Gibbs-preserving maps outperform thermal operations in the quantum regime

Faist, Philippe; Oppenheim, Jonathan; Renner, Renato

doi:10.1088/1367-2630/17/4/043003

Cited by 108 publications

(138 citation statements)

References 31 publications

(31 reference statements)

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“…The most general quantum operations that fulfill Eq. (4) are known as Gibbs-preserving operations, and it has been shown that such operations can create coherence [55]. Here, we contribute to this discussion by introducing the set of Gibbs-preserving SIO, and giving a full solution for the mixed-state conversion problem on a single qubit.…”

Section: Summary Of Resultsmentioning

confidence: 99%

Structure of the Resource Theory of Quantum Coherence

et al. 2017

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Quantum coherence is an essential feature of quantum mechanics which is responsible for the departure between classical and quantum world. The recently established resource theory of quantum coherence studies possible quantum technological applications of quantum coherence, and limitations which arise if one is lacking the ability to establish superpositions. An important open problem in this context is a simple characterization for incoherent operations, constituted by all possible transformations allowed within the resource theory of coherence. In this work, we contribute to such a characterization by proving several upper bounds on the maximum number of incoherent Kraus operators in a general incoherent operation. For a single qubit, we show that the number of incoherent Kraus operators is not more than 5, and it remains an open question if this number can be reduced to 4. The presented results are also relevant for quantum thermodynamics, as we demonstrate by introducing the class of Gibbs-preserving strictly incoherent operations, and solving the corresponding mixedstate conversion problem for a single qubit.Quantum resource theories [1, 2] provide a strong framework for studying fundamental properties of quantum systems and their applications for quantum technology. The basis of any quantum resource theory is the definition of free states and free operations. Free states are quantum states which can be prepared at no additional cost, while free operations capture those physical transformations which can be implemented without consumption of resources. Having identified these two main features, one can study the basic properties of the corresponding theory, such as possibility of state conversion, resource distillation, and quantification. An important example is the resource theory of entanglement, where free states are separable states, and free operations are local operations and classical communication [3,4].In the resource theory of quantum coherence [5-9], free states are identified as incoherent statesi.e., states which are diagonal in a fixed specified basis {|i }. The choice of this basis depends on the particular problem under study, and in many relevant scenarios such a basis is naturally singled out by the unavoidable decoherence [10]. The definition of free operations within the theory of coherence is not unique, and several approaches have been discussed in the literature, based on different physical (or mathematical) considerations [8]. Two important frameworks are known as incoherent [6] and strictly incoherent operations [7,11], which will be denoted by IO and SIO, respectively. The characterizing feature of IO is the fact that they admit an incoherent Kraus decomposition, i.e., they can be written as [6] where each of the Kraus operators K j cannot create coherence individually, K j |m ∼ |n for suitable integers n and m. This approach is motivated by the fact that any quantum operation can be interpreted as a selective measurement in which outcome j occurs with probability p j = Tr[K j ρK ...

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Section: Summary Of Resultsmentioning

confidence: 99%

Structure of the Resource Theory of Quantum Coherence

et al. 2017

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“…Another theorem used in [97] and other studies [98] of quantum thermodynamics is the channelstate duality or Choi-Jamio lkowski isomorphism. It says that there is a state ρ Φ isomorphic to every CPTP map Φ, given by…”

Section: Three Theorems Involving Cptp Mapsmentioning

confidence: 99%

“…(34). We note that these theorems are often implicitly assumed while discussing quantum thermodynamics from the standpoint of CPTP maps, see [98,100,101] for examples.…”

Section: Three Theorems Involving Cptp Mapsmentioning

confidence: 99%

Quantum thermodynamics

Vinjanampathy¹,

Anders²

2016

Contemporary Physics

869

806

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Quantum thermodynamics is an emerging research field aiming to extend standard thermodynamics and non-equilibrium statistical physics to ensembles of sizes well below the thermodynamic limit, in non-equilibrium situations, and with the full inclusion of quantum effects. Fueled by experimental advances and the potential of future nanoscale applications this research effort is pursued by scientists with different backgrounds, including statistical physics, many-body theory, mesoscopic physics and quantum information theory, who bring various tools and methods to the field. A multitude of theoretical questions are being addressed ranging from issues of thermalisation of quantum systems and various definitions of "work", to the efficiency and power of quantum engines. This overview provides a perspective on a selection of these current trends accessible to postgraduate students and researchers alike.

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“…The literature about thermodynamic resource theories has exploded recently. Since the first draft of the present paper was released, for example, coherences [29,30] and correlations have been explored [31], connections have been drawn to fluctuation relations [32][33][34], and free operations have been generalized [23].…”

Section: B Generalized Thermodynamic Resource Theoriesmentioning

confidence: 99%

“…Nonequilibrium states' values have been quantified with a family of equivalent resource theories, each associated with an inverse temperature β of the bath [18][19][20][21][22][23]. We call these resource theories Helmholtz theories, Many experiments involve baths other than heat baths, involve interactions other heat exchanges, and are characterized by free energies other than the Helmholtz free energy.…”

Section: Introductionmentioning

confidence: 99%

Beyond heat baths: Generalized resource theories for small-scale thermodynamics

2016

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Thermodynamics has recently been extended to small scales with resource theories that model heat exchanges. Real physical systems exchange diverse quantities: heat, particles, angular momentum, etc. We generalize thermodynamic resource theories to exchanges of observables other than heat, to baths other than heat baths, and to free energies other than the Helmholtz free energy. These generalizations are illustrated with "grand-potential" theories that model movements of heat and particles. Free operations include unitaries that conserve energy and particle number. From this conservation law and from resource-theory principles, the grand-canonical form of the free states is derived. States are shown to form a quasiorder characterized by free operations, d majorization, the hypothesis-testing entropy, and rescaled Lorenz curves. We calculate the work distillable from-and we bound the work cost of creating-a state. These work quantities can differ but converge to the grand potential in the thermodynamic limit. Extending thermodynamic resource theories beyond heat baths, we open diverse realistic systems to modeling with one-shot statistical mechanics. Prospective applications such as electrochemical batteries are hoped to bridge one-shot theory to experiments.

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Gibbs-preserving maps outperform thermal operations in the quantum regime

Cited by 108 publications

References 31 publications

Structure of the Resource Theory of Quantum Coherence

Structure of the Resource Theory of Quantum Coherence

Quantum thermodynamics

Beyond heat baths: Generalized resource theories for small-scale thermodynamics

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