a qualitative relation between the cost of obtaining information about work and the trustworthiness of this information. Moreover, we show that Jarzynski's equality can be maintained exactly at the expense of a correction that depends only on the system's energy scale, while the more general fluctuation relation due to Crooks no longer holds when the cost of the work estimation procedure is finite. We show that precise links between dissipation and irreversibility can be extended to the non-ideal situation.

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“…2. These five points are A =p (1, 1, 1) , B =p (7, 1, 1) , C =p (13,7,1) , D =p (9,7,1) , and E =p since p 0 (β) ≥ p 1 (β) and p 0 (β) + p 1 (β) ≥ 1 2 for any Hamiltonian and any temperature. This means the point (0, y(β), z(β)) is contained in polytope since it can be obtained as a convex combination of A and B.…”

Section: Axii Geometry Of Equal Thermal Marginals For Two Ququartsmentioning

confidence: 99%

“…Here, we explore the specific quantitative relation between correlations and energy [7]. While general qualitative insights can help to understand some quandaries arising from Maxwell's demon or Szilard's engine [8][9][10], and correlations play various interesting roles in quantum thermodynamics (see, e.g., [2,3,[11][12][13][14][15][16][17][18]), precise quantitative statements about the trade-off between work and correlations are generally complicated.…”

Section: Introductionmentioning

confidence: 99%

“…While general qualitative insights can help to understand some quandaries arising from Maxwell's demon or Szilard's engine [8][9][10], and correlations play various interesting roles in quantum thermodynamics (see, e.g., [2,3,[11][12][13][14][15][16][17][18]), precise quantitative statements about the trade-off between work and correlations are generally complicated. For example, by allowing arbitrarily slow quasi-static operations and perfect control over arbitrarily many auxiliary systems, one may provide tight lower bounds on the work cost of creating bipartite correlations as measured by the mutual information [7,11,12,19,20]. However, for two identical systems, these bounds are tight only in the case when specific so-called symmetrically thermalizing unitaries (STUs) exist, i.e., unitaries that map initial thermal states to locally thermal states at higher local effective temperatures.…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamically optimal creation of correlations

Bakhshinezhad

Clivaz

Vitagliano

et al. 2019

J. Phys. A: Math. Theor.

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Correlations lie at the heart of almost all scientific predictions. It is therefore of interest to ask whether there exist general limitations to the amount of correlations that can be created at a finite amount of invested energy. Within quantum thermodynamics such limitations can be derived from first principles. In particular, it can be shown that establishing correlations between initially uncorrelated systems in a thermal background has an energetic cost. This cost, which depends on the system dimension and the details of the energy-level structure, can be bounded from below but whether these bounds are achievable is an open question. Here, we put forward a framework for studying the process of optimally correlating identical (thermal) quantum systems. The framework is based on decompositions into subspaces that each support only states with diagonal (classical) marginals. Using methods from stochastic majorisation theory, we show that the creation of correlations at minimal energy cost is possible for all pairs of three-and four-dimensional quantum systems. For higher dimensions we provide sufficient conditions for the existence of such optimally correlating operations, which we conjecture to exist in all dimensions. * These authors contributed equally to this work. †

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Trade-Off Between Work and Correlations in Quantum Thermodynamics

Cited by 15 publications

References 58 publications

Correlations as a resource in quantum thermodynamics

Correlations as a resource in quantum thermodynamics

Work estimation and work fluctuations in the presence of non-ideal measurements

Thermodynamically optimal creation of correlations

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