Giuseppe Florio

Maximally multipartite entangled states

We introduce the notion of maximally multipartite entangled states of

Statistical mechanics of the cluster Ising model

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Entanglement of two blocks of spins in the critical Ising model

qubits as a generalization of the bipartite case. These pure states have a bipartite entanglement that does not depend on the bipartition and is maximal for all possible bipartitions. They are solutions of a minimization problem. Examples for small

Bang-bang control of a qubit coupled to a quantum critical spin bath

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Probability-density-function characterization of multipartite entanglement

are investigated, both analytically and numerically.

Classical statistical mechanics approach to multipartite entanglement

We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.

Multipartite Entanglement and Frustration

We compute the entropy of entanglement of two blocks of L spins at a distance d in the ground state of an Ising chain in an external transverse magnetic field. We numerically study the von Neumann entropy for different values of the transverse field. At the critical point we obtain analytical results for blocks of size L =1 and 2. In the general case, the critical entropy is shown to be additive when d →. Finally, based on simple arguments, we derive an expression for the entropy at the critical point as a function of both L and d. This formula is in excellent agreement with numerical results.

Robust gates for holonomic quantum computation

Institute for Scientific Interchange, Viale Settimio Severo 65, I-10133 Torino, Italy(Dated: May 20, 2008)We analytically and numerically study the effects of pulsed control on the decoherence of a qubitcoupled to a quantum spin bath. When the environment is critical, decoherence is faster and weshow that the control is relatively more effective. Two coupling models are investigated, namely aqubit coupled to a bath via a single link and a spin star model, yielding results that are similar andconsistent.

Statistical mechanics of multipartite entanglement

We propose a method to characterize and quantify multipartite entanglement for pure states. The method hinges upon the study of the probability density function of bipartite entanglement and is tested on an ensemble of qubits in a variety of situations. This characterization is also compared to several measures of multipartite entanglement.

Entropy-driven phase transitions of entanglement

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions. We search for maximally multipartite entangled states, whose average purity is minimal, and recast this optimization problem into a problem of statistical mechanics, by introducing a cost function, a fictitious temperature and a partition function. By investigating the high-temperature expansion, we obtain the first three moments of the distribution. We find that the problem exhibits frustration.