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arXiv:2403.08073

Experimental demonstration of Contextual Advantage in minimum error and maximum confidence mirror-state discrimination

Xuan Fan, Ya Ping Xiao, Yongjian Gu

Published Mar 12, 2024• 0 citations
arXivHTMLPDF

Abstract

Contextuality is well known as a vital resource for locating the boundary between classical and quantum theories, as well as identifying tasks showing quantum advantage. In a surge of recent works [Schmid and Spekkens, Phys.Rev.X 8, 011015 (2018); Mukherjee, Naonit and Pan, Phys.Rev.A 106, 012216 (2022); Flatt, Lee, Carceller, Brask and Bae, PRX QUANTUM 3, 030337 (2022)], it has also been shown that contextuality is the crucial resource in quantum state discrimination (QSD) tasks, including minimum error discrimination (MED) and maximum confidence discrimination (MCD), together with many other figure-of-merits. Despite the fundamental progress made by those aforementioned works, none of them mention about how to realize their fancy proposals, which is doubtlessly necessary for the final goal of applying this resource in real QSD tasks. In this paper, we report the first experimental demonstration of contextual advantage in both MED and MCD for three mirror-symmetric states using interferometric quantum walk, which can be easily generalized to any figure-of-merit in QSD. Our experiment agrees well with the result of theoretical simulation, and also shows the great potentiality of leveraging this method to explore a simpler version for the witness of contextuality, as well as demonstrating quanutm advantage of various tasks that require QSD.

