Low-temperature thermodynamics with quantum coherence

Narasimhachar, Varun; Gour, Gilad

doi:10.1038/ncomms8689

Cited by 289 publications

(233 citation statements)

References 37 publications

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“…The concept of wave particle duality introduced the importance of quantum coherence in physical phenomena such as low temperature thermodynamics [1], quantum thermodynamics [2][3][4], nanoscale physics [5], biological systems [6,7], and is one of the most basic aspects of quantum information science [8]. For this reason, understanding quantum coherence has a long history and is of fundamental importance to many fields.…”

mentioning

confidence: 99%

Distribution of Quantum Coherence in Multipartite Systems

Radhakrishnan

Parthasarathy²,

Jambulingam³

et al. 2016

Phys. Rev. Lett.

200

216

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The distribution of coherence in multipartite systems is examined. We use a new coherence measure with entropic nature and metric properties, based on the quantum Jensen-Shannon divergence. The metric property allows for the coherence to be decomposed into various contributions, which arise from local and intrinsic coherences. We find that there are trade-off relations between the various contributions of coherence, as a function of parameters of the quantum state. In bipartite systems the coherence resides on individual sites or distributed among the sites, which contribute in a complementary way. In more complex systems, the characteristics of the coherence can display more subtle changes with respect to the parameters of the quantum state. In the case of the XXZ Heisenberg model, the coherence changes from a monogamous to a polygamous nature. This allows us to define the shareability of coherence, leading to monogamy relations for coherence. The concept of wave particle duality introduced the importance of quantum coherence in physical phenomena such as low temperature thermodynamics [1], quantum thermodynamics [2-4], nanoscale physics [5], biological systems [6,7], and is one of the most basic aspects of quantum information science [8]. For this reason, understanding quantum coherence has a long history and is of fundamental importance to many fields. In quantum optics [9,10], the approach has been typically to examine quantities such as phase space distributions and higher order correlation functions [11]. While this method distinguishes between quantum and classical coherence, it does not quantify coherence in a rigorous sense. More recently, a procedure to quantify coherence using methods of quantum information science was developed [12][13][14][15]. In the seminal work of Ref. [12], basic quantities such as incoherent states, incoherent operations, maximally coherent states were defined and the set of properties a functional should satisfy to be considered as a coherence measure were listed.One fundamental task that is desirable is to pinpoint what part of a quantum system is responsible for any coherence that is present. To understand the possibilities, let us consider a two qubit system as an example. Coherence is a basis-dependent quantity [15,16], and the reference incoherent states are chosen as |0 , |1 . We can consider then two types of states which possess coher- S is the set of separable states in a fixed basis b. ρ d is the solution of (2) and σ min S is the solution of (4).ence, (|0 − |1 )(|0 − |1 ) and |0 |0 − |1 |1 . In the former, the coherence lies on each qubit, while the latter has a kind of collective coherence, i.e. entanglement. An interesting aspect of this is that the types of coherence are complementary to each other -an increase in one type leads to a corresponding decrease in the other. In order to have maximum coherence on a particular qubit, it is optimal to create a superposition on each one, which excludes entanglement. On the other hand, for the Bell state, tracing out one o...

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mentioning

confidence: 99%

Distribution of Quantum Coherence in Multipartite Systems

Radhakrishnan

Parthasarathy²,

Jambulingam³

et al. 2016

Phys. Rev. Lett.

200

216

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confidence: 99%

“…The coherence effect of a state is usually ascribed to the offdiagonal elements of its density matrix with respect to a particular reference basis, which is determined according to the physical problem under consideration. It is an essential ingredient in quantum information processing [1], and plays a central role in emergent fields, such as quantum metrology [2][3][4], nanoscale thermodynamics [5][6][7][8][9][10][11], and quantum biology [12][13][14][15][16].It is only recent years that the quantification of coherence has become a hot topic due to the development of quantum information science, although the theory of quantum coherence is historically well developed in quantum optics [17][18][19]. A rigorous framework to quantify the coherence of quantum states in the resource theories has been recently proposed after a series of efforts [20][21][22][23][24][25][26][27][28][29].…”

