The Information of Quantum Channels

Tong Liu

In quantum information theory, in order for two (or more) parties to communicate, there must be a communication channel. The two central quantities that must be considered are quantum channel capacity and the quantum coherent information. The first describes the capability for a given channel to communicate the required quantum information and the latter describes the amount of information that has been successfully transmitted through the corresponding quantum channel. The capacity of a quantum channel is actually a function of the coherent information, and so the basic step for getting the channel capacity is to calculate its coherent information which serves as a lower bound on the capacity. Generally speaking, it is hard to find the capacity of a given quantum channel, this is because of regularization which is to introduce additional process to solve an ill-conditioned problem. Comparing to general quantum channels, the capacity is easily achieved for the two fundamental classes of quantum channels, degradable and antidegradable, in such a way that degradable channels have capacity given exactly by the coherent information and antidegradable channels have zero coherent information. However, this is not true for general quantum channels, by all means that, under certain restrictions, it is possible to find a non-Pauli quantum channel such that its coherent information is zero but its capacity is non-zero.

Mark M. Wilde

Yuan Li, Shunlong Luo, Yuan Sun +1 more

Quantum channels often cause information loss of a quantum system, and it is desirable to quantify such loss. Alternatively, one may ask how much information can be preserved by a quantum channel. In this work we introduce a quantifier for information loss of quantum channels via uncertainty of the corresponding Choi states determined by the channel-state duality, reveal its basic properties, derive its ranges for various channels, and identify the extremal channels (which depend crucially on the relation between the input and output system dimensions) with the minimal and maximal information loss. Furthermore, we evaluate this quantifier for some prototypical quantum channels and their corresponding complementary channels. We further compare information loss and irreversibility by illuminating their similarities and differences. These results shed light on channel structures from an information-theoretic perspective.

Alexander Semenovich Holevo

NASSER METWALLY

A theoretical quantum teleportation protocol is suggested to teleport accelerated and nonaccelerated information over different classes of accelerated quantum channels. For the accelerated information, it is shown that the fidelity of the teleported state increases as the entanglement of the initial quantum channel increases. However, as the difference between the accelerations of the channel and the teleported state decreases, the fidelity of the teleported information increases. The fidelity of the nonaccelerated information increases as the entanglement of the initial quantum channel increases, while the accelerations of the quantum channel have a little effect. The possibility of sending quantum information over accelerated quantum channels is much better than sending classical information.