Universal recovery and P-Fidelity in von neumann algebras
Year: 2020
Type: preprint
Abstract: Scenarios ranging from quantum error correction to high energy physics use recovery maps, which try to reverse the effects of generally irreversible quantum channels. The decrease in quantum relative entropy between two states under the same channel quantifies information lost. A small decrease in relative entropy often implies recoverability via a universal map depending only the second argument to the relative entropy. We find such a universal recovery map for arbitrary channels on von Neumann algebras, and we generalize to p-fidelity via subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that non-decrease of relative entropy is equivalent to the existence of an L 1 -isometry implementing the channel on both input states. Our primary technique is a reduction method by Haagerup, approximating a non-tracial, type III von Neumann algebra by a finite algebra. This technique has many potential applications in porting results from quantum information theory to high energy settings.
Source: arXiv (Cornell University)
Authors: Marius Junge, Nicholas LaRacuente
Institution: University of Illinois Urbana-Champaign
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3089304818