The Measure Aspect of Quantum Uncertainty, of Entanglement, and the Associated Entropies

0547337 - ÚJF 2022 RIV CH eng J - Journal Article
Horváth, Ivan
The Measure Aspect of Quantum Uncertainty, of Entanglement, and the Associated Entropies.
Quantum Reports. Roč. 3, č. 3 (2021), s. 534-548. E-ISSN 2624-960X
Institutional support: RVO:61389005
Keywords : effective measure * effective number * entropy * localization * quantum effective number * quantum entanglement * quantum uncertainty
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Method of publishing: Open access
https://doi.org/10.3390/quantum3030035

Indeterminacy associated with the probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here, we express it as an effective amount (measure) of distinct outcomes instead. The resulting µ-uncertainties are described by the effective number theory whose central result, the existence of a minimal amount, leads to a well-defined notion of intrinsic irremovable uncertainty. We derive µ-uncertainty formulas for arbitrary set of commuting operators, including the cases with continuous spectra. The associated entropy-like characteristics, the µ-entropies, convey how many degrees of freedom are effectively involved in a given measurement process. In order to construct quantum µ-entropies, we are led to quantum effective numbers designed to count independent, mutually orthogonal states effectively comprising a density matrix. This concept is basis-independent and leads to a measure-based characterization of entanglement.
Permanent Link: http://hdl.handle.net/11104/0323583