Quantumness certification via non-demolition measurements

TL;DR

This paper reviews how Quantum Non-Demolition Measurements (QNDM) can be used to certify genuine quantum features like entanglement and superposition in finite-dimensional systems, offering a real-time, robust method linked to Leggett-Garg inequalities.

Contribution

It establishes a necessary and sufficient condition for quantumness certification via QNDM, connecting it to quasi-probability negativity and demonstrating its advantages over traditional Leggett-Garg tests.

Findings

QNDM can directly detect negative quasi-probability terms indicating quantumness.

QNDM protocols are robust against noise and effective in tracking quantum-to-classical transitions.

QNDM offers advantages over standard Leggett-Garg inequalities in certifying quantum features.

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.