Cohering power of quantum operations

Bu, Kaifeng; Kumar, Asutosh; Zhang, Lin; Wu, Junde

doi:10.1016/j.physleta.2017.03.022

Cited by 84 publications

(70 citation statements)

References 41 publications

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“…The cohering power of a unitary operation U corresponds to the maximal coherence that can be obtained from an incoherent state by U . It can be quantified by the cohering power of a quantum channel [37],…”

Section: Details On the Experimental CMmentioning

confidence: 99%

Experimentally reducing the quantum measurement back action in work distributions by a collective measurement

Yuan

Xiang

et al. 2019

Sci. Adv.

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In quantum thermodynamics, the standard approach to estimating work fluctuations in unitary processes is based on two projective measurements, one performed at the beginning of the process and one at the end. The first measurement destroys any initial coherence in the energy basis, thus preventing later interference effects. To decrease this back action, a scheme based on collective measurements has been proposed by Perarnau-Llobetet al. Here, we report its experimental implementation in an optical system. The experiment consists of a deterministic collective measurement on two identically prepared qubit states, encoded in the polarization and path degree of a single photon. The standard two-projective measurement approach is also experimentally realized for comparison. Our results show the potential of collective schemes to decrease the back action of projective measurements, and capture subtle effects arising from quantum coherence.

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Section: Details On the Experimental CMmentioning

confidence: 99%

Experimentally reducing the quantum measurement back action in work distributions by a collective measurement

Yuan

Xiang

et al. 2019

Sci. Adv.

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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.…”

mentioning

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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confidence: 99%

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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“…investigated by García Díaz et al [23] and Bu et al [24]. Let us also introduce the same maximization restricted to pure input states,…”

Section: Theorem 1 For a General Cptp Mapmentioning

confidence: 99%

Resource theory of coherence: Beyond states

et al. 2017

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We generalize the recently proposed resource theory of coherence (or superposition) [Baumgratz, Cramer & Plenio, Phys. Rev. Lett. 113:140401; Winter & Yang, Phys. Rev. Lett. 116:120404] to the setting where not only the free ("incoherent") resources, but also the objects manipulated, are quantum operations rather than states.In particular, we discuss an information theoretic notion of coherence capacity of a quantum channel, and prove a single-letter formula for it in the case of unitaries. Then we move to the coherence cost of simulating a channel, and prove achievability results for unitaries and general channels acting on a d-dimensional system; we show that a maximally coherent state of rank d is always sufficient as a resource if incoherent operations are allowed, and rank d 2 for "strictly incoherent" operations. We also show lower bounds on the simulation cost of channels that allow us to conclude that there exists bound coherence in operations, i.e. maps with non-zero cost of implementing them but zero coherence capacity; this is in contrast to states, which do not exhibit bound coherence.

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Cohering power of quantum operations

Cited by 84 publications

References 41 publications

Experimentally reducing the quantum measurement back action in work distributions by a collective measurement

Experimentally reducing the quantum measurement back action in work distributions by a collective measurement

Operational resource theory of quantum channels

Resource theory of coherence: Beyond states

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