Work

Approximating quantum channels by completely positive maps with small Kraus rank

Year: 2024

Type: article

Abstract: We study the problem of approximating a quantum channel by one with as few Kraus operators as possible (in the sense that, for any input state, the output states of the two channels should be close to one another). Our main result is that any quantum channel mapping states on some input Hilbert space A to states on some output Hilbert space B can be compressed into one with order dlog⁡d Kraus operators, where d=max(|A|,|B|) , hence much less than |A||B| . In the case where the channel's outputs are all very mixed, this can be improved to order d . We discuss the optimality of this result as well as some consequences.

Source: Quantum

DOI: 10.22331/q-2024-04-30-1320

Authors: Cécilia Lancien, Andreas Winter

Institutions: Centre National de la Recherche Scientifique, Institut Fourier, Université Grenoble Alpes, Institució Catalana de Recerca i Estudis Avançats, Universitat Autònoma de Barcelona

Language: English

Topic: Quantum Information and Cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $215