Volume of the space of qubit-qubit channels and state transformations under random quantum channels

Abstract

The simplest building blocks for quantum computations are the qubit-qubit quantum channels. In this paper, we analyze the structure of these channels via their Choi representation. The restriction of a quantum channel to the space of classical states (i.e. probability distributions) is called the underlying classical channel. The structure of quantum channels over a fixed classical channel is studied, the volume of general and unital qubit channels with respect to the Lebesgue measure is computed and explicit formulas are presented for the distribution of the volume of quantum channels over given classical channels. We study the state transformation under uniformly random quantum channels. If one applies a uniformly random quantum channel (general or unital) to a given qubit state, the distribution of the resulted quantum states is presented.

18 pages, 3 figures. arXiv admin note: text overlap with arXiv:1607.01215

References in corpus (3)

• Superdense coding of quantum states
• Random Quantum Operations
• Volume of the quantum mechanical state space

Cited by in corpus (7)

• Generating random quantum channels
• Dirac Delta Function of Matrix Argument
• Geometry of the Pauli maps and Pauli channels
• Measure of positive and not completely positive single-qubit Pauli maps
• Geometry of generalized Pauli channels
• Geometry of symmetric and non-invertible Pauli channels
• Optimal convex approximations of quantum states based on fidelity