Correlations in typicality and an affirmative solution to the exact catalytic entropy conjecture
 authored by
 Henrik Wilming
 Abstract
It is well known that if a (finitedimensional) density matrix ρ has smaller entropy than ρ0, then the tensor product of sufficiently many copies of ρ majorizes a quantum state arbitrarily close to the tensor product of correspondingly many copies of ρ0. In this short note I show that if additionally rank(ρ) ≤ rank(ρ0), then n copies of ρ also majorize a state where all singlebody marginals are exactly identical to ρ0 but arbitrary correlations are allowed (for some sufficiently large n). An immediate application of this is an affirmative solution of the exact catalytic entropy conjecture introduced by Boes et al. [PRL 122, 210402 (2019)]: If H(ρ) < H(ρ0) and rank(ρ) ≤ rank(ρ0) there exists a finite dimensional density matrix σ and a unitary U such that Uρ⊗ σU has marginals ρ0 and σ exactly. All the results transfer to the classical setting of probability distributions over finite alphabets with unitaries replaced by permutations.
 Organisation(s)

Institute of Theoretical Physics
CRC 1227 Designed Quantum States of Matter (DQmat)
 Type
 Article
 Journal
 Quantum
 Volume
 6
 No. of pages
 5
 ISSN
 2521327X
 Publication date
 10.11.2022
 Publication status
 Published
 Peer reviewed
 Yes
 ASJC Scopus subject areas
 Atomic and Molecular Physics, and Optics, Physics and Astronomy (miscellaneous)
 Electronic version(s)

https://doi.org/10.48550/arXiv.2205.08915 (Access:
Open)
https://doi.org/10.22331/Q20221110858 (Access: Open)