DOI
10.48550/arxiv.2403.08073

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Contextuality is well known as a vital resource for locating the boundary between classical and quantum theories, as well as identifying tasks showing quantum advantage. In a surge of recent works [Schmid and Spekkens, Phys.Rev.X 8, 011015 (2018); Mukherjee, Naonit and Pan, Phys.Rev.A 106, 012216 (2022); Flatt, Lee, Carceller, Brask and Bae, PRX QUANTUM 3, 030337 (2022)], it has also been shown that contextuality is the crucial resource in quantum state discrimination (QSD) tasks, including minimum error discrimination (MED) and maximum confidence discrimination (MCD), together with many other figure-of-merits. Despite the fundamental progress made by those aforementioned works, none of them mention about how to realize their fancy proposals, which is doubtlessly necessary for the final goal of applying this resource in real QSD tasks. In this paper, we report the first experimental demonstration of contextual advantage in both MED and MCD for three mirror-symmetric states using interferometric quantum walk, which can be easily generalized to any figure-of-merit in QSD. Our experiment agrees well with the result of theoretical simulation, and also shows the great potentiality of leveraging this method to explore a simpler version for the witness of contextuality, as well as demonstrating quanutm advantage of various tasks that require QSD.
The generalized notion of noncontextuality provides an avenue to explore the fundamental departure of quantum theory from a classical explanation. Recently, extracting different forms of quantum advantages in various information processing tasks has received an upsurge of attention. In a recent work [Schmid and Spekkens, Phys. Rev. X 8, 011015 (2018)] it has been demonstrated that minimum error discrimination of two nonorthogonal pure quantum states entails contextual advantage when the states are supplied with equal prior probabilities. We generalize their work for arbitrary prior probabilities and extend the investigation for three arbitrary mirror-symmetric states. We show that the contextual advantage can be obtained for any value of prior probability when only two quantum states are present in the task. But surprisingly, for the case of three mirror-symmetric states, the contextual advantage can be revealed only for a restrictive range of prior probabilities with which the states are supplied. Further, we extend our study to examine the contextual advantage for maximum confidence state discrimination. We demonstrate that the prior probabilities of state preparation play a similar role in exploiting the quantum advantage in maximum confidence discrimination.
In the past decades, researches on parity-time (PT) and anti-parity-time(APT) systems have garnered unprecedented attention, showcasing their various intriguing characteristics and promising potentiality in extending canonical Hermitian quantum mechanics. However, despite significant endeavors devoted to this new field of physics, non-Hermitian dynamics of contextuality still remains an uncharted region, either in PT-symmetry or APT-symmetry systems. Since contextuality has also been proven to be the core resource for quantum state discrimination (QSD) tasks, here we systematically investigate the novel performance of contextuality through QSD in both systems, taking mirror-symmetric three-state minimum error discrimination (MED) and maximum confidence discrimination (MCD) scenarios as two examples. The time evolution of contextuality in two scenarios and eight regimes (four regimes for each scenario) are comprehensively compared and analyzed, with the difference of initial states also considered. In the symmetry-unbroken regimes, our simulation shows periodic oscillations of contextuality for both MED and MCD scenarios, the period of which is state-independent but related to non-Hermiticity of the system. Both MED and MCD shows non-trivial recovery of contextuality exceeding its initial value in PT system, which is only existent for MCD in APT system. In the symmetry-broken regimes, the success probabilities of both scenarios start from a prompt decay at first, ending up with a stable value which is constantly 1/3. Non-triviality is found only for MCD scenario in PT system, where the recovered contextuality exceeds its initial value.
Quantum state discrimination, alongside its other applications, has recently found use as a tool for witnessing generalised contextuality. In this article, we derive noncontextuality inequalities for both conclusive and inconclusive outcomes across various guessing strategies. For minimum-error discrimination, the advantage is in terms of the confidences of individual outcomes, while for unambiguous state discrimination, it is in terms of the average guessing probability. For maximum-confidence discrimination, we show that contextual advantages occur not only for the confidence but also their average, the guessing probability, as well as the inconclusive outcome rate. Our results show that contextual advantages are observed across all two-state discrimination schemes and figures of merit. We envisage that various quantum information applications based on state discrimination may offer advantages over noncontextual theories.
One of the most fundamental results in quantum information theory is that no measurement can perfectly discriminate between nonorthogonal quantum states.In this work, we investigate quantum advantages for discrimination tasks over noncontextual theories by considering a maximum-confidence measurement that unifies different strategies of quantum state discrimination, including minimum-error and unambiguous discrimination.We first show that maximum-confidence discrimination, as well as unambiguous discrimination, contains contextual advantages.We then consider a semi-device-independent scenario of certifying maximum-confidence measurement.The scenario naturally contains undetected events, making it a natural setting to explore maximum-confidence measurements.We show that the certified maximum confidence in quantum theory also contains contextual advantages.Our results establish how the advantages of quantum theory over a classical model may appear in a realistic scenario of a discrimination task.
Nonorthogonal quantum states cannot be perfectly distinguished; seeking the optimal discrimination strategy is a critical task in quantum information processing. Maximum-confidence measurements provide the highest confidence that represents the conditional probability of the prepared state being correct given an observed outcome. In this work, we experimentally investigate maximum-confidence measurements by discrete-time quantum walks for geometrically uniform states and tetrahedron states, and our experimental results clearly show that the maximum-confidence measurements coincide with minimum-error discrimination in these cases. Meanwhile, we also provide experimental evidence for the contextual advantage of maximum-confidence measurements in quantum theory over classical theory, using two quantum pure states as an example. Our work provides a unified experimental approach to quantum state discrimination that highlights the practical value of maximum-confidence measurements in quantum information processing.
Quantum state discrimination enables the accurate identification of quantum states, which are generally nonorthogonal. Among various strategies, minimum-error discrimination and unambiguous state discrimination exhibit contextuality-enhanced success probabilities that surpass classical bounds, offering significant advantages for quantum sensing and communication. However, in practice, both error and failure outcomes can occur, suggesting the need for a unified strategy that incorporates both aspects while exploring the potential for contextuality enhancement. In this work, we theoretically demonstrate contextuality enhancement in quantum state discrimination under a fixed failure probability. We show that this enhancement disappears within a certain intermediate range of failure probabilities--a phenomenon absent in conventional strategies, where both minimum-error and unambiguous discrimination consistently outperform the noncontextual bound for equal priors. Moreover, we analyze how the existence of this non-enhancement region depends on the confusability of the quantum states, which corresponds to their fidelity in a quantum model. We further extend the discussion to the noisy state discrimination, which even encompasses the maximal-confidence discrimination. In this extended discussion, we observe that the non-enhancement region tends to disappear with increasing noise strength.