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arXiv:2512.09734 · Advances in Physics X

Quantumness certification via non-demolition measurements

Paolo Solinas, Stefano Gherardini

quant-phSubmitted Dec 10, 2025• Announced Dec 11, 2025• 0 citations• Revised Feb 23, 2026 (v2)
v1 · Dec 10, 2025v2 · Feb 23, 2026
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Abstract

The fundamental question of when a static or dynamic system should be deemed intrinsically quantum remains a challenge to address in absolute terms. In this regard, a critical requirement lies in the certification (ideally, in real-time) of the emergence and persistence of genuine quantum features, principally entanglement and quantum superposition. Quantum Non-Demolition Measurements (QNDM) serve as the appropriate instrument for this certification, both from a theoretical and experimental standpoint. In this review paper, we explain, with accessible clarity, how the implementation of QNDM can be directly linked to a necessary and sufficient condition for the presence of genuinely quantum features in the system's state monitored over time in finite-dimensional systems, establishing a conceptual parallel with Leggett-Garg inequalities. Using concrete examples that detail the detection of negative terms in the quasi-probability density function resulting from QNDM, we introduce the core concepts for quantumness certification. As specific examples, we discuss an application where the quantum-to-classical transition due to the interaction with an environment can be tracked by QNDM. Moreover, we argue about the robustness of QNDM protocols in the presence of noise sources and their advantages with respect to standard Leggett-Garg inequalities defined by two-time correlators.

Journal reference
Advances in Physics: X 11 (1), 2637832 (2026)
DOI
10.1080/23746149.2026.2637832
Comments
21 pages, 5 figures. Comments and feedback are welcome

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The fundamental question of when a static or dynamic system should be deemed intrinsically quantum remains a challenge to address in absolute terms. In this regard, a critical requirement lies in the certification (ideally, in real-time) of the emergence and persistence of genuine quantum features, principally entanglement and quantum superposition. Quantum Non-Demolition Measurements (QNDM) serve as the appropriate instrument for this certification, both from a theoretical and experimental standpoint. In this review paper, we explain, with accessible clarity, how the implementation of QNDM can be directly linked to a necessary and sufficient condition for the presence of genuinely quantum features in the system's state monitored over time in finite-dimensional systems, establishing a conceptual parallel with Leggett-Garg inequalities. Using concrete examples that detail the detection of negative terms in the quasi-probability density function resulting from QNDM, we introduce the core concepts for quantumness certification. As specific examples, we discuss an application where the quantum-to-classical transition due to the interaction with an environment can be tracked by QNDM. Moreover, we argue about the robustness of QNDM protocols in the presence of noise sources and their advantages with respect to standard Leggett-Garg inequalities defined by two-time correlators.
The Leggett-Garg inequalities have been proposed to identify the quantum behaviour of a system; specifically, the violation of macrorealism. They are usually implemented by performing two sequential measurements on quantum systems, calculating the correlators of such measurements and then combining them arriving at Leggett-Garg inequalities. However, this approach only provides sufficient conditions for the violation of macrorealism. Recently, it was proposed an alternative approach that uses non-demolition measurements and gives both a necessary and sufficient condition for the violation of macrorealism. By storing the information in a quantum detector, it is possible to construct a quasi-probability distribution whose negative regions unequivocally identify the quantum behaviour of the system. Here, we perform a detailed comparison between these two approaches. The use of the IBM quantum simulators allows us to evaluate the performance in real-case situations and to include both the statistical and environmental noise. We find that the non-demolition approach is not only able to always identify the quantum features but it requires fewer resources than the standard Leggett-Garg inequalities. In addition, while the efficiency of the latter is strongly affected by the presence of the noise, the non-demolition approach results incredibly robust and its efficiency remains unchanged by the noise. These results make the non-demolition approach a viable alternative to the Leggett-Garg inequalities to identify the violation of macrorealism.
The Leggett-Garg inequalities have been proposed to identify the quantum behavior of a system; specifically, the violation of macrorealism. They are usually implemented by performing two sequential measurements on quantum systems, calculating the correlators of such measurements and then combining them arriving at Leggett-Garg inequalities. However, this approach only provides sufficient conditions for the violation of macrorealism. Recently, an alternative approach was proposed that uses nondemolition measurements and gives both a necessary and sufficient condition for the violation of macrorealism. By storing the information in a quantum detector, it is possible to construct a quasiprobability distribution whose negative regions unequivocally identify the quantum behavior of the system. Here, we perform a detailed comparison between these two approaches. The use of the IBM quantum simulators allows us to evaluate the performance in real-case situations and to include both the statistical and environmental noise. We find that the nondemolition approach is not only able to always identify the quantum features, but it requires fewer resources than the standard Leggett-Garg inequalities. In addition, while the efficiency of the latter is strongly affected by the presence of the noise, the nondemolition approach results incredibly robust and its efficiency remains unchanged by the noise. These results make the nondemolition approach a viable alternative to the Leggett-Garg inequalities to identify the violation of macrorealism.
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.
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.
In this paper we address the issue of the interplay between non-Markovianity and nonclassicality of a system. We consider the action of non-Markovian environments on a qubit in terms of two models, a classical noise model and a quantum microscopic collision model. For both models we use the violation of the Leggett-Garg inequality (LGI) as a criterion of quantumness, and use the conditional past-future (CPF) correlation to measure non-Markovianity. Besides for the collision model, we also use violation of the nondiscord generating and detecting (NDGD) dynamics to indicate the nonclassicality. And LGI, NDGD, and CPF are probed sequentially by three projective measurements of some observable. In this paper we do not use the assumption of the quantum regression theorem and especially for the collision model the measurement backaction on the environment is explicitly considered. We find that compared with the Markovian dynamics the LGI can be violated for a longer time interval, i.e., non-Markovianity can preserve the quantumness of the system. For the collision model we find that for a specific measurement process, although the non-Markovianity cannot be detected, the effect of non-Markovianity of the system dynamics on nonclassicality still exists, and for some specific measurement operator the violation of both LGI and NDGD will never occur for the Markovian dynamics while with the enhancement of non-Markovianity the quantumness can appear. We also find that the NDGD can be violated for a much wider parameter regime than the LGI.
Entanglement is a key resource for many quantum applications. Understanding fundamental properties of entangled states is an important step towards their practical exploitation. We characterize entanglement in the context of Gaussian and non-Gaussian processes and identify entangled states that cannot be produced by any Gaussian evolution acting on separable states. This distinction exposes intrinsic limitations of Gaussian operations and highlights the role of non-Gaussian operations as an important resource. We apply this framework to develop a certification method that connects entanglement theory with quantum non-Gaussianity - an advanced quantum feature that is essential for several quantum applications. Our approach tailors the certification to experimentally relevant states that can be produced in current quantum optics experiments. We demonstrate this certification for recognizing the genuine non-Gaussian entanglement of various entangled Fock states and hybrid entangled states.