We introduce generalized cat states for d-level systems and obtain concise formulas for their entanglement swapping with generalized Bell states. We then use this to provide both a generalization to the d-level case and a transparent proof of validity for an already proposed protocol of secret sharing based on entanglement swapping.

We introduce the concepts of cohering and de-cohering power of quantum channels. Using the axiomatic defintion of coherence measure, we show that the optimization required for calculations of these measures can be restricted to pure input states and hence greatly simplified. We then use two examples of this measure, one based on the skew information and the other based on l1 norm, we find the cohering and de-cohering measures of a number of one, two and n-qubit channels. Contrary to a view at first sight, it is seen that quantum channels can have cohering power. It is also shown that a specific property of a qubit unitary map, is that it has equal cohering and de-cohering power in any basis. Finally we derive simple relations between cohering and de-cohering powers of unitary qubit gates and their tensor products, results which have physically interesting implications.

We study the effect of inhomogeneities in the magnetic field on the thermal entanglement of a two spin system. We show that in the ferromagnetic case a very small inhomogeneity is capable to produce large values of thermal entanglement. This shows that the absence of entanglement in the ferromagnetic Heisenberg system is highly unstable against inhomogeneoity of magnetic fields which is inevitably present in any solid state realization of qubits. 1

We introduce a protocol for quantum secret sharing based on reusable entangled states. The entangled state between the sender and the receiver acts only as a carrier to which data bits are entangled by the sender and disentangled from it by the receivers, all by local actions of simple gates. We also show that the interception by Eve or the cheating of one of the receivers introduces a quantum bit error rate (QBER) larger than 25 percent which can be detected by comparing a subsequence of the bits.

Using the matrix product formalism we formulate a natural p-species generalization of the asymmetric simple exclusion process. In this model particles hop with their own specific rate and fast particles can overtake slow ones with a rate equal to their relative speed. We obtain the algebraic structure and study the properties of the representations in detail. The uncorrelated steady state for the open system is obtained and in the ( p −→ ∞) limit, the dependence of its characteristics on the distribution of velocities is determined. It is shown that when the total arrival rate of particles exceeds a certain value, the density of the slowest particles rises abroptly.