Relations between Coherence and Path Information

Bagán, E.; Bergou, János A.; Cottrell, Seth; Hillery, Mark

doi:10.1103/physrevlett.116.160406

Cited by 209 publications

(204 citation statements)

References 25 publications

(35 reference statements)

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“…where the minimum is taken over all pure state decompositions p , i i y ñ { | }of the state ρ [14,47,48]. We also note that coherence of formation is equal to coherence cost under IO [14], and l 1 -norm of coherence is related to the path information in multi-path interferometer [49,50].…”

Section: Resource Theory Of Quantum Coherencementioning

confidence: 99%

Maximal coherence and the resource theory of purity

et al. 2018

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The resource theory of quantum coherence studies the off-diagonal elements of a density matrix in a distinguished basis, whereas the resource theory of purity studies all deviations from the maximally mixed state. We establish a direct connection between the two resource theories, by identifying purity as the maximal coherence which is achievable by unitary operations. The states that saturate this maximum identify a universal family of maximally coherent mixed states. These states are optimal resources under maximally incoherent operations, and thus independent of the way coherence is quantified. For all distance-based coherence quantifiers the maximal coherence can be evaluated exactly, and is shown to coincide with the corresponding distance-based purity quantifier. We further show that purity bounds the maximal amount of entanglement and discord that can be generated by unitary operations, thus demonstrating that purity is the most elementary resource for quantum information processing.

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Section: Resource Theory Of Quantum Coherencementioning

confidence: 99%

Maximal coherence and the resource theory of purity

et al. 2018

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“…18 are established in the finite-dimensional setting and thus can not be directly applied to the infinite-dimensional systems. Moreover, explicit physical (or operational) meanings of existing measures of quantum coherence are to be pursued by the community, though partial results have been obtained314041. Secondly, as indicated by Marvian et al ., distinct approaches of quantifying quantum coherence will lead to different conclusions in a diverse set of tasks.…”

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confidence: 99%

Frobenius-norm-based measures of quantum coherence and asymmetry

Yao

Dong

Xing

et al. 2016

Sci Rep

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We formulate the Frobenius-norm-based measures for quantum coherence and asymmetry respectively. In contrast to the resource theory of coherence and asymmetry, we construct a natural measure of quantum coherence inspired from optical coherence theory while the group theoretical approach is employed to quantify the asymmetry of quantum states. Besides their simple structures and explicit physical meanings, we observe that these quantities are intimately related to the purity (or linear entropy) of the corresponding quantum states. Remarkably, we demonstrate that the proposed coherence quantifier is not only a measure of mixedness, but also an intrinsic (basis-independent) quantification of quantum coherence contained in quantum states, which can also be viewed as a normalized version of Brukner-Zeilinger invariant information. In our context, the asymmetry of N-qubit quantum systems is considered under local independent and collective transformations. In- triguingly, it is illustrated that the collective effect has a significant impact on the asymmetry measure, and quantum correlation between subsystems plays a non-negligible role in this circumstance.

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“…On the other hand, the development of quantum information science provides a perspective to reassess these correlations in the formulation of resource theory [1,5]. Recently, this perspective has been used to quantify coherence [6], which gained widely attention and raised a subsequent stream of works relevant to quantum coherence [7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Intrinsic coherence in assisted sub-state discrimination

Zhang

Wang

2017

EPL

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We study intrinsic coherence in the tripartite process to unambiguously discriminate two nonorthogonal states of a qubit, entangled with another one, and assisted by an auxiliary system. The optimal success probability is found to be benefited by initial intrinsic coherence, but no extra one is required. The transformations among different contributions of intrinsic coherence are necessary in this procedure, which increase with the overlap between the states to recognize. Such state discrimination is a key step of the probabilistic teleportation protocol. Entanglement of the quantum channel decreases the coherence characterizing the reliance on an ancilla.

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Relations between Coherence and Path Information

Cited by 209 publications

References 25 publications

Maximal coherence and the resource theory of purity

Maximal coherence and the resource theory of purity

Frobenius-norm-based measures of quantum coherence and asymmetry

Intrinsic coherence in assisted sub-state discrimination

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