Coherence-generating power of quantum unitary maps and beyond

Zanardi, Paolo; Styliaris, Georgios; Venuti, Lorenzo Campos

doi:10.1103/physreva.95.052306

Cited by 58 publications

(99 citation statements)

References 32 publications

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“…Now we construct a channel resource theory of coherence to characterize the coherence generating power. This has been partially done in several works [39,40,60,[68][69][70][71], whereas they did not treat channel coherence as an operational resource. Following our resource framework, we define free channels as resource non-generating 5 channels, i.e., MIO.…”

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confidence: 99%

“…The resource generating power R g (N ) characterizes the maximal output resource that can be generated from free input states, while the resource boosting power R b (N ) characterizes the maximal boosted resource between the output and input states. Similar concepts have been studied in several specific resource theories, including coherence [39,40,[68][69][70][71], thermodynamics [72], non-Gaussianity [54], and others [25]. For a general resource theory, the resource generating/boosting power has been initially proposed by Li et al [42] with an optimization only over states of system A.…”

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Operational resource theory of quantum channels

Liu

Yuan

2020

Phys. Rev. Research

142

104

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Quantum resource theories have been widely studied to systematically characterize the nonclassicality of quantum systems. Most resource theories focus on quantum states and study their interconversions. Although quantum channels are generally used as the tool for state manipulation, such a manipulation capability can be naturally regarded as a generalized quantum resource, leading to an open research direction in the resource theories of quantum channels. Various resourcetheoretic properties of channels have been investigated, however, without treating channels themselves as operational resources that can also be manipulated and converted. In this Letter, we address this problem by first proposing a general resource framework for quantum channels and introducing resource monotones based on general distance quantifiers of channels. We study the interplay between channel and state resource theories by relating resource monotones of a quantum channel to its manipulation power of the state resource. Regarding channels as operational resources, we introduce asymptotic channel distillation and dilution, the most important tasks in an operational resource theory, and show how to bound the conversion rates with channel resource monotones. Finally, we apply our results to quantum coherence as an example and introduce the coherence of channels, which characterizes the coherence generation ability of channels. We consider asymptotic channel distillation and dilution with maximally incoherent operations and find the theory asymptotically irreversible, in contrast to the asymptotic reversibility of the coherence of states.Quantum resource theories have been developed as systematic frameworks for the characterization, quantification, and operational interpretation for various quantum effects, including coherence [1][2][3], discord [4][5][6], entanglement [7][8][9], thermodynamics [10,11], magic in stabilizer computation [12][13][14], etc. The advances in quantum resource theories not only lead to a deeper understanding of the underlying physics, but also provide new insights and mathematical tools for various quantum information processing tasks that exploit the resources, such as quantum key distribution [15,16], quantum random number generation [17][18][19], and quantum computing [13,[20][21][22][23][24]. We refer to Ref.[25] for a recent review.A quantum resource theory usually starts by defining three important components: free states, free operations and resource measures. Free states are those quantum states that do not possess any resource. Free operations are quantum operations that cannot generate resource from free states, and their precise definitions are guided by physical motivations. Resource measures are functionals that map quantum states to real numbers, which cannot be increased under free operations. In an operational resource theory, one of the most important tasks is to study state conversion under free operations. Resource distillation and dilution are optimal schemes that convert between a given state an...

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confidence: 99%

Operational resource theory of quantum channels

Liu

Yuan

2020

Phys. Rev. Research

142

104

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“…(i) We follow a procedure similar to the one in Ref. [17]. We make use of the Hilbert-Schmidt inner product…”

Section: Discussionmentioning

confidence: 99%

“…Finally, we comment on our findings from the typicality point of view. In [17] it was shown that, if the intertwiner is chosen at random from the unitary group V ∈ U (d) according to the Haar measure, then C…”

Section: Coherence-generating Power and Many-body Localizationmentioning

confidence: 99%

Quantum coherence and the localization transition

et al. 2019

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A dynamical signature of localization in quantum systems is the absence of transport which is governed by the amount of coherence that configuration space states possess with respect to the Hamiltonian eigenbasis. To make this observation precise, we study the localization transition via quantum coherence measures arising from the resource theory of coherence. We show that the escape probability, which is known to show distinct behavior in the ergodic and localized phases, arises naturally as the average of a coherence measure. Moreover, using the theory of majorization, we argue that broad families of coherence measures can detect the uniformity of the transition matrix (between the Hamiltonian and configuration bases) and hence act as probes to localization. We provide supporting numerical evidence for Anderson and Many-Body Localization (MBL).For infinitesimal perturbations of the Hamiltonian, the differential coherence defines an associated Riemannian metric. We show that the latter is exactly given by the dynamical conductivity, a quantity of experimental relevance which is known to have a distinctively different behavior in the ergodic and in the many-body localized phases. Our results suggest that the quantum informationtheoretic notion of coherence and its associated geometrical structures can provide useful insights into the elusive nature of the ergodic-MBL transition.arXiv:1906.09242v2 [quant-ph]

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“…Two particular measures of coherence that we will focus on in this work are the relative entropy of coherence, 6 Within this work we will use S(·) to denote both the von Neumann entropy of a density matrix, as well as the Shannon entropy of a probability distribution. 7 We note that from the resource-theoretic perspective [2] 2  does not strictly satisfy all desirable requirements for a coherence measure. While it is true that under incoherent CPTP maps the 2-norm of coherence is non-increasing, it can increase on average under selective measurements.…”

Section: Introductionmentioning

confidence: 99%

Coherifying quantum channels

et al. 2018

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Is it always possible to explain random stochastic transitions between states of a finite-dimensional system as arising from the deterministic quantum evolution of the system? If not, then what is the minimal amount of randomness required by quantum theory to explain a given stochastic process? Here, we address this problem by studying possible coherifications of a quantum channel Φ, i.e., we look for channels  F that induce the same classical transitions T, but are 'more coherent'. To quantify the coherence of a channel Φ we measure the coherence of the corresponding Jamiołkowski state J Φ . We show that the classical transition matrix T can be coherified to reversible unitary dynamics if and only if T is unistochastic. Otherwise the Jamiołkowski state J  F of the optimally coherified channel is mixed, and the dynamics must necessarily be irreversible. To assess the extent to which an optimal process  F is indeterministic we find explicit bounds on the entropy and purity of J  F , and relate the latter to the unitarity of  F . We also find optimal coherifications for several classes of channels, including all onequbit channels. Finally, we provide a non-optimal coherification procedure that works for an arbitrary channel Φ and reduces its rank (the minimal number of required Kraus operators) from d 2 to d.

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Coherence-generating power of quantum unitary maps and beyond

Cited by 58 publications

References 32 publications

Operational resource theory of quantum channels

Operational resource theory of quantum channels

Quantum coherence and the localization transition

Coherifying quantum channels

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