Paola Verrucchi

Studying Quantum Spin Systems through Entanglement Estimators

We study the field dependence of the entanglement of formation in anisotropic S=1/2 antiferromagnetic chains displaying a T=0 field-driven quantum phase transition. The analysis is carried out via quantum Monte Carlo simulations. At zero temperature the entanglement estimators show abrupt changes at and around criticality, vanishing below the critical field, in correspondence with an exactly factorized state, and then immediately recovering a finite value upon passing through the quantum phase transition. At the quantum-critical point, a deep minimum in the pairwise-to-global entanglement ratio shows that multispin entanglement is strongly enhanced; moreover this signature represents a novel way of detecting the quantum phase transition of the system, relying entirely on entanglement estimators.

Entanglement and factorized ground states in two-dimensional quantum antiferromagnets.

Making use of exact results and quantum Monte Carlo data for the entanglement of formation, we show that the ground state of anisotropic two-dimensional S=1/2 antiferromagnets in a uniform field takes the classical-like form of a product state for a particular value and orientation of the field, at which the purely quantum correlations due to entanglement disappear. Analytical expressions for the energy and the form of such states are given, and a novel type of exactly solvable two-dimensional quantum models is therefore singled out. Moreover, we show that the field-induced quantum phase transition present in the models is unambiguously characterized by a cusp minimum in the pairwise-to-global entanglement ratio R, marking the quantum-critical enhancement of multipartite entanglement.

Nonperturbative Entangling Gates between Distant Qubits Using Uniform Cold Atom Chains

We propose a new fast scalable method for achieving a two-qubit entangling gate between arbitrary distant qubits in a network by exploiting dispersionless propagation in uniform chains. This is achieved dynamically by switching on a strong interaction between the qubits and a bus formed by a nonengineered chain of interacting qubits. The quality of the gate scales very efficiently with qubit separations. Surprisingly, a sudden switching of the couplings is not necessary. Moreover, our gate mechanism works for multiple gate operations without resetting the bus. We propose a possible experimental realization in cold atoms trapped in optical lattices and near field Fresnel trapping potentials.

Long quantum channels for high-quality entanglement transfer

High-quality quantum-state and entanglement transfer can be achieved in an unmodulated spin bus operating in the ballistic regime, which occurs when the endpoint qubits A and B are nonperturbatively coupled to the chain by a suitable exchange interaction j0. Indeed, the transition amplitude characterizing the transfer quality exhibits a maximum for a finite optimal value jopt0(N), where N is the channel length. We show that jopt0(N) scales as N?1/6 for large N and that it ensures a high-quality entanglement transfer even in the limit of arbitrarily long channels, almost independently of the channel initialization. For instance, for any chain length the average quantum-state transmission fidelity exceeds 90% and decreases very little in a broad neighbourhood of jopt0(N). We emphasize that, taking the reverse point of view, should j0 be experimentally constrained, high-quality transfer can still be obtained by adjusting the channel length to its optimal value.

Divergence of the entanglement range in low-dimensional quantum systems

We study the pairwise entanglement close to separable ground states of a class of one dimensional quantum spin models. At T=0 we find that such ground states separate regions, in the space of the Hamiltonian parameters, which are characterized by qualitatively different types of entanglement, namely parallel and antiparallel entanglement; we further demonstrate that the range of the Concurrence diverges while approaching separable ground states, therefore evidencing that such states, with uncorrelated fluctuations, are reached by a long range reshuffling of the entanglement. We generalize our results to the analysis of quantum phase transitions occurring in bosonic and fermionic systems. Finally, the effects of finite temperature are considered: At T>0 we evidence the existence of a region where no pairwise entanglement survives, so that entanglement, if present, is genuinely multipartite.

Optimal dynamics for quantum-state and entanglement transfer through homogeneous quantum systems

It is shown that eective quantum-state and entanglement transfer can be obtained by inducing a coherent dynamics in quantum wires with homogeneous intrawire interactions. This goal is accom- plished by tuning the coupling between the wire endpoints and the two qubits there attached, to an optimal value. A general procedure to determine such value is devised, and scaling laws between the optimal coupling and the length of the wire are found. The procedure is implemented in the case of a wire consisting of a spin- 1 XY chain: results for the time dependence of the quantities which characterize quantum-state and entanglement transfer are found of extremely good quality and al- most independent of the wire length. The present approach does not require ad hoc engineering of the intrawire interactions nor a specic initial pulse shaping, and can be applied to a vast class of quantum channels. One of the most commonly requested conditions in quantum communication and computation protocols is that two distant parties, typically Alice and Bob, share a couple of entangled qubits. When the physical objects encoding the qubits can travel, as in the case of optical photons, the above goal can be accomplished by creat- ing the entangled couple in a limited region of space and then letting the qubits fly where necessary. On the other hand, when qubits are realized via intrinsically localized

99%-fidelity ballistic quantum-state transfer through long uniform channels

Quantum-state transfer with fidelity higher than 0.99 can be achieved in the ballistic regime of an arbitrarily long one-dimensional chain with uniform nearest-neighbor interaction, except for the two pairs of mirror symmetric extremal bonds, say x (first and last) and y (second and last-but-one). These have to be roughly tuned to suitable values x ~ 2 N^{-1/3} and y ~ 2^{3/4} N^{-1/6}, N being the chain length. The general framework can describe the end-to-end response in different models, such as fermion or boson hopping models and XX spin chains.

Reading entanglement in terms of spin configurations in quantum magnets

Abstract. We consider a quantum many-body system made of N interacting S=1/2 spins on a lattice, and develop a formalism which allows to extract, out of conventional magnetic observables, the quantum probabilities for any selected spin pair to be in maximally entangled or factorized two-spin states. This result is used in order to capture the meaning of entanglement properties in terms of magnetic behavior. In particular, we consider the concurrence between two spins and show how its expression extracts information on the presence of bipartite entanglement out of the probability distributions relative to specific sets of two-spin quantum states. We apply the above findings to the antiferromagnetic Heisenberg model in a uniform magnetic field, both on a chain and on a two-leg ladder. Using Quantum Monte Carlo simulations, we obtain the above probability distributions and the associated entanglement, discussing their evolution under application of the field.

Detection of XY behavior in weakly anisotropic quantum antiferromagnets on the square lattice

We consider the Heisenberg antiferromagnet on the square lattice with S=1/2 and very weak easy-plane exchange anisotropy; by means of the quantum Monte Carlo method, based on the continuous-time loop algorithm, we find that the thermodynamics of the model is highly sensitive to the presence of tiny anisotropies and is characterized by a crossover between isotropic and planar behavior. We discuss the mechanism underlying the crossover phenomenon and show that it occurs at a temperature which is characteristic of the model. The expected Berezinskii-Kosterlitz-Thouless transition is observed below the crossover: a finite range of temperatures consequently opens for experimental detection of noncritical 2D XY behavior. Direct comparison is made with uniform susceptibility data relative to the S=1/2 layered antiferromagnet Sr2CuO2Cl2.

Two-dimensional quantum Heisenberg antiferromagnet: Effective-Hamiltonian approach to the thermodynamics

In this paper we present an extensive study of the thermodynamic properties of the two-dimensional quantum Heisenberg antiferromagnet on the square lattice; the problem is tackled by the pure-quantum self-consistent harmonic approximation, previously applied to quantum spin systems with easy-plane anisotropies, modeled to fit the peculiar features of an isotropic system. Internal energy, specific heat, correlation functions, staggered susceptibility, and correlation length are shown for different values of the spin, and compared with the available high-temperature expansion and quantum Monte Carlo results, as well as with the available experimental data.