Multipartite entanglement percolation

We present percolation strategies based on multipartite measurements to propagate entanglement in quantum networks. We consider networks spanned on regular lattices whose bonds correspond to pure but non-maximally entangled pairs of qubits, with any quantum operation allowed at the nodes. Despite significant effort in the past, improvements over naive (classical) percolation strategies have been found for only few lattices, often with restrictions on the initial amount of entanglement in the bonds. In contrast, multipartite entanglement percolation outperform the classical percolation protocols, as well as all previously known quantum ones, over the entire range of initial entanglement and for every lattice that we considered.Comment: revtex4, 4 page

Connecting the generalized robustness and the geometric measure of entanglement

The main goal of this paper is to provide a connection between the generalized robustness of entanglement ($R_g$) and the geometric measure of entanglement ($E_{GME}$). First, we show that the generalized robustness is always higher than or equal to the geometric measure. Then we find a tighter lower bound to $R_g(\rho)$ based only on the purity of $\rho$ and its maximal overlap to a separable state. As we will see it is also possible to express this lower bound in terms of $E_{GME}$.Comment: 4 pages, 2 figures. Comments welcome. v2: text improved - some completely symmetric states were used to illustrate the results. Comments are always welcome! v3: minor changes. Accepted by Phys. Rev. A. v4: results on symmetric states fixe

On Lie-algebraic solutions of the type IIB matrix model

A systematic search for Lie algebra solutions of the type IIB matrix model is performed. Our survey is based on the classification of all Lie algebras for dimensions up to five and of all nilpotent Lie algebras of dimension six. It is shown that Lie-type solutions of the equations of motion of the type IIB matrix model exist and they correspond to certain nilpotent and solvable Lie algebras. Their representation in terms of Hermitian matrices is discussed in detail. These algebras give rise to certain non-commutative spaces for which the corresponding star-products are provided. Finally the issue of constructing quantized compact nilmanifolds and solvmanifolds based on the above algebras is addressed.Comment: 22 page

Are all maximally entangled states pure?

We study if all maximally entangled states are pure through several entanglement monotones. In the bipartite case, we find that the same conditions which lead to the uniqueness of the entropy of entanglement as a measure of entanglement, exclude the existence of maximally mixed entangled states. In the multipartite scenario, our conclusions allow us to generalize the idea of monogamy of entanglement: we establish the \textit{polygamy of entanglement}, expressing that if a general state is maximally entangled with respect to some kind of multipartite entanglement, then it is necessarily factorized of any other system.Comment: 5 pages, 1 figure. Proof of theorem 3 corrected e new results concerning the asymptotic regime include

Quantum Structure of Space Near a Black Hole Horizon

We describe a midi-superspace quantization scheme for generic single horizon black holes in which only the spatial diffeomorphisms are fixed. The remaining Hamiltonian constraint yields an infinite set of decoupled eigenvalue equations: one at each spatial point. The corresponding operator at each point is the product of the outgoing and ingoing null convergences, and describes the scale invariant quantum mechanics of a particle moving in an attractive $1/X^2$ potential. The variable $X$ that is analoguous to particle position is the square root of the conformal mode of the metric. We quantize the theory via Bohr quantization, which by construction turns the Hamiltonian constraint eigenvalue equation into a finite difference equation. The resulting spectrum gives rise to a discrete spatial topology exterior to the horizon. The spectrum approaches the continuum in the asymptotic region.Comment: References added and typos corrected. 21 pages, 1 figur