Coherence measures and optimal conversion for coherent states

Du, Shuanping; Bai, Zhaofang; Qi, Xiaofei

doi:10.48550/arxiv.1504.02862

Cited by 10 publications

(18 citation statements)

References 22 publications

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“…) t in the decreasing order, and extending it over the whole set of density matrices as C l (ρ) = min pj ,ρj j p j C l (ρ j ), where the minimization is to be performed over all the pure-state ensembles of ρ, i.e., ρ = j p j ρ j . In [21], we show that C l are coherence measures.…”

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Conditions for coherence transformations under incoherent operations

2015

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We build the counterpart of the celebrated Nielsen's theorem for coherence manipulation in this paper. This offers an affirmative answer to the open question: whether, given two states $\rho$ and $\sigma$, either $\rho$ can be transformed into $\sigma$ or vice versa under incoherent operations [Phys. Rev. Lett. \textbf{113}, 140401(2014)]. As a consequence, we find that there exist essentially different types of coherence. Moreover, incoherent operations can be enhanced in the presence of certain coherent states. These extra states are coherent catalysts: they allow uncertain incoherent operations to be realized, without being consumed in any way. Our main result also sheds a new light on the construction of coherence measures.Comment: arXiv admin note: text overlap with arXiv:1311.0275 by other authors. 03.65.Ud, 03.67.Ta. in Physical Review A 201

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“…Which is the greatest probability of success in such a conversion? In [21], we give the explicit formula of the greatest probability P (|ψ ICO − −− → |φ ). A parallel result in entanglement theory is optimal local conversion strategy between any two pure entangled states of a bipartite system [8].…”

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confidence: 99%

Conditions for coherence transformations under incoherent operations

2015

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“…In this work the authors defined a number of coherence measures and outlined, following the example of the theory of entanglement, various extensions that would have to be completed to explore all the aspects of the resource theory of coherence. This includes the study of the interconversion of coherent states by means of incoherent operations both, in the single copy [10][11][12] and the asymptotic regime [13] as well as the characterisation of incoherent operations [14,15]. Although not addressed from the perspective of resource theory, [16,17] have also dealt with the quantification of quantum coherence and the formal characterization of coherencedecreasing processes.…”

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A note on coherence power of N-dimensional unitary operators

García-Díaz¹,

Egloff²,

Plenio³

2015

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The coherence power of a quantum channel, that is, its ability to increase the coherence of input states, is a fundamental concept within the framework of the resource theory of coherence. In this note we discuss various possible definitions of coherence power. Then we prove that the coherence power of a unitary operator acting on a qubit, computed with respect to the l1-coherence measure, can be calculated by maximizing its coherence gain over pure incoherent states. We proceed to show that this result fails for dimensions N > 2, that is, the maximal coherence gain is found when acting on a state with non-vanishing coherence.

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“…Triggered by these recent developments, much effort is put into understanding the role of coherence as a resource in quantum theory [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Several new quantifiers of coherence have been proposed [39][40][41][42][43][44][45][46][47][48][49][50][51][52], and the dynamics of some of these quantities under noisy evolution has been investigated [53][54][55][56][57].…”

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Entanglement and Coherence in Quantum State Merging

et al. 2016

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Understanding the resource consumption in distributed scenarios is one of the main goals of quantum information theory. A prominent example for such a scenario is the task of quantum state merging where two parties aim to merge their parts of a tripartite quantum state. In standard quantum state merging, entanglement is considered as an expensive resource, while local quantum operations can be performed at no additional cost. However, recent developments show that some local operations could be more expensive than others: it is reasonable to distinguish between local incoherent operations and local operations which can create coherence. This idea leads us to the task of incoherent quantum state merging, where one of the parties has free access to local incoherent operations only. In this case the resources of the process are quantified by pairs of entanglement and coherence. Here, we develop tools for studying this process, and apply them to several relevant scenarios. While quantum state merging can lead to a gain of entanglement, our results imply that no merging procedure can gain entanglement and coherence at the same time. We also provide a general lower bound on the entanglement-coherence sum, and show that the bound is tight for all pure states. Our results also lead to an incoherent version of Schumacher compression: in this case the compression rate is equal to the von Neumann entropy of the diagonal elements of the corresponding quantum state.Introduction. While coherence has long been known in classical physics as a fundamental waves property [1], in quantum mechanics coherent superposition is elevated to a universal principle governing all processes. Indeed, the fact that all matter exhibits wave behavior was first understood by de Broglie [2], which became the basis of the now standard formulation of quantum mechanics in Schrödinger's wave equation [3]. The universality of the superposition principle, i.e. the tenet that any two valid states of a system can be superposed to form a new valid state, marks a radical departure from classical physics. It is at the heart of the many counterintuitive features of quantum theory, perhaps most famously in Schrödinger's Gedankenexperiment of the cat [4]. Quantum entanglement can be considered as a particular manifestation of coherence, and both of these nonclassical phenomena have led to extensive debates in the early days of quantum mechanics [5,6].While the study of the resource theory of entanglement has a long tradition [7,8], the resource theory of quantum coherence has been formulated only recently [9,10], although other attempts in this direction have been also presented earlier [11][12][13][14][15][16]. The basis of any resource theory are free states, these are states which can be created at no cost. In entanglement theory, these are all separable states. In coherence theory these are incoherent states [9], i.e., states which are diagonal in a fixed basis |i . The second important ingredient of any resource theory are free operations, i.e., operations...

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Coherence measures and optimal conversion for coherent states

Cited by 10 publications

References 22 publications

Conditions for coherence transformations under incoherent operations

Conditions for coherence transformations under incoherent operations

A note on coherence power of N-dimensional unitary operators

Entanglement and Coherence in Quantum State Merging

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