Lower bound of concurrence based on D-type positive map

In this paper, by using the D-type map, we provide an analytical lower bound of concurrence of arbitrary dimensional bipartite quantum system. It is shown that this lower bound is able to improve the existing bounds and detect entanglement better.

Structure of states for which each localized dynamics reduces to a localized subdynamics

We consider a bipartite quantum system [Formula: see text] (including parties [Formula: see text] and [Formula: see text]), interacting with an environment [Formula: see text] through a localized quantum dynamics [Formula: see text]. We call a quantum dynamics [Formula: see text] localized if, e.g. the party [Formula: see text] is isolated from the environment and only [Formula: see text] interacts with the environment: [Formula: see text], where [Formula: see text] is the identity map on the part [Formula: see text] and [Formula: see text] is a completely positive (CP) map on the both [Formula: see text] and [Formula: see text]. We will show that the reduced dynamics of the system is also localized as [Formula: see text], where [Formula: see text] is a CP map on [Formula: see text], if and only if the initial state of the system-environment is a Markov state. We then generalize this result to the two following cases: when both [Formula: see text] and [Formula: see text] interact with a same environment, and when each party interacts with its local environment.

On the von Neumann entropy of certain quantum walks subject to decoherence

In this paper, we consider a discrete-time quantum walk on the N-cycle governed by the condition that at every time step of the walk, the option persists, with probability p, of exercising a projective measurement on the coin degree of freedom. For a bipartite quantum system of this kind, we prove that the von Neumann entropy of the total density operator converges to its maximum value. Thus, when influenced by decoherence, the mutual information between the two subsystems corresponding to the space of the coin and the space of the walker must eventually diminish to zero. Put plainly, any level of decoherence greater than zero forces the system to become completely ‘disentangled’ eventually.