Maximally nonlocal and monogamous quantum correlations

We introduce a version of the chained Bell inequality for an arbitrary number of measurement outcomes and use it to give a simple proof that the maximally entangled state of two d-dimensional quantum systems has no local component. That is, if we write its quantum correlations as a mixture of local correlations and general (not necessarily quantum) correlations, the coefficient of the local correlations must be zero. This suggests an experimental program to obtain as good an upper bound as possible on the fraction of local states and provides a lower bound on the amount of classical communication needed to simulate a maximally entangled state in dxd dimensions. We also prove that the quantum correlations violating the inequality are monogamous among nonsignaling correlations and, hence, can be used for quantum key distribution secure against postquantum (but nonsignaling) eavesdroppers.     

Entropy, entanglement, and area: analytical results for harmonic lattice systems

We revisit the question of the relation between entanglement, entropy, and area for harmonic lattice Hamiltonians corresponding to discrete versions of real free Klein-Gordon fields. For the ground state of the d-dimensional cubic harmonic lattice we establish a strict relationship between the surface area of a distinguished hypercube and the degree of entanglement between the hypercube and the rest of the lattice analytically, without resorting to numerical means. We outline extensions of these results to longer ranged interactions, finite temperatures, and for classical correlations in classical harmonic lattice systems. These findings further suggest that the tools of quantum information science may help in establishing results in quantum field theory that were previously less accessible.     

Recurrence and Pólya number of quantum walks

We analyze the recurrence probability (Pólya number) for d-dimensional unbiased quantum walks. A sufficient condition for a quantum walk to be recurrent is derived. As a by-product we find a simple criterion for localization of quantum walks. In contrast with classical walks, where the Pólya number is characteristic for the given dimension, the recurrence probability of a quantum walk depends in general on the topology of the walk, choice of the coin and the initial state. This allows us to change the character of the quantum walk from recurrent to transient by altering the initial state.     

Classical Limit and Quantum Logic

The analysis of the classical limit of quantum mechanics usually focuses on the state of the system. The general idea is to explain the disappearance of the interference terms of quantum states appealing to the decoherence process induced by the environment. However, in these approaches it is not explained how the structure of quantum properties becomes classical. In this paper, we consider the classical limit from a different perspective. We consider the set of properties of a quantum system and we study the quantum-to-classical transition of its logical structure. The aim is to open the door to a new study based on dynamical logics, that is, logics that change over time. In particular, we appeal to the notion of hybrid logics to describe semiclassical systems. Moreover, we consider systems with many characteristic decoherence times, whose sublattices of properties become distributive at different times.     

Optimal conclusive teleportation of a d-dimensional two-particle unknown quantum state

A conclusive teleportation protocol of a d-dimensional two-particle unknown quantum state using three d- dimensional particles in an arbitrary pure state is proposed. A sender teleports the unknown state conclusively to a receiver by using the positive operator valued measure（POVM） and introducing an ancillary qudit to perform the generalized Bell basis measurement, We calculate the optimal teleportation fidelity. We also discuss and analyse the reason why the information on the teleported state is lost in the course of the protocol,     

Optimal Conclusive Teleportation of an Arbitrary d-Dimensional N-Particle Unknown State via a Partially Entangled Quantum Channel

In the paper we generalize the standard teleportation to the conclusive teleportation case which can teleportan arbitrary d-dimensional N-particle unknown state via the partially entangled quantum channel. We show that onlyif the quantum channel satisfies a constraint condition can the most general d-dimensional N-particle unknown state beperfect conclusively teleported. We also present a method for optimal conclusively teleportation of the N-particle statesand for constructing the joint POVM which can discern the quantum states on the sender's (Alice's) side. Two typicalexamples are given so that one can see how our method works.     

Commensurate two-component bosons in an optical lattice: ground state phase diagram

Two sorts of bosons in an optical lattice at commensurate filling factors can form five stable super-fluid and insulating ground states with rich and nontrivial phase diagram. The structure of the ground state diagram is established by mapping a d-dimensional quantum system onto a (d+1)-dimensional classical loop-current model and Monte Carlo (MC) simulations of the latter. Surprisingly, the quantum phase diagram features, besides second-order lines, first-order transitions and two multicritical points. We explain why first-order transitions are generic for models with pairing interactions using microscopic and mean-field (MF) arguments. In some cases, the MC results strongly deviate from the MF predictions.     

Remote Preparation of Multipartite Equatorial Entangled States in High Dimensions with Three Parties

A scheme for probabilistic remotely preparing N-particle d-dimensional equatorial entangled states via entangled swapping with three parties is presented. The quantum channel is composed of N - 1 pairs of bipartite d-dimensional non-maximally entangled states and a tripartite d-dimension non-maximally entangled state. It is shown that the sender can help either of the two receivers to remotely prepare the original state, and the N-particle projective measurement and the generalized Hadamard transformation are needed in this scheme. The total success probability and classical communication cost are calculated.     

