Quantum Channels

Peter P. Rohde

Da Zu Huang, Zhi Gang Chen, Xin Li +1 more

Quantum channel combining and splitting, called quantum channel polarization, is suggested to design qubit sequences that achieve the symmetric capacity for any given discrete memoryless quantum channels. The polarized quantum channels can be well-conditioned for quantum channel codes, through which one need to send data at rate 1 by employing quantum channels with capacity near 1 and at rate 0 by employing the remaining quantum channels.

Attila Lovas, Attila Andai

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 the 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.

Attila Lovas, Attila Andai

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 the 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.