One-Shot Coherence Dilution

Zhao, Qi; Liu, Yunchao; Yuan, Xiao; Chitambar, Eric; Ma, Xiongfeng

doi:10.1103/physrevlett.120.070403

Cited by 82 publications

(115 citation statements)

References 55 publications

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“…These results allow us to obtain nontrivial bounds for resource trading in specific theories by computing the modification coefficients (which can be efficiently done in many cases [9,[67][68][69][70][71][72]). For example, the golden coefficients of coherence, entanglement and purity theories induce bounds directly given by the smooth resource measures without modification, which is consistent with previous results [44,46,47,73]. As a more informative example, we briefly remark on the theory of magic states.…”

Section: Optimal Rates Of One-shot Resource Manipulationsupporting

confidence: 87%

“…j=1 |j |j where d is the dimension of the bipartite system with local dimension √ d, and g d = 1/2 for all d ∈ D = {k 2 |k ∈ Z + }. Note that the simple forms of one-shot entanglement/coherence manipulation results [44,[46][47][48] rely heavily on this specific property of the golden coefficients being constant for any valid dimension. The theory of magic states has golden statê Φ 2 = 1 2 (I +(X +Y +Z)/ √ 3) with g 2 = log(3− √ 3) ≈ 0.34 [31] for a single-qubit system, where X, Y, Z are Pauli matrices.…”

Section: Resource Currencies and Modification Coefficientsmentioning

confidence: 99%

“…Unlike the asymptotic theory (the limit of infinite i.i.d. copies) [21], only a few resource-specific results about entanglement [44,45], coherence [46][47][48], and (generalized) quantum thermodynamics [14,[49][50][51][52] (and magic states in a very recent work [53]) are known. Here we consider two important classes of free operations easily characterized by the theory of resource destroying (RD) maps [25]: the maximal free operations (e.g.…”

Section: Introductionmentioning

confidence: 99%

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One-Shot Operational Quantum Resource Theory

2019

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A fundamental approach for the characterization and quantification of all kinds of resources is to study the conversion between different resource objects under certain constraints. Here we analyze, from a resource-non-specific standpoint, the optimal efficiency of resource formation and distillation tasks with only a single copy of the given quantum state, thereby establishing a unified framework of one-shot quantum resource manipulation. We find general bounds on the optimal rates characterized by resource measures based on the smooth max/min-relative entropies and hypothesis testing relative entropy, as well as the free robustness measure, providing them with general operational meanings in terms of optimal state conversion. Our results encompass a wide class of resource theories via the theory-dependent coefficients we introduce, and the discussions are solidified by important examples, such as entanglement, coherence, superposition, magic states, asymmetry, and thermal

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Section: Optimal Rates Of One-shot Resource Manipulationsupporting

confidence: 87%

Section: Resource Currencies and Modification Coefficientsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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One-Shot Operational Quantum Resource Theory

2019

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“…In many resource theories, such as coherence and entanglement, the distillation and dilution tasks are generally characterized by resource measures based on the relative entropy and α-Rényi divergences in the asymptotic i.i.d. [26][27][28] and the general one-shot scenario [29][30][31][32][33][34][35], respectively.Existing developments in quantum resource theories are mainly centered around quantum states, while quantum channels are used as the tool for state resource manipulation. In principle, we can also regard a quantum channel as the resource object and study the resource theory of channels.…”

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confidence: 99%

Operational resource theory of quantum channels

Liu

Yuan

2020

Phys. Rev. Research

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142

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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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“…Quantum coherence has close connections with entanglement and other quantum correlations in many-body systems, and interestingly these measures can be transformed into each other [5][6][7][8]. Also, various concepts can be mapped from quantum entanglement to quantum coherence, such as coherence of assistance [9], coherence distillation and cost [10][11][12][13][14], and coherence evolutions [15]. It turns out that coherence, as an essential resource, plays an important role in various tasks including quantum algorithms [16], quantum biology [17], and quantum thermodynamics [18].In reality, it is crucial to judge whether a quantum source is capable for certain quantum information processing tasks.…”

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confidence: 99%

Quantum Coherence Witness with Untrusted Measurement Devices

et al. 2019

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Coherence is a fundamental resource in quantum information processing, which can be certified by a coherence witness. Due to the imperfection of measurement devices, a conventional coherence witness may lead to fallacious results. We show that the conventional witness could mistake an incoherent state as a state with coherence due to the inaccurate settings of measurement bases. In order to make the witness result reliable, we propose a measurement-device-independent coherence witness scheme without any assumptions on the measurement settings. We introduce the decoy-state method to significantly increase the capability of recognizing states with coherence. Furthermore, we experimentally demonstrate the scheme in a time-bin encoding optical system. Superposition explains many striking phenomena of quantum mechanics, such as the interference in the double-slit experiment of electrons and Schrödinger's cat gedanken experiment. According to Born's rule, measuring a superposed system would lead to a random projection, whose outcome cannot be predicted in principle. This feature can be employed in quantum information processing for designing quantum random number generators (QRNGs) [1,2]. Recently, the strength of superposition is quantified under the framework of quantum coherence [3,4], which is a rapidly developing field in quantum foundation. Quantum coherence has close connections with entanglement and other quantum correlations in many-body systems, and interestingly these measures can be transformed into each other [5][6][7][8]. Also, various concepts can be mapped from quantum entanglement to quantum coherence, such as coherence of assistance [9], coherence distillation and cost [10][11][12][13][14], and coherence evolutions [15]. It turns out that coherence, as an essential resource, plays an important role in various tasks including quantum algorithms [16], quantum biology [17], and quantum thermodynamics [18].In reality, it is crucial to judge whether a quantum source is capable for certain quantum information processing tasks. Coherence witness has been introduced to detect the existence of coherence for an unknown state [19]. A valid coherence witness W is a Hermitian operator which is positive semidefinite after dephasing on the coherence computational basis ∆(W ) ≥ 0. This condition is equivalent to that of tr(ρW ) ≥ 0 for all incoherent states. Then, tr(ρW ) < 0 shows coherence in ρ. Coherence witness has a close connection with a coherence measure called robustness of coherence C R (ρ) [19]. If we optimize the observable W to maximize −tr(ρW ), the maximum value is the robustness of coherence of ρ. In other words, the witness can be used to lower bound the coherence of an unknown system [20]; i.e., the relation C R (ρ) ≥ −tr(ρW ) always holds for a valid witness W [19]. This property can also be applied to construct a source-independent QRNG [21]. Several experiments relevant to coherence witness have been reported recently [20,22,23].The key problem is that the correctness of coherence witness highly ...

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One-Shot Coherence Dilution

Cited by 82 publications

References 55 publications

One-Shot Operational Quantum Resource Theory

One-Shot Operational Quantum Resource Theory

Operational resource theory of quantum channels

Quantum Coherence Witness with Untrusted Measurement Devices

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