Reversibility-unitality-disturbance tradeoff in quantum channels

In this work, we employ the squared Hilbert-Schmidt norm of the Gram matrix for a quantum channel as a reversibility quantifier of this channel, which is shown to be complementary to the entropy of this channel, and derive a complementary relation between the reversibility of a quantum channel and its complementary channel. For a natural unitality measure of a quantum channel, we show that it is equivalent to the entropy of the corresponding complementary channel. By quantifying the disturbance of a quantum channel as the decrease of correlations in a maximally entangled state locally passing through this channel, we eventually establish a reversibility-unitality-disturbance triality relation. To illustrate and compare these quantities, we further evaluate them for some prototypical channels associated with some special quantum information processing tasks and computations, such as the quantum teleportation channel, DQC1 channel, Mach-Zehnder interferometry channel, dephrasure channel and so on, including both unital and nonunital cases.