Maximally coherent states

Bai, Zhaofang; Du, Shuanping

doi:10.48550/arxiv.1503.07103

Cited by 7 publications

(9 citation statements)

References 40 publications

(50 reference statements)

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“…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]. Several works also study maximally coherent states [58,59], the role of coherence in spin models [60,61], cohering power of quantum channels [62][63][64], and relations between coherence and other measures of quantumness [65][66][67][68][69][70][71]. Coherence also plays an important role in quantum thermodynamics [72][73][74][75][76][77][78][79][80][81][82], and its investigation in biological systems is an important step towards finding quantum phenomena in living objects [83][84]…”

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confidence: 99%

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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confidence: 99%

Entanglement and Coherence in Quantum State Merging

et al. 2016

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“…Firstly, all the unitary incoherent operations are CVPOs of an arbitrary valid coherence measure according to Lemma From Theorem 1 and Theorem 2, we can see that though the coherence measure satisfying the original four criteria of Ref [13] would count any MCS as a MCVS, many of them also give other states the maximal coherence values. A typical example of such inefficient but valid coherence measure is C trivial which as mentioned gives zero to all incoherent states but one to all coherent states, similar situation happens to the valid measures C f [15] which are continuous but still inefficient. Additionally, Theorem 1 indicates that there could be differences among the sets of MCVSs of different measures.…”

Section: Coherence-value Preservingmentioning

confidence: 74%

“…Another example is a continuous coherence measure C f presented in Ref. [15] for d = 4. And we can follow the same way to construct a family of C f for arbitrary dimension d. Also, S C MCVS could be different from one another for different C.…”

Section: Maximal Coherence-value Statesmentioning

confidence: 99%

“…[13]. Following this seminal work, fruitful researches have been done, some of which are mainly devoted to study the properties of specific coherence measures [14][15][16][17][18][19] or explore new possible coherence measures [20][21][22]. There are also many considerations about the manipulation of coherence [19,[21][22][23][24], and the connections of coherence with quantum entanglement, quantum discord, quantum deficit, and many-body systems critical phenomena [22,23,25,26].…”

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Maximally coherent states and coherence-preserving operations

2016

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We investigate the maximally coherent states to provide a refinement in quantifying coherence and give a measure-independent definition of the coherence-preserving operations. A maximally coherent state can be considered as the resource to create arbitrary quantum states of the same dimension by merely incoherent operations. We propose that only the maximally coherent states should achieve the maximal value for a coherence measure and use this condition as an additional criterion for coherence measures to obtain a refinement in quantifying coherence which excludes the invalid and inefficient coherence measures. Under this new criterion, we then give a measure-independent definition of the coherence-preserving operations, which play a similar role in quantifying coherence as that played by the local unitary operations in the scenario of studying entanglement.

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“…For example, a two-qubit quantum state is able to teleport qubit iff its entanglement fraction is greater than 1 2 . In this paper, we have developed the idea of coherence fraction of a quantum state in the theory of quantum coherence that quantifies the maximum overlap of a quantum state with a maximally coherent state [24,37]. Considering the task of quantifying coherence fraction of a state we study its properties and explain its resource theoretic connections.…”

Section: Introductionmentioning

confidence: 99%

Coherence fraction

Karmakar

Sen

Chattopadhyay

et al. 2019

Quantum Inf Process

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The concept of entanglement fraction is generalized to define coherence fraction of a quantum state. Precisely, it quantifies the proximity of a quantum state to maximally coherent state and it can be used as a measure of coherence. Coherence fraction has a connection with l1-norm coherence and provides the criteria of coherence distillability. Optimal coherence fraction corresponding to a channel, defined from this new idea of coherence fraction, obeys a complementary relation with its decohering power. The connection between coherence fraction and l1-norm coherence turns to hold for bipartite pure states and X states too. The bipartite generalization shows that the local coherence fractions of a quantum state are not free and they are bounded by linear function of its global coherence fraction. Dynamics of optimal coherence fraction is also studied for single sided and both sided application of channels. Numerical results are provided in exploring properties of optimal coherence fraction.

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Maximally coherent states

Cited by 7 publications

References 40 publications

Entanglement and Coherence in Quantum State Merging

Entanglement and Coherence in Quantum State Merging

Maximally coherent states and coherence-preserving operations

Coherence fraction

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