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 unify the contextual advantages across all state discrimination schemes and figures of merit. We envisage that various quantum information applications based on state discrimination may offer advantages over non-contextual theories.
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 unify the contextual advantages across all state discrimination schemes and figures of merit. We envisage that various quantum information applications based on state discrimination may offer advantages over non-contextual 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.
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.
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.
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.
Sequential quantum information processing may lie in the peaceful coexistence of no-go theorems on quantum operations, such as the no-cloning theorem, the monogamy of correlations, and the no-signalling principle. In this work, we investigate a sequential scenario of quantum state discrimination with maximum confidence, called maximum-confidence discrimination, which generalizes other strategies such as minimum-error and unambiguous discrimination. We show that sequential discrimination with equally high confidence can be realized if and only if positive-operator-valued measure elements for a maximum-confidence measurement can be unambiguously discriminated, i.e., linearly independent; otherwise, a party will have strictly less confidence in measurement outcomes than the previous one. We investigate the tradeoff between state disturbance and information gain in sequential state discrimination and show that the less guessing probability there is from conclusive outcomes for each party, the more parties can participate in the sequential scenario.
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.