Year: 2021
Type: article
Abstract: Herein we study the problem of recovering a density operator from a set of compatible marginals, motivated by limitations of physical observations. Given that the set of compatible density operators is not singular, we adopt Jaynes’ principle and wish to characterize a compatible density operator with maximum entropy. We first show that comparing the entropy of compatible density operators is complete for the quantum computational complexity class QSZK, even for the simplest case of 3-chains. Then, we focus on the particular case of quantum Markov chains and trees and establish that for these cases, there exists a procedure polynomial in the number of subsystems that constructs the maximum entropy compatible density operator. Moreover, we extend the Chow–Liu algorithm to the same subclass of quantum states.
Source: Mathematics
DOI: 10.3390/math9020193
Authors: Serena Di Giorgio, Paulo Mateus
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,728
Awards: G1516346500, G1578237752, G1763632427, G2144570049, G241473106, Instituto de Telecomunicações, G3838636553, G3840324753, G3850789590, G3891694003, G4194598094, G4730158122, G4792409162, G5224927334, G5421018868, G5454278309, G59476441, G6126344035, G6681517377, Terapia personalizada para doenças reumáticas por intermédio de aprendizagem automática, G8419648384
OpenAlex ID: W3030111579