Threshold size for the emergence of a classical-like behaviour

• Main Authors: Coppo, Alessandro, Pranzini, Nicola, Verrucchi, Paola
• Format: Journal Article
• Language: English
• Published: 25-03-2022
• Subjects: Physics - General Relativity and Quantum Cosmology; Physics - High Energy Physics - Theory; Physics - Quantum Physics
• DOI: 10.48550/arxiv.2203.13587

Phys. Rev. A 106, 042208 (2022) In this work we design a procedure to estimate the minimum size beyond which
a system is amenable to a classical-like description, i.e. a description based
on representative points in classical phase-spaces. This is obtained by
relating quantum states to representative points via Generalized Coherent
States (GCS), and designing a POVM for GCS discrimination. Conditions upon this
discrimination are defined, such that the POVM results convey enough
information to meet our needs for reliability and precision, as gauged by two
parameters $\epsilon$, of our arbitrary choice, and $\delta$, set by the
experimental apparatus, respectively. The procedure implies a definition of
what is meant by "size" of the system, in terms of the number $N$ of elementary
constituents that provide the global algebra leading to the phase-space for the
emergent classical-like description. The above conditions on GCS discrimination
can be thus turned into $N>N_{\rm t}(\epsilon,\delta)$, where $N_{\rm
t}(\epsilon,\delta)$ is the threshold size mentioned in the title. The specific
case of a magnetic system is considered, with details of a gedanken experiment
presented and thoroughly commented. Results for pseudo-spin and bosonic systems
are also given.