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Keywords = QSZK-completeness

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24 pages, 433 KiB  
Article
On the Complexity of Finding the Maximum Entropy Compatible Quantum State
by Serena Di Giorgio and Paulo Mateus
Mathematics 2021, 9(2), 193; https://doi.org/10.3390/math9020193 - 19 Jan 2021
Cited by 4 | Viewed by 2772
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Quantum Computing Algorithms and Computational Complexity)
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