Quantifying Dynamical Coherence with Dynamical Entanglement

Theurer, Thomas; Satyajit, Saipriya; Plenio, Martin B.

doi:10.1103/physrevlett.125.130401

Cited by 34 publications

(28 citation statements)

References 85 publications

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“…Related to this, the resource theory of coherence for quantum channels has been investigated [34], [35], [36], [37], too. Although notions such as that of relative entropy of entanglement of a quantum channel had been previously utilized in the study of quantum communication [38], this renewed interest in channel resource theories prompted a systematic study of dynamical properties of entanglement [39], resulting in sophisticated theories of dynamic entanglement developed for free resources such as LOCC channels [40], [41] and PPT channels [42], [43], [44], [40], [41].…”

Section: Introductionmentioning

confidence: 99%

One-Shot Manipulation of Entanglement for Quantum Channels

Kim

Lee

Lami

et al. 2021

IEEE Trans. Inform. Theory

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We show that the dynamic resource theory of quantum entanglement can be formulated using the superchannel theory. In this formulation, we identify the separable channels and the class of free superchannels that preserve channel separability as free resources, and choose the swap channels as dynamic entanglement golden units. Our first result is that the one-shot dynamic entanglement cost of a bipartite quantum channel under the free superchannels is bounded by the standard log-robustness of channels. The oneshot distillable dynamic entanglement of a bipartite quantum channel under the free superchannels is found to be bounded by a resource monotone that we construct from the hypothesistesting relative entropy of channels with minimization over separable channels. We also address the one-shot catalytic dynamic entanglement cost of a bipartite quantum channel under a larger class of free superchannels that could generate the dynamic entanglement which is asymptotically negligible; it is bounded by the generalized log-robustness of channels.

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Section: Introductionmentioning

confidence: 99%

One-Shot Manipulation of Entanglement for Quantum Channels

Kim

Lee

Lami

et al. 2021

IEEE Trans. Inform. Theory

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“…Dynamical systems carry higher dimensional information, which implies that quantum features in quantum chan- * ycs@dlut.edu.cn nels can also be taken regard as resources. Therefore, the dynamical QRT [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63]could also been established similar to but quite different from the QRT in static systems. Ref.…”

Section: Introductionmentioning

confidence: 92%

“…[54], and a quantitative connection between the coherence and entanglement on the level of operations are introduced in Ref. [55]. All the relevant researches are based on the resource non-generating (RNG) [56] or its upgraded completely resource non-generating (CRNG) frameworks, namely, the free operations are defined as those that cannot generate any resource from free resource (even assisted by an ancillary reference).…”

Section: Introductionmentioning

confidence: 99%

“…To establish the QRT, we also consider the superoperations in the sense of quantum computing pre-requests analogous to similar to Ref. [55]. The alternative candidates have been presented to quantify dynamical resources under the RNI framework and the quantification of the total quantum coherence has been deeply studied as one demonstration.…”

Section: Introductionmentioning

confidence: 99%

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Quantifying Dynamical Total Coherence in a Resource Non-increasing Framework

Yang¹,

Yu²

2021

Preprint

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We quantify the dynamical quantum resource in the resource non-increasing (RNI) framework, namely, the free dynamical resource is defined by the channels that cannot increase the static "resourcefulness" of any input state. We present two kinds of approaches to quantifying the dynamical resource, the distance measures and the maximal increasing static resource (MISR). As a demonstration, we quantify the dynamical total coherence with our presented measures. It is shown that the distance based measures have good operational interpretation through quantum processing tasks and can be numerically calculated by semidefinite programming (SDP) and the measures based on MISR could lead to the analytical solution. As an application, we consider the dynamical total coherence of the qubit amplitude damping channel. Both the analytical measure based on the static l 2 norm and the numerical illustrations based on the SDP are given.

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“…Universal transformations of quantum states have played an essential role in the fundamental understanding of quantum information theory and its applications [1]. Recently, higher-order quantum transformations, namely, universal transformations of quantum operations given as black boxes, have been studied in the contexts of processing unitary operations , non-Markovian quantum process [24][25][26][27][28][29][30][31][32][33][34][35][36], and dynamical resource theory [37][38][39][40][41][42][43][44][45][46][47][48]. They can also be interpreted as quantum functional programming [49,50].…”

Section: Introductionmentioning

confidence: 99%