Work

Concentration of Quantum Channels With Random Kraus Operators via Matrix Bernstein Inequality

Year: 2025

Type: article

Abstract: . In this study, we generate quantum channels with random Kraus operators to typically obtain almost twirling quantum channels and quantum expanders. To prove the concentration phenomena, we use matrix Bernstein’s inequality. In this way, our random models do not utilize Haar-distributed unitary matrices or Gaussian matrices. Rather, as in the preceding research, we use unitary t-designs to generate mixed tensor-product unitary channels acting on Cdt. Although our bounds in Schatten p-norm are valid only for 1 ≤p≤ 2, we show that they are typically quantum ϵ-twirling channels with the tail bound proportional to 1/poly(dt), while such bounds were previously constants. The number of required Kraus operators was also improved by powers of logdandt, to be proportional todtlogd/ϵ2. Such random quantum channels are also typically quantum expanders, but the number of Kraus operators must grow proportionally totlogdin our case. Finally, a new non-unital model of super-operators generated by bounded and isotropic random Kraus operators was introduced, which can be typically rectified to yield almost randomizing quantum channels and quantum expanders.

Source: IEEE Transactions on Information Theory

DOI: 10.1109/tit.2025.3567085

Author: Motohisa Fukuda

Institution: Yamagata University

Language: English

Topic: Quantum Information and Cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Award: Research on deep learning using random matrices, free probability, and tensor networks