Decorrelating capabilities of operations with application to decoherence

Decoherence, interpreted broadly, is essentially the leakage of system information into the environment and is often accompanied by dissipation. The basic questions arise: how to quantify decoherence induced by an operation and how to quantitatively compare decoherence induced by different operations. In this paper, based on a joint ancilla-system-environment tripartite purification for the initial system state and the operation, and by exploiting the intrinsic relations between the loss of correlations in the ancilla-system and the correlations established in the system-environment, we characterize and quantify decoherence from a decorrelating perspective. For this purpose, we first address the issue of separating and quantifying the classical and quantum parts of decorrelation. By use of the canonical isomorphism between operations and bipartite states, we propose two intrinsic decorrelation measures: One is the classical decorrelation based on the loss of classical correlations, and the other is the quantum decorrelation based on the loss of quantum correlations. With the help of quantum decorrelation, we introduce an intuitive measure of (quantum) decoherence. We further employ these informational quantities to analyze some widely used channels such as the complete decoherent channel, the depolarizing channel, the bit-flip channel, the transpose depolarizing channel, the amplitude damping channel, and the phase damping channel. Our analysis illustrates the intriguing interplay between classical and quantum decorrelations and sheds some light on the informational nature of decoherence.