Work

Random Covariant Quantum Channels

Year: 2025

Type: article

Abstract: The group symmetries inherent in quantum channels often make them tractable and applicable to various problems in quantum information theory. In this paper, we introduce natural probability distributions for covariant quantum channels. Specifically, this is achieved through the application of “twirling operations” on random quantum channels derived from the Stinespring representation that uses Haar-distributed random isometries. We explore various types of group symmetries, including unitary and orthogonal covariance, hyperoctahedral covariance, and diagonal orthogonal covariance (DOC), and analyze their properties related to quantum entanglement based on the model parameters. In particular, we discuss the threshold phenomenon for positive partial transpose and entanglement breaking properties, comparing thresholds among different classes of random covariant channels. Finally, we contribute to the $$\hbox {PPT}^2$$ PPT 2 conjecture by showing that the composition between two random DOC channels is generically entanglement breaking.

Source: Annales Henri Poincaré

DOI: 10.1007/s00023-025-01558-y

Authors: Ion Nechita, Sang-Jun Park

Institutions: Centre National de la Recherche Scientifique, Université Toulouse III - Paul Sabatier, Laboratoire de Physique Théorique, Université de Toulouse

Language: English

Topic: Quantum Information and Cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Agence Nationale de la Recherche, Université de Toulouse