Local noise can enhance entanglement teleportation

Recently we have considered two-qubit teleportation via mixed states of four qubits and defined the generalized singlet fraction. For single-qubit teleportation, Badziag {\em et al.} [Phys. Rev. A {\bf 62}, 012311 (2000)] and Bandyopadhyay [Phys. Rev. A {\bf 65}, 022302 (2002)] have obtained a family of entangled two-qubit mixed states whose teleportation fidelity can be enhanced by subjecting one of the qubits to dissipative interaction with the environment via an amplitude damping channel. Here, we show that a dissipative interaction with the local environment via a pair of time-correlated amplitude damping channels can enhance fidelity of entanglement teleportation for a class of entangled four-qubit mixed states. Interestingly, we find that this enhancement corresponds to an enhancement in the quantum discord for some states.Comment: 10 page

The metastable minima of the Heisenberg spin glass in a random magnetic field

We have studied zero temperature metastable states in classical $m$-vector component spin glasses in the presence of $m$-component random fields (of strength $h_{r}$) for a variety of models, including the Sherrington Kirkpatrick (SK) model, the Viana Bray (VB) model and the randomly diluted one-dimensional models with long-range power law interactions. For the SK model we have calculated analytically its complexity (the log of the number of minima) for both the annealed case and the quenched case, both for fields above and below the de Almeida Thouless (AT) field ($h_{AT} > 0$ for $m>2$). We have done quenches starting from a random initial state by putting spins parallel to their local fields until convergence and found that in zero field it always produces minima which have zero overlap with each other. For the $m=2$ and $m=3$ cases in the SK model the final energy reached in the quench is very close to the energy $E_c$ at which the overlap of the states would acquire replica symmetry breaking features. These minima have marginal stability and will have long-range correlations between them. In the SK limit we have analytically studied the density of states $\rho(\lambda)$ of the Hessian matrix in the annealed approximation. Despite the absence of continuous symmetries, the spectrum extends down to zero with the usual $\sqrt{\lambda}$ form for the density of states for $h_{r}<h_{AT}$. However, when $h_{r}>h_{AT}$, there is a gap in the spectrum which closes up as $h_{AT}$ is approached. For the VB model and the other models our numerical work shows that there always exist some low-lying eigenvalues and there never seems to be a gap. There is no sign of the AT transition in the quenched states reached from infinite temperature for any model but the SK model, which is the only model which has zero complexity above $h_{AT}$.Comment: 16 pages, 8 figures (with modifications), rewritten text and abstrac

Teleportation with a Mixed State of Four Qubits and the Generalized Singlet Fraction

Recently, an explicit protocol ${\cal E}_0$ for faithfully teleporting arbitrary two-qubit states using genuine four-qubit entangled states was presented by us [Phys. Rev. Lett. {\bf 96}, 060502 (2006)]. Here, we show that ${\cal E}_0$ with an arbitrary four-qubit mixed state resource $\Xi$ is equivalent to a generalized depolarizing bichannel with probabilities given by the maximally entangled components of the resource. These are defined in terms of our four-qubit entangled states. We define the generalized singlet fraction ${\cal G}[\Xi]$, and illustrate its physical significance with several examples. We argue that in order to teleport arbitrary two-qubit states with average fidelity better than is classically possible, we have to demand that ${\cal G}[\Xi] > 1/2$. In addition, we conjecture that when ${\cal G}[\Xi] < 1/4$ then no entanglement can be teleported. It is shown that to determine the usefulness of $\Xi$ for ${\cal E}_0$, it is necessary to analyze ${\cal G}[\Xi]$.Comment: 11 page

The Complexity of Vector Spin Glasses

We study the annealed complexity of the m-vector spin glasses in the Sherrington-Kirkpatrick limit. The eigenvalue spectrum of the Hessian matrix of the Thouless-Anderson-Palmer (TAP) free energy is found to consist of a continuous band of positive eigenvalues in addition to an isolated eigenvalue and (m-1) null eigenvalues due to rotational invariance. Rather surprisingly, the band does not extend to zero at any finite temperature. The isolated eigenvalue becomes zero in the thermodynamic limit, as in the Ising case (m=1), indicating that the same supersymmetry breaking recently found in Ising spin glasses occurs in vector spin glasses.Comment: 4 pages, 2 figure

Teleportation and Dense Coding with Genuine Multipartite Entanglement

We present an explicit protocol ${\cal E}_0$ for faithfully teleporting an arbitrary two-qubit state via a genunie four-qubit entangled state. By construction, our four-partite state is not reducible to a pair of Bell states. Its properties are compared and contrasted with those of the four-party GHZ and W states. We also give a dense coding scheme ${\cal D}_0$ involving our state as a shared resource of entanglement. Both ${\cal D}_0$ and ${\cal E}_0$ indicate that our four-qubit state is a likely candidate for the genunine four-partite analogue to a Bell state.Comment: 9 pages, 0 figur

Origin of the Growing Length Scale in M-p-Spin Glass Models

Two versions of the M-p-spin glass model have been studied with the Migdal-Kadanoff renormalization group approximation. The model with p=3 and M=3 has at mean-field level the ideal glass transition at the Kauzmann temperature and at lower temperatures still the Gardner transition to a state like that of an Ising spin glass in a field. The model with p=3 and M=2 has only the Gardner transition. In the dimensions studied, d=2,3 and 4, both models behave almost identically, indicating that the growing correlation length as the temperature is reduced in these models -- the analogue of the point-to-set length scale -- is not due to the mechanism postulated in the random first order transition theory of glasses, but is more like that expected on the analogy of glasses to the Ising spin glass in a field.Comment: 5 pages, 3 figures, revised versio

First-Order Transition and Critical End-Point in Vortex Liquids in Layered Superconductors

We calculate various thermodynamic quantities of vortex liquids in a layered superconductor by using the nonperturbative parquet approximation method, which was previously used to study the effect of thermal fluctuations in two-dimensional vortex systems. We find there is a first-order transition between two vortex liquid phases which differ in the magnitude of their correlation lengths. As the coupling between the layers increases,the first-order transition line ends at a critical point. We discuss the possible relation between this critical end-point and the disappearance of the first-order transition which is observed in experiments on high temperature superconductors at low magnetic fields.Comment: 9 pages, 5 figure