ZhiHua Guo

Distinguishing classical correlations from quantum correlations

The aim of this paper is to distinguish classical correlations from quantum ones. First, a new characterization of a classical correlated (CC) state is established. Corresponding results for the left and right classical correlations are also obtained. Second, a sufficient and necessary condition for a convex combination of two CC states to be CC is given. It is proved that the set CC(HA ⊗ HB) of all CC states on HA ⊗ HB is a perfect, nowhere dense and compact subset of the metric space D(HA ⊗ HB) of all states (density operators) on HA ⊗ HB. Based on our new characterization of CC states, a quantity Q(ρ) is associated with a state ρ. It is shown that a state ρ is CC if and only if Q(ρ) = 0. In particular, we prove that the Werner state Wλ in a two-qubit system with a single real parameter λ is CC if and only if λ = 0.25.

An upper bound for the adiabatic approximation error

In this paper, we derive an upper bound for the adiabatic approximation error, which is the distance between the exact solution to a Schrödinger equation and the adiabatic approximation solution. As an application, we obtain an upper bound for 1 minus the fidelity of the exact solution and the adiabatic approximation solution to a Schrödinger equation.

Robustness of quantum correlations against linear noise

Relative robustness of quantum correlations (RRoQC) of a bipartite state is firstly introduced relative to a classically correlated state. Robustness of quantum correlations (RoQC) of a bipartite state is then defined as the minimum of RRoQC of the state relative to all classically correlated ones. It is proved that as a function on quantum states, RoQC is nonnegative, lower semi-continuous and neither convex nor concave; especially, it is zero if and only if the state is classically correlated. Thus, RoQC not only quantifies the endurance of quantum correlations of a state against linear noise, but also can be used to distinguish between quantum and classically correlated states. Furthermore, the effects of local quantum channels on the robustness are explored and characterized.