Unification of different views of decoherence and discord

Macroscopic behavior such as the lack of interference patterns has been attributed to “decoherence,” a word with several possible definitions such as (1) the loss of off-diagonal density matrix elements, (2) the flow of information to the environment, (3) the loss of complementary information, and (4) the loss of the ability to create entanglement in a measurement. In this article, we attempt to unify these distinct definitions by providing general quantitative connections between them, valid for all finite-dimensional quantum systems or quantum processes. The most important application of our results is to the understanding of quantum discord, a measure of the nonclassicality of the correlations between quantum systems. We show that some popular measures of discord measure the information missing from the purifying system and hence quantify security, which can be stated operationally in terms of distillable secure bits. The results also give some strategies for constructing discord measures.

Figure 1

Two-path interferometer for single photons, with a phase shifter inserted in the lower arm. Identifying $\left\{\right|0\rangle ,|1\rangle \}$ as the which-path basis, the apparatus to the right of the vertical dashed line measures in the basis $\left(\right|0\rangle \pm e^{-i\phi }|1\rangle )/\sqrt{2}$. An environment $E$ may obtain some which-path information prior to this measurement.

Figure 2

How to convert the dynamical evolution of the system into a tripartite pure state.