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arXiv:2603.27917

Contextuality of quantum non-demolition measurement via state discrimination

Min Namkung, Ilhwan Kim, Hyang-Tag Lim

quant-phSubmitted Mar 30, 2026• Announced Mar 31, 2026• 0 citations
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Abstract

Quantum non-demolition measurements facilitate various quantum technologies, including quantum communication. Notably, their operational structure can be replicated by a classical model--referred to as a noncontextual model--making it crucial to identify which features prevents such models from reproducing the corresponding quantum measurements. In this work, we theoretically demonstrate contextual features inherent in the structure of quantum non-demolition measurements. These features not only reveal the nonclassicality of unambiguous state discrimination, but also extend to sequential unambiguous discrimination and probabilistic quantum cloning, both of which involve post-measurement states. Moreover, our analysis extends to noisy scenarios, highlighting its potential relevance for practical implementations. We believe that our results broaden the scope of observing nonclassicality in quantum systems and ultimately contribute to the advancement of various quantum technologies.

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16 pages, 5 figures

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Quantum non-demolition measurements facilitate various quantum technologies, including quantum communication. Notably, their operational structure can be replicated by a classical model--referred to as a noncontextual model--making it crucial to identify which features prevents such models from reproducing the corresponding quantum measurements. In this work, we theoretically demonstrate contextual features inherent in the structure of quantum non-demolition measurements. These features not only reveal the nonclassicality of unambiguous state discrimination, but also extend to sequential unambiguous discrimination and probabilistic quantum cloning, both of which involve post-measurement states. Moreover, our analysis extends to noisy scenarios, highlighting its potential relevance for practical implementations. We believe that our results broaden the scope of observing nonclassicality in quantum systems and ultimately contribute to the advancement of various quantum technologies.
Quantum contextuality is a key nonclassical feature underlying advantages in quantum computation and communication. We introduce a new method to study contextuality in quantum information-processing tasks and protocols, relying solely on observed information-processing statistics. Building on the framework of Shahandeh, Yianni and Doosti in arXiv:2512.10000 and employing rank separation techniques, we prove that contextuality is the necessary resource in both phase-covariant and universal optimal quantum cloning, thereby establishing its role as a fundamental source of nonclassicality in all known optimal cloning scenarios and resolving an open problem on the connection between cloning and contextuality. As a second application, we demonstrate the power of our method by providing a new, streamlined proof of contextuality in minimum-error quantum state discrimination.
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.
Quantum theory fundamentally forbids the perfect copying of an arbitrary unknown quantum state, according to a principle known as the no-cloning theorem. Nevertheless, it is possible to construct a deterministic quantum map that produces multiple approximate copies of an unknown quantum state. This task is referred to as universal quantum cloning, further facilitating numerous quantum technologies such as quantum cryptography and quantum communication. In this work, we theoretically verify that the universal quantum cloning cannot be realized within a noncontextual theory, highlighting its intrinsically nonclassical nature. Our verification first {focuses on revealing that} 1→21\rightarrow21→2 cloning scenario {is fully contextual}, and {further covers general examples to observe the contextual behavior of} N→MN\rightarrow MN→M scenario. We believe that our results regarding quantum cloning serve a key role for understanding both quantum foundation and application.
This is a limited overview of quantum non-demolition (QND) measurements, with brief discussions of illustrative examples meant to clarify the essential features. In a QND measurement, the predictability of a subsequent value of a precisely measured observable is maintained and any random back-action from uncertainty introduced into a noncommuting observable is avoided. The fundamental ideas, relevant theory and the conditions and scope for applicability are discussed with some examples. Precision measurements have indeed gained from developing QND measurements. Some implementations in quantum optics, gravitational wave detectors and spin-magnetometry are discussed.
A number of noncontextual models exist which reproduce different subsets of quantum theory and admit a no-cloning theorem. Therefore, if one chooses noncontextuality as one's notion of classicality, no-cloning cannot be regarded as a nonclassical phenomenon. In this work, however, we show that there are aspects of the phenomenology of quantum state cloning which are indeed nonclassical according to this principle. Specifically, we focus on the task of state-dependent cloning and prove that the optimal cloning fidelity predicted by quantum theory cannot be explained by any noncontextual model. We derive a noise-robust noncontextuality inequality whose violation by quantum theory not only implies a quantum advantage for the task of state-dependent cloning relative to noncontextual models, but also provides an experimental witness of noncontextuality.
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.