Quantumness certification via non-demolition measurements

Year: 2026

Authors: Solinas P., Gherardini S.

Autors Affiliation: Univ Genoa, Dipartimento Fis, Genoa, Italy; Ist Nazl Fis Nucl, Sez Genova, Genoa, Italy; CNR, Ist Nazl Ott, Largo Enrico Fermi 6, I-50125 Florence, Italy; Univ Firenze, European Lab Nonlinear Spect, I-50019 Sesto Fiorentino, Italy.

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 context, 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 an 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 for 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/Review: ADVANCES IN PHYSICS-X

Volume: 11 (1)      Pages from: 2637832-1  to: 2637832-25

More Information: This research was supported by the PRIN project Quantum Reservoir Computing (QuReCo) (2022FEXLYB), PNRR MUR project NQSTI funded by the European Union, Next Generation EU (PE0000023-NQSTI).
KeyWords: Foundations of quantum mechanics; quantumness certification; quantum non-demolition measurements; quasi-probability; Leggett-Garg inequalities; quantum-to-classical transition
DOI: 10.1080/23746149.2026.2637832