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confidence: 99%

Measure-independent freezing of quantum coherence

et al. 2016

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We find that all measures of coherence are frozen for an initial state in a strictly incoherent channel if and only if the relative entropy of coherence is frozen for the state. Our finding reveals the existence of measure-independent freezing of coherence, and provides an entropy-based dynamical condition in which the coherence of an open quantum system is totally unaffected by noise.Quantum coherence is a fundamental feature of quantum mechanics, describing the capability of a quantum state to exhibit quantum interference phenomena. The coherence effect of a state is usually ascribed to the offdiagonal elements of its density matrix with respect to a particular reference basis, which is determined according to the physical problem under consideration. It is an essential ingredient in quantum information processing [1], and plays a central role in emergent fields, such as quantum metrology [2][3][4], nanoscale thermodynamics [5][6][7][8][9][10][11], and quantum biology [12][13][14][15][16].It is only recent years that the quantification of coherence has become a hot topic due to the development of quantum information science, although the theory of quantum coherence is historically well developed in quantum optics [17][18][19]. A rigorous framework to quantify the coherence of quantum states in the resource theories has been recently proposed after a series of efforts [20][21][22][23][24][25][26][27][28][29]. By following the rigorous framework comprising four postulates [20], a number of coherence measures based on various physical contexts have been put forward. The l 1 norm of coherence and the relative entropy of coherence were first suggested as two coherence measures based on distance. The coherence measures based on entanglement [30], the coherence measures based on operation [31,32], and the coherence measures based on convex-roof construction [33,34] were subsequently proposed. With coherence measures, various properties of quantum coherence, such as the relations between quantum coherence and other quantum resources [30,35,36], the quantum coherence in infinite-dimensional systems [37,38], the complementarity relations of quantum coherence [39], and the measure of macroscopic coherence [40], have been discussed. Quantum coherence is a useful physical resource, but coherence of a quantum state is often destroyed by noise. A challenge in exploiting the resource is to protect coherence from the decoherence caused by noise, as the loss of coherence may weaken the abilities of a state to perform quantum information processing tasks. Today, after having been equipped with the knowledge of coherence measures, it becomes possible to analyze under which dynamical conditions the coherence of an open system is frozen in a noisy channel. Studies on this topic have been started in Ref. [41], where the authors found that the coherence measures based on bona fide distances are frozen for some initial states of a quantum system with even number of qubits undergoing local identical bit flip channels. This finding illu...

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“…Recently, quantum resource theories have been formulated in different areas of physics such as the resource theory of athermality in thermodynamics [1][2][3][4][5][6] and the resource theory of asymmetry [7,8]. Furthermore, general structural frameworks of quantum resource theories have been proposed [9].…”

Section: Introductionmentioning

confidence: 99%

Resource theory of coherence: Beyond states

et al. 2017

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We generalize the recently proposed resource theory of coherence (or superposition) [Baumgratz, Cramer & Plenio, Phys. Rev. Lett. 113:140401; Winter & Yang, Phys. Rev. Lett. 116:120404] to the setting where not only the free ("incoherent") resources, but also the objects manipulated, are quantum operations rather than states.In particular, we discuss an information theoretic notion of coherence capacity of a quantum channel, and prove a single-letter formula for it in the case of unitaries. Then we move to the coherence cost of simulating a channel, and prove achievability results for unitaries and general channels acting on a d-dimensional system; we show that a maximally coherent state of rank d is always sufficient as a resource if incoherent operations are allowed, and rank d 2 for "strictly incoherent" operations. We also show lower bounds on the simulation cost of channels that allow us to conclude that there exists bound coherence in operations, i.e. maps with non-zero cost of implementing them but zero coherence capacity; this is in contrast to states, which do not exhibit bound coherence.

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Low-temperature thermodynamics with quantum coherence

Cited by 289 publications

References 37 publications

Distribution of Quantum Coherence in Multipartite Systems

Distribution of Quantum Coherence in Multipartite Systems

Measure-independent freezing of quantum coherence

Resource theory of coherence: Beyond states

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