Certification and Quantification of Multilevel Quantum Coherence

Ringbauer, Martin; Bromley, Thomas R.; Cianciaruso, Marco; Lami, Ludovico; Lau, W. Y. Sarah; Adesso, Gerardo; White, A. G.; Fedrizzi, Alessandro; Piani, Marco

doi:10.1103/physrevx.8.041007

Cited by 76 publications

(98 citation statements)

References 84 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].…”

Section: Optimal Rates Of One-shot Resource Manipulationmentioning

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 Manipulationmentioning

confidence: 99%

“…We also note that the resource measures considered in this work often admit efficient SDP formulation [9,71] as well as analytical expressions [9,[67][68][69][70]72], which make our bounds of practical use in many important circumstances.…”

Section: Optimal Rates Of One-shot Resource Manipulationmentioning

confidence: 99%

One-Shot Operational Quantum Resource Theory

2019

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“…How to properly verify the function of a quantum device is one of the more increasingly important problems in quantum information science . For a general certification protocol, we define a proper quantity f to evaluate the quality of the quantum device, for example, we can use the fidelity between the experimentally prepared states and the target states to evaluate the quality of the quantum‐state‐preparation setup.…”

Section: Certification Protocolmentioning

confidence: 99%

Experimental certification for nonclassical teleportation

Zhang

et al. 2019

Quantum Engineering

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Summary How to properly certify the quantum function of a quantum process (device) is one of the key problems in quantum information science, particularly, for a function beyond its classical counterpart. To properly verify quantum teleportation is a critical task because of its fundamental roles in quantum communication and quantum computation. Here, we experimentally certified nonclassical quantum teleportation with one setting by the random teleportation robustness introduced by [Phys. Rev. Lett. 119, 110501 (2017)]. Our results show that the random teleportation robustness is experimentally convenient and powerful for verifying nonclassical teleportation and entanglement.

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“…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 relies on the implementations of W , whose results may be unreliable due to measurement device imperfections or malfunction. As an example, we propose a simple basis-rotating attack (as a way to mimic device malfunction) on the measurement devices.…”

mentioning

confidence: 99%

“…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].…”

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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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Certification and Quantification of Multilevel Quantum Coherence

Abstract: 1 For brevity, we will omit the qualifier "quantum" in the following. arXiv:1707.05282v3 [quant-ph]

Cited by 76 publications

References 84 publications

One-Shot Operational Quantum Resource Theory

One-Shot Operational Quantum Resource Theory

Experimental certification for nonclassical teleportation

Quantum Coherence Witness with Untrusted Measurement Devices

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