Fundamental limitations for quantum and nanoscale thermodynamics

Horodecki, Michał; Oppenheim, Jonathan

doi:10.1038/ncomms3059

Cited by 736 publications

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“…where H os is obtained by substituting Ω = ω in Equation (1). Here ρ c and ρ h are respectively the initial and the final density matrices in Stage 1.…”

Section: Single System As a Heat Enginementioning

confidence: 99%

“…This Hamiltonian has a similar structure as the oscillator Hamiltonian given in Equation (1). Now consider a cycle constructed such that frequency Ω varies from ω to ω in Stage 2 and returns to the initial value (ω → ω) in Stage 4.…”

Section: Single System As a Heat Enginementioning

confidence: 99%

“…As an example, the statement of the second law of thermodynamics in the presence of an ancilla [1,2] or, when the system has coherence [3,4], has been established in great details, from where the classical version of the second law emerges under appropriate limits. The study of thermodynamics in quantum domain can be approached from different directions such as information-theoretic point of view [5][6][7][8][9][10] or resource-theoretic aspect [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

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Implications of Coupling in Quantum Thermodynamic Machines

Thomas

Banik

Ghosh

2017

Entropy

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Abstract:We study coupled quantum systems as the working media of thermodynamic machines. Under a suitable phase-space transformation, the coupled systems can be expressed as a composition of independent subsystems. We find that for the coupled systems, the figures of merit, that is the efficiency for engine and the coefficient of performance for refrigerator, are bounded (both from above and from below) by the corresponding figures of merit of the independent subsystems. We also show that the optimum work extractable from a coupled system is upper bounded by the optimum work obtained from the uncoupled system, thereby showing that the quantum correlations do not help in optimal work extraction. Further, we study two explicit examples; coupled spin-1/2 systems and coupled quantum oscillators with analogous interactions. Interestingly, for particular kind of interactions, the efficiency of the coupled oscillators outperforms that of the coupled spin-1/2 systems when they work as heat engines. However, for the same interaction, the coefficient of performance behaves in a reverse manner, while the systems work as the refrigerator. Thus, the same coupling can cause opposite effects in the figures of merit of heat engine and refrigerator.

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“…where H os is obtained by substituting Ω = ω in Equation (1). Here ρ c and ρ h are respectively the initial and the final density matrices in Stage 1.…”

Section: Single System As a Heat Enginementioning

confidence: 99%

Section: Single System As a Heat Enginementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Implications of Coupling in Quantum Thermodynamic Machines

Thomas

Banik

Ghosh

2017

Entropy

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“…Several QRTs were constructed along these lines, some them indeed irreversible: entanglement theory (with respect to LOCC) [8,9], thermodynamics (w.r.t. energy-conserving operations and thermal states) [10,11], reference frames (w.r.t. group-covariant operations) [12], etc.…”

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confidence: 99%

Operational Resource Theory of Coherence

2016

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We establish an operational theory of coherence (or of superposition) in quantum systems, by focusing on the optimal rate of performance of certain tasks. Namely, we introduce the two basic concepts -"coherence distillation" and "coherence cost" in the processing quantum states under so-called incoherent operations [Baumgratz/Cramer/Plenio, Phys. Rev. Lett. 113:140401 (2014)]. We then show that in the asymptotic limit of many copies of a state, both are given by simple singleletter formulas: the distillable coherence is given by the relative entropy of coherence (in other words, we give the relative entropy of coherence its operational interpretation), and the coherence cost by the coherence of formation, which is an optimization over convex decompositions of the state. An immediate corollary is that there exists no bound coherent state in the sense that one would need to consume coherence to create the state but no coherence could be distilled from it. Further we demonstrate that the coherence theory is generically an irreversible theory by a simple criterion that completely characterizes all reversible states.PACS numbers: 03.65. Aa, 03.67.Mn Introduction.-The universality of the superposition principle is the fundamental non-classical characteristic of quantum mechanics: Given any configuration space X, its elements x label an orthogonal basis |x of a Hilbert space, and we have all superpositions x ψ x |x as the possible states of the system. In particular, we could choose a completely different orthonormal basis as an equally valid computational basis, in which to express the superpositions. However, often a basis is distinguished, be it the eigenbasis of an observable or of the system's Hamiltonian, so that conservation laws or even superselection rules apply. In such a case, the eigenstates |x are distinguished as "simple" and superpositions are "complex". Indeed, in the presence of conservation laws, structured superpositions of eigenstates can serve as so-called "reference frames", which are resources to overcome the conservation laws [1][2][3]. Based on this idea,Åberg [4] and more recently Baumgratz et al. [5] have proposed to consider any non-trivial superposition as a resource, and to create a theory in which computational basis states and their probabilistic mixtures are for free (or worthless), and operations preserving these "incoherent" states are free as well. This suggests that coherence theory can be regarded as a resource theory.Let us briefly recall the general structure of a quantum resource theory (QRT) and basic questions that be asked in a QRT through entanglement theory (ET), which is a well-known QRT. For our purposes, a QRT has three ingredients: (1) free states (separable state in ET), (2) resource states (entangled state in ET), (3) the restricted or free operations (LOCC in ET). A necessary requirement for a consistent QRT is that no resource state can be created from any free state under any free operation. The QRT is then the study of interconversion between resource states u...

