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Janzing, Dominik; Wocjan, Paweł; Zeier, Robert; Geiß, Rubino; Beth, Thomas

doi:10.1023/a:1026422630734

Cited by 249 publications

(315 citation statements)

References 11 publications

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“…These set of monotones are closely related to monotones under thermal operations. In the resource theory of quantum theormodynamics, the free (or "thermal") operations take the form ρ A → Tr B [U (ρ A ⊗ γ B is the Gibbs state at temperature T [38,39]. It was also observed in [40] that Thermal operations are time-translation symmetric, and in particular belongs to DIO when the incoherent basis is taken to be the energy eigenstates, assuming no-degeneracy in the energy eigenstates.…”

Section: B Monotonesmentioning

confidence: 99%

Comparison of incoherent operations and measures of coherence

2016

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Section: B Monotonesmentioning

confidence: 99%

Comparison of incoherent operations and measures of coherence

2016

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“…In particular, if τ = e −βH /Tr[e −βH ] is the Gibbs state of a system with Hamiltonian H, then the condition (4) is known to hold for thermal operations [16,17,51]. For a non-degenerate Hamitonian H thermal operations cannot create coherence in the eigenbasis of H, and conditions for state transformations under these operations and the role of coherence therein have been extensively studied in Refs.…”

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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“…The restricted class of operations which defines our resource theory includes only those that can be achieved through energy-conserving unitaries and the preparation of any ancillary system in a thermal state at temperature T, as first studied by Janzing et al [6] in the context of Landauer's principle. Here, the ancillary systems can have an arbitrary Hilbert space and an arbitrary Hamiltonian, and may be described as having access to a single heat bath at temperature T. States that are not in thermal equilibrium at temperature T are the resource in this approach.…”

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confidence: 99%

“…Observe that Eð T Þ ¼ T , where T is the Gibbs state at temperature T associated with H. Any other state Þ T is a resource state. While, here, we consider the case that input and output systems and their Hamiltonians are identical, this framework can be easily extended to the more general case, as done by Janzing et al [6].…”

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Resource Theory of Quantum States Out of Thermal Equilibrium

et al. 2013

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The ideas of thermodynamics have proved fruitful in the setting of quantum information theory, in particular the notion that when the allowed transformations of a system are restricted, certain states of the system become useful resources with which one can prepare previously inaccessible states. The theory of entanglement is perhaps the best-known and most well-understood resource theory in this sense. Here, we return to the basic questions of thermodynamics using the formalism of resource theories developed in quantum information theory and show that the free energy of thermodynamics emerges naturally from the resource theory of energy-preserving transformations. Specifically, the free energy quantifies the amount of useful work which can be extracted from asymptotically many copies of a quantum system when using only reversible energy-preserving transformations and a thermal bath at fixed temperature. The free energy also quantifies the rate at which resource states can be reversibly interconverted asymptotically, provided that a sublinear amount of coherent superposition over energy levels is available, a situation analogous to the sublinear amount of classical communication required for entanglement dilution. Quantum resource theories are specified by a restriction on the quantum operations (state preparations, measurements, and transformations) that can be implemented by one or more parties. This singles out a set of states which can be prepared under the restricted operations. If the parties facing the restriction acquire a quantum state outside the restricted set of states, then they can use this state to implement measurements and transformations that are outside the class of allowed operations, consuming the state in the process. Thus, such states are useful resources.A few prominent examples serve to illustrate the idea: if two or more parties are restricted to communicating classically and implementing local quantum operations, then entangled states become a resource [1]; if a party is restricted to quantum operations that have a particular symmetry, then states that break this symmetry become a resource [2][3][4]; if a party is restricted to preparing states that are completely mixed and performing unitary operations, then any state that is not completely mixed, i.e., any state that has some purity, becomes a resource [5].In this Letter, we develop the quantum resource theory of states that are T athermal, i.e., not thermal at temperature T. This provides a useful new formulation of equilibrium and nonequilibrium thermodynamics for finite-dimensional quantum systems, and allows us to apply new mathematical tools to the subject. The restricted class of operations which defines our resource theory includes only those that can be achieved through energy-conserving unitaries and the preparation of any ancillary system in a thermal state at temperature T, as first studied by Janzing et al. [6] in the context of Landauer's principle. Here, the ancillary systems can have an arbitrary Hilbert space and an a...

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Untitled

Cited by 249 publications

References 11 publications

Comparison of incoherent operations and measures of coherence

Comparison of incoherent operations and measures of coherence

Structure of the Resource Theory of Quantum Coherence

Resource Theory of Quantum States Out of Thermal Equilibrium

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