Work

Bridging Classical and Quantum Worlds: Maps, States, and Evolutions

Year: 2026

Type: article

Abstract: In this work, we present several aspects of the interplay between classical and quantum theories. After reviewing the equivalence between positivity and complete positivity in the commutative setting, we introduce and analyze intermediate notions that interpolate between these two properties for linear maps on the space of operators on a Hilbert space, highlighting their natural connections to quantum dynamics and entanglement theory. Finally, we discuss possible constructions that allow one to derive quantum states and evolutions from classical counterparts, and vice versa.

Source: Open Systems & Information Dynamics

DOI: 10.1142/s1230161226500113

Authors: Daniele Amato, Paolo Facchi, Giuseppe Marmo

Institutions: Istituto Nazionale di Fisica Nucleare, Sezione di Bari, University of Bari Aldo Moro, Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, University of Naples Federico II

Language: English

Topic: Quantum Information and Cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Dipartimenti di Eccellenza, Gruppo Nazionale per la Fisica Matematica

Awards: G1303340219, G4476456880