Directly Measuring the Degree of Quantum Coherence using Interference Fringes

Wang, Yi Tao; Tang, Jian‐Shun; Wei, Zhi-Yuan; Yu, Shang; Ke, Zhi‐Jin; Xu, Xiao‐Ye; Li, Chuan‐Feng; Guo, Guang-Can

doi:10.1103/physrevlett.118.020403

Cited by 87 publications

(45 citation statements)

References 45 publications

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“…3 as functions of p and γ, defining the prepared state in Eq. (5). The shown results enable us to quantify the measurement-induced decoherence because one can straightforwardly prove [66] that the square of trace distance betweenρ andρ is identical to ∆V for θ ≈ π/2.…”

Section: Resultsmentioning

confidence: 88%

“…For this purpose, we fix the value of p = sin 2 (2α) at α = 12 • and study the difference of the variances as a function of γ [Eq. (5)]. We can observe that, in general, the highest purity (γ → 1) yields the most significant verification of quantum coherence, ∆V = 0, which also represents the scenario with the highest coherence of the probe stateρ.…”

Section: Resultsmentioning

confidence: 90%

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Measuring coherence of quantum measurements

Cimini

Gianani

Sbroscia

et al. 2019

Phys. Rev. Research

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The superposition of quantum states lies at the heart of physics and has been recently found to serve as a versatile resource for quantum information protocols, defining the notion of quantum coherence. In this contribution, we report on the implementation of its complementary concept, coherence from quantum measurements. By devising an accessible criterion which holds true in any classical statistical theory, we demonstrate that noncommutative quantum measurements violate this constraint, rendering it possible to perform an operational assessment of the measurement-based quantum coherence. In particular, we verify that polarization measurements of a single photonic qubit, an essential carrier of one unit of quantum information, are already incompatible with classical, i.e., incoherent, models of a measurement apparatus. Thus, we realize a method that enables us to quantitatively certify which quantum measurements follow fundamentally different statistical laws than expected from classical theories and, at the same time, quantify their usefulness within the modern framework of resources for quantum information technology.

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Section: Resultsmentioning

confidence: 88%

Section: Resultsmentioning

confidence: 90%

Measuring coherence of quantum measurements

Cimini

Gianani

Sbroscia

et al. 2019

Phys. Rev. Research

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show abstract

“…Some known measures include geometric measures [2], the robustness of coherence [6][7][8], and entanglement based measures [9]. Coherence measures have now been studied in relation to a diverse range of quantum effects such as quantum interference [10], exponential speed-up in quantum algorithms [11,12] and quantum metrology [13,14], nonclassical light [15][16][17], quantum macroscopicity [18,19] and quantum correlations [20][21][22][23][24][25]. An overview of coherence measures and their structure may be found in [26,27].…”

Section: Introductionmentioning

confidence: 99%

Optimizing nontrivial quantum observables using coherence

2019

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In this paper we consider the quantum resources required to maximize the mean values of any nontrivial quantum observable. We show that the task of maximizing the mean value of an observable is equivalent to maximizing some form of coherence, up to the application of an incoherent operation. For any nontrivial observable, there always exists a set of preferred basis states where the superposition between such states is always useful for optimizing the mean value of a quantum observable. The usefulness of such states is expressed in terms of an infinitely large family of valid coherence measures which is then shown to be efficiently computable via a semidefinite program. We also show that these coherence measures respect a hierarchy that gives the robustness of coherence and the l 1 norm of coherence additional operational significance in terms of such optimization tasks.

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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].…”

mentioning

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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Directly Measuring the Degree of Quantum Coherence using Interference Fringes

Cited by 87 publications

References 45 publications

Measuring coherence of quantum measurements

Measuring coherence of quantum measurements

Optimizing nontrivial quantum observables using coherence

Quantum Coherence Witness with Untrusted Measurement Devices

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