A class of quantum many-body states that can be efficiently simulated

We introduce the multi-scale entanglement renormalization ansatz (MERA), an efficient representation of certain quantum many-body states on a D-dimensional lattice. Equivalent to a quantum circuit with logarithmic depth and distinctive causal structure, the MERA allows for an exact evaluation of local expectation values. It is also the structure underlying entanglement renormalization, a coarse-graining scheme for quantum systems on a lattice that is focused on preserving entanglement.Comment: 4 pages, 5 figure

Optimal distillation of a GHZ state

We present the optimal local protocol to distill a Greenberger-Horne-Zeilinger (GHZ) state from a single copy of any pure state of three qubits.Comment: RevTex, 4 pages, 2 figures. Published version, some references adde

Entanglement for rank-2 mixed states

In a recent paper, Rungta et. al. [Phys. Rev. A, 64, 042315, 2001] introduced a measure of mixed-state entanglement called the I-concurrence for arbitrary pairs of qudits. We find an exact formula for an entanglement measure closely related to the I-concurrence, the I-tangle, for all mixed states of two qudits having no more than two nonzero eigenvalues. We use this formula to provide a tight upper bound for the entanglement of formation for rank-2 mixed states of a qubit and a qudit.Comment: 5 pages, uses amsthm and mathrsf

Frustrated antiferromagnets with entanglement renormalization: ground state of the spin-1/2 Heisenberg model on a kagome lattice

Entanglement renormalization techniques are applied to numerically investigate the ground state of the spin-1/2 Heisenberg model on a kagome lattice. Lattices of N={36,144,inf} sites with periodic boundary conditions are considered. For the infinite lattice, the best approximation to the ground state is found to be a valence bond crystal (VBC) with a 36-site unit cell, compatible with a previous proposal. Its energy per site, E=-0.43221, is an exact upper bound and is lower than the energy of any previous (gapped or algebraic) spin liquid candidate for the ground state.Comment: 6 pages, 7 figures, RevTeX 4. Revised version with improved numerical results

Strong monotonicity in mixed-state entanglement manipulation

A strong entanglement monotone, which never increases under local operations and classical communications (LOCC), restricts quantum entanglement manipulation more strongly than the usual monotone since the usual one does not increase on average under LOCC. We propose new strong monotones in mixed-state entanglement manipulation under LOCC. These are related to the decomposability and 1-positivity of an operator constructed from a quantum state, and reveal geometrical characteristics of entangled states. These are lower bounded by the negativity or generalized robustness of entanglement.Comment: 6 pages and 1 figure. A brief discussion about the connection to asymptotic distillability was adde

Entanglement dynamics in the Lipkin-Meshkov-Glick model

The dynamics of the one-tangle and the concurrence is analyzed in the Lipkin-Meshkov-Glick model which describes many physical systems such as the two-mode Bose-Einstein condensates. We consider two different initial states which are physically relevant and show that their entanglement dynamics are very different. A semiclassical analysis is used to compute the one-tangle which measures the entanglement of one spin with all the others, whereas the frozen-spin approximation allows us to compute the concurrence using its mapping onto the spin squeezing parameter.Comment: 11 pages, 11 EPS figures, published versio

Entanglement in a second order quantum phase transition

We consider a system of mutually interacting spin 1/2 embedded in a transverse magnetic field which undergo a second order quantum phase transition. We analyze the entanglement properties and the spin squeezing of the ground state and show that, contrarily to the one-dimensional case, a cusp-like singularity appears at the critical point $\lambda_c$, in the thermodynamic limit. We also show that there exists a value $\lambda_0 \geq \lambda_c$ above which the ground state is not spin squeezed despite a nonvanishing concurrence.Comment: 4 pages, 4 EPS figures, minor corrections added and title change