The group symmetries inherent in quantum channels often make them tractable and applicable to various problems in quantum information theory. In this talk, 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 use Haar-distributed random isometries. We explore various types of group symmetries,including unitary covaraince, orthogonal 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 PPT-squared conjecture by showing that the composition between two random DOC channels is generically entanglement breaking.
This talk is joint work with Ion Nechita.
报告人简介：Dr. Sang-Jun Park is currently a postdoc researcher at Univeristy of Toulouse. His research interests lie in the mathematical aspects of Quantum Information Theory (QIT), in particular, entanglement theory and the study of random quantum objects, with a focus on techniques from functional analysis and probability theory.