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“…If, in the above expression, the ancilla is in a Gibbs state of temperature T and the unitary V commutes with the total Hamiltonian H T = H S ⊗ ½ A + ½ S ⊗ H A of the target-ancilla system, the resulting map is called a thermal channel. These will be the free operations in our theory, while any non-thermal map Ω will be considered as a resource.In this scenario, we define quantum work W as the process of exciting a two-level system with Hamiltonian H = W |1 1| from its ground state |0 to the excited state |1 [6]. Different authors have explored how much work one can extract from a non-thermal quantum state [6][7][8][9][10][11][12].…”

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confidence: 99%

Nonthermal Quantum Channels as a Thermodynamical Resource

Navascués

García-Pintos

2015

Phys. Rev. Lett.

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Quantum thermodynamics can be understood as a resource theory, whereby thermal states are free and the only allowed operations are unitary transformations commuting with the total Hamiltonian of the system. Previous literature on the subject has just focused on transformations between different state resources, overlooking the fact that quantum operations which do not commute with the total energy also constitute a potentially valuable resource. In this Letter, given a number of non-thermal quantum channels, we study the problem of how to integrate them in a thermal engine so as to distill a maximum amount of work. We find that, in the limit of asymptotically many uses of each channel, the distillable work is an additive function of the considered channels, computable for both finite dimensional quantum operations and bosonic channels. We apply our results to bound the amount of distillable work due to the natural non-thermal processes postulated in the Ghirardi-Rimini-Weber (GRW) collapse model. We find that, although GRW theory predicts the possibility to extract work from the vacuum at no cost, the power which a collapse engine could in principle generate is extremely low.The field of quantum thermodynamics has seen a surge in interest in the past years, with increasing attention towards testing the validity of the rules of classical thermodynamics in the quantum regime. A major topic within thermodynamics is that of extracting work out of a given system and the optimal way to perform this. One way this has been approached in the quantum case was by considering it from the perspective of a resource theory.The idea of a resource theory of thermodynamics is to assume one has unlimited access to thermal baths (i.e. Gibbs states of a fixed temperature T ), the freedom to apply any energy conserving unitary on system plus the bath (any unitary V that commutes with the total Hamiltonian), and the possibility of discarding part of the system or bath (i.e. apply partial traces). These rules are imported from classical thermodynamics, where one assumes access to infinite baths of constant temperature and any evolution where energy is conserved.As a matter of fact, resource theories have been very useful in different topics within quantum information theory [1][2][3][4]. The idea is similar to above: considering free access to certain operations and/or states, any state and/or operation that is not in the above set can in principle be used as a resource.This work complements previous research in quantum thermodynamics by accommodating the possibility of considering non-thermal maps, or channels, as a resource.Physical operations are represented by quantum channels, i.e., completely positive trace preserving maps Ω : B(H) → B(H ′ ) acting on a state space B(H). For simplicity, we will assume that the input and output spaces (and, as we will see later, Hamiltonians) of each channel are the same, although the results can be easily generalized.Unitary evolution is a particular instance of a quantum channel, determined by t...

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Fundamental limitations for quantum and nanoscale thermodynamics

Cited by 736 publications

References 47 publications

Implications of Coupling in Quantum Thermodynamic Machines

Implications of Coupling in Quantum Thermodynamic Machines

Operational Resource Theory of Coherence

Nonthermal Quantum Channels as a Thermodynamical Resource

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