International Journal of Quantum Information

For a discrete two-state quantum walk (QW) on the half-line with a general condition at the boundary, we formulate and prove a weak limit theorem describing the terminal behavior of its transition probabilities. In this context, localization is possible even for a walk predicated on the assumption of homogeneity. For the Hadamard walk on the half-line, the weak limit is shown to be independent of the initial coin state and to exhibit no localization.

We propose a scheme to implement a nondestructive Greenberger–Horne–Zeilinger (GHZ) state analyzer with atoms in low-Q cavities by taking the coherent light as quantum channel. It can also be applied to generate multi-atom entanglement state with high fidelity and entanglement degree. The analysis for the effect of atomic spontaneous emission on the fidelity and homodyne detection (HD) shows that the present scheme is not only robust in the condition of a bad cavity, but also feasible with the current technology due to the relaxed experimental condition.

A conjecture of Ramanujan that was later proved by Nagell is used to show on the basis of matching dimensions that only three n-qubit systems, for n = 1, 2, 6, can possibly share an isomorphism of their symmetry algebras with those of rotations in corresponding dimensions 3, 6, 91. Such isomorphisms are valuable for use in quantum information. Simple algebraic analysis, however, already rules out the last case so that one and two qubits are the only instances of such isomorphism of the algebras and of a local homomorphism of the corresponding symmetry groups. A more mathematical topological analysis of the group spaces is also provided demonstrating their topological inequivalence.

A model of dynamics of quantum correlations of two modes quasi-Bell cat states, based on Glauber coherent states, is considered. The analytic expressions of pairwise entanglement of formation, quantum discord and its geometrized variant are explicitly derived. We analyze the distribution of quantum correlations between the two modes and the environment. We show that, in contrast with squared concurrence, entanglement of formation, quantum discord and geometric quantum discord do not follow the property of monogamy except in some particular situations that we discuss.

We study bipartite and multipartite correlations of several coupled qubits within a common non-Markovian bath using the hierarchy equation method. This method does not use the rotating-wave and Born–Markovian approximations. The interaction between the qubits and their coupling strength with the bath have remarkable influence on the dynamics of quantum correlations. The entanglement sudden death (ESD) phenomenon, the amount of stationary state concurrence and spin squeezing can be controled by the non-Markovianity of the environment and interactions between qubits. These properties may be useful for purposes of quantum information processing with multiqubit system in non-Markovian environments.

We study the entanglement conditions of two quite general classes of two-mode non-Gaussian states. Using computable cross norm and realignment criterion, we obtain the sufficient conditions of entanglement for coherently added or subtracted two-mode squeezed thermal states, and the sufficient condition of entanglement for any photon number entangled state (PNES) evolving in a thermal noise and amplitude damping channel.

In this work, the quantum discord and tripartite entanglement in the presence of an asymptotically flat static black hole are discussed. The total correlation, quantum discord, and classical correlation are found to exhibit decreasing behavior with increasing Hawking temperature. It is shown that the classical correlation is less than the quantum discord in the full range of Hawking temperature. The tripartite entanglements for Greenberger–Horne–Zeilinger (GHZ) and W-states also exhibit decreasing behavior with increasing Hawking temperature. When the Hawking temperature approaches the infinite limit, the tripartite entanglements of the GHZ and W-states reduce, in terms of the π-tangle, to 52% and 33% of the corresponding values in the flat space limit, respectively.