Generalized coherence concurrence and path distinguishability

Chin, Seungbeom

doi:10.1088/1751-8121/aa908d

Cited by 17 publications

(35 citation statements)

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“…The other necessary condition for stochastic transformations on qubits was that the initial state is not incoherent. For higher dimensions, this can be generalized by the statement that the coherence rank or number [3, [35][36][37] can only decrease under a stochastic IO (and therefore SIO) transformation, which we show now for completeness.…”

Section: Theoremmentioning

confidence: 84%

Quantum coherence and state conversion: theory and experiment

Theurer

Xiang

et al. 2020

npj Quantum Inf

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The resource theory of coherence [1-6] studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and inter-conversion [3, 7-10] of the resource. Here we solve this question completely for qubit states by determining the optimal probabilities for mixed state conversions via stochastic incoherent operations. Extending the discussion to distributed scenarios, we introduce and address the task of assisted incoherent state conversion where the process is enhanced by making use of correlations with a second party. Building on these results, we demonstrate experimentally that the optimal state conversion probabilities can be achieved in a linear optics set-up. This paves the way towards real world applications of coherence transformations in current quantum technologies.Practical constraints on our ability to manipulate physical systems restrict the control we can exert on them. It is, for example, exceedingly difficult to exchange quantum systems undisturbed over long distances [11]. When manipulating spatially separated subsystems, effectively, this limits us to Local Operations and Classical Communication (LOCC). Under these operations, it is only possible to prepare certain states, i.e. separable ones. The states which cannot be produced under LOCC are called entangled and elevated to resources: Consuming them allows to implement operations such as quantum state teleportation [12] to achieve perfect quantum state transfer which would not be possible with LOCC alone. This has important consequences, e.g. in quantum communication and other quantum technologies, but also for our understanding of the view of the fundamental laws of nature [11,[13][14][15].Entanglement is explored within the framework of quantum resource theories, which can also be used to investigate other non-classical features of quantum mechanics in a systematic way. A concept underlying many * These authors contributed equally to this work. †

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Section: Theoremmentioning

confidence: 84%

Quantum coherence and state conversion: theory and experiment

Theurer

Xiang

et al. 2020

npj Quantum Inf

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“…We acknowledge financial support from the European Research Council Note. During completion of this work, an independent investigation of k-coherence and its relation to bipartite entanglement of Schmidt rank k was presented by SChin [58,68]. Bartosz Regula https://orcid.org/0000-0001-7225-071X Marco Piani https:/ /orcid.org/0000-0002-4698-9497 Gerardo Adesso https:/ /orcid.org/0000-0001-7136-3755…”

Section: Acknowledgmentsmentioning

confidence: 99%

Converting multilevel nonclassicality into genuine multipartite entanglement

et al. 2018

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Characterizing genuine quantum resources and determining operational rules for their manipulation are crucial steps to appraise possibilities and limitations of quantum technologies. Two such key resources are nonclassicality, manifested as quantum superposition between reference states of a single system, and entanglement, capturing quantum correlations among two or more subsystems.Here we present a general formalism for the conversion of nonclassicality into multipartite entanglement, showing that a faithful reversible transformation between the two resources is always possible within a precise resource-theoretic framework. Specializing to quantum coherence between the levels of a quantum system as an instance of nonclassicality, we introduce explicit protocols for such a mapping. We further show that the conversion relates multilevel coherence and multipartite entanglement not only qualitatively, but also quantitatively, restricting the amount of entanglement achievable in the process and in particular yielding an equality between the two resources when quantified by fidelity-based geometric measures.

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“…After finishing the manuscript, we find that a coherence measure similar to r ( ) C G is also put forward in [42], dubbed generalized coherence concurrence, by analog to the generalized concurrence for entanglement [34]. However, the analytical solutions and its relationship with polynomial coherence measure are not presented in [42]. , there is at least one zero-coherence state in the superposition space of them.…”

Section: Discussionmentioning

confidence: 99%

Polynomial measure of coherence

et al. 2017

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Coherence, the superposition of orthogonal quantum states, is indispensable in various quantum processes. Inspired by the polynomial invariant for classifying and quantifying entanglement, we first define polynomial coherence measure and systematically investigate its properties. Except for the qubit case, we show that there is no polynomial coherence measure satisfying the criterion that its value takes zero if and only if for incoherent states. Then, we release this strict criterion and obtain a necessary condition for polynomial coherence measure. Furthermore, we give a typical example of polynomial coherence measure for pure states and extend it to mixed states via a convex-roof construction. Analytical formula of our convex-roof polynomial coherence measure is obtained for symmetric states which are invariant under arbitrary basis permutation. Consequently, for general mixed states, we give a lower bound of our coherence measure.

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Generalized coherence concurrence and path distinguishability

Cited by 17 publications

References 50 publications

Quantum coherence and state conversion: theory and experiment

Quantum coherence and state conversion: theory and experiment

Converting multilevel nonclassicality into genuine multipartite entanglement

Polynomial measure of coherence

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