This article is cited in 1 paper

Generating Quantum Channels

R. N. Gumerov, R. L. Khazhin

N. I. Lobachevsky Institute of Mathematics and Mechanics, Kazan Federal University, Kremlevskaya ul. 35, Kazan, 420008 Russia

Abstract: For composite quantum systems, we consider quantum channels that uniquely determine the channels of the subsystems. Such channels of composite systems are called generating channels. Examples of generating channels are given by tensor products of two quantum channels of subsystems and their convex combinations. The paper deals with the properties of generating channels. In particular, we show that these channels form a convex compact set in the norm topology. We prove a criterion for a quantum channel to be generating. For composite systems consisting of two qubits, we construct generating phase-damping channels. For subsystems, these channels generate both phase-damping channels and depolarizing channels. Examples of nongenerating phase-damping channels are also presented.

Keywords: Hilbert space, phase-damping channel, depolarizing channel, operator norm, generating map, generating quantum channel, induced map, induced quantum channel, trace norm, composite quantum system, partial trace.

UDC: 517.98+519.72+530.145

Received: June 14, 2023
Revised: July 30, 2023
Accepted: August 7, 2023

DOI: 10.4213/tm4369

 English version: Proceedings of the Steklov Institute of Mathematics, 2024, 324, 75–85

Bibliographic databases:

• 
• 
•