Dynamic localization in quantum dots: analytical theory

We analyze the response of a complex quantum-mechanical system (e.g., a quantum dot) to a time-dependent perturbation phi(t). Assuming the dot to be described by random-matrix theory for the Gaussian orthogonal ensemble, we find the quantum correction to the energy absorption rate as a function of the dephasing time t(phi). If phi(t) is a sum of d harmonics with incommensurate frequencies, the correction behaves similarly to that for the conductivity deltasigma(d)(t(phi)) in the d-dimensional Anderson model of the orthogonal symmetry class. For a generic periodic perturbation, the leading quantum correction is absent as in the systems of the unitary symmetry class, unless phi(-t+tau)=phi(t+tau) for some tau, which falls into the quasi-1D orthogonal universality class.     

Scaling functions for classical to quantum crossover in the transverse Ising model via an effective Wilsonian renormalization group approach in 4 – ε dimensions

The classical to quantum crossover, which occurs in d-dimensional transverse field Ising model-like systems decreasing the temperature to zero in the influence domain of the quantum critical point (QCP), is described by employing an effective Wilsonian renormalization group approach in 4 - ε dimensions. The basic ingredient of the treatment is the static action arising from a preliminary one-loop averaging over non-zero frequency modes, which enter the original quantum one. The crossover scaling functions for susceptibility and related thermodynamic quantities are obtained to first order in ε as explicit functions of the temperature and the applied magnetic field. In our static framework, which can be easily extended to other quantum systems exhibiting a critical line which terminates in a QCP, the suitable procedure for observing this type of crossover through genuine thermodynamic measurements is clarified consistently with available experiments. Remarkably, our basic idea and results may be usefully employed to explore also the dimensional crossover which takes place in classical Ising-like systems with slab or film geometry and, possibly, in other finite-size classical systems.     

Qudit state estimation with a fixed set of bases

We analyse the estimation of a pure d-dimensional quantum state with a finite number of measurements and compare several estimation schemes. In this paper we concentrate on consecutive von Neumann measurements on a finite number of identically prepared systems in dimensions d=2, d=4 and d=8. We propose two schemes with different types of fixed measurement directions. Inspired by integration theory our first approach uses the Halton sequence (a so-called quasi-Monte Carlo sequence) to obtain measurement directions (`sampling points') with high uniformity over the configuration space. Our second approach extends this idea and optimises the distribution of the measurement directions to yield a rather high fidelity in quantum state estimation. This optimisation results in a uniform distribution of the directions and large quantum distances between the directions. Furthermore we establish a link to mutually unbiased bases.     

Spin gases: quantum entanglement driven by classical kinematics

A spin gas is a natural extension of a classical gas. It consists of a large number of particles whose (random) motion is described classically, but, in addition, have internal (quantum mechanical) degrees of freedom that interact during collisions. For specific types of quantum interactions we determine the entanglement that occurs naturally in such systems. We analyze how the evolution of the quantum state is determined by the underlying classical kinematics of the gas. For the Boltzmann gas, we calculate the rate at which entanglement is produced and characterize the entanglement properties of the equilibrium state.     

Classical Representation of a Quantum System at Equilibrium

A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g., MD, integral equations, DFT) to describe quantum systems. The classical system has an effective temperature, local chemical potential, and pair interaction that are defined by requiring equivalence of the grand potential and its functional derivatives with respect to the external and pair potentials for the classical and quantum systems. Practical inversion of this mapping for the classical properties is effected via the hypernetted chain approximation, leading to representations as functionals of the quantum pair correlation function. As an illustration, the parameters of the classical system are determined approximately such that ideal gas and weak coupling RPA limits are preserved (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Classical Analog of Random Quantum States

We examine the statistical properties of a pure quantum state randomly chosen with respect to the uniform measure in a Hilbert space. Namely, we consider the distribution of outcomes of a fixed measurement performed on the random quantum state. We show that such distribution is completely analogous to the distribution of measurement outcomes of an a priori unknown classical random system. In particular, Shannon entropies of both distributions coincide. We study this correspondence between quantum and classical random systems and clarify its origin.     

Optimization through quantum annealing: theory and some applications

Quantum annealing is a promising tool for solving optimization problems, similar in some ways to the traditional (classical) simulated annealing of Kirkpatrick et al. Simulated annealing takes advantage of thermal fluctuations in order to explore the optimization landscape of the problem at hand, whereas quantum annealing employs quantum fluctuations. Intriguingly, quantum annealing has been proved to be more effective than its classical counterpart in many applications. We illustrate the theory and the practical implementation of both classical and quantum annealing – highlighting the crucial differences between these two methods – by means of results recently obtained in experiments, in simple toy-models, and more challenging combinatorial optimization problems (namely, Random Ising model and Travelling Salesman Problem). The techniques used to implement quantum and classical annealing are either deterministic evolutions, for the simplest models, or Monte Carlo approaches, for harder optimization tasks. We discuss the pro and cons of these approaches and their possible connections to the landscape of the problem addressed.     

Single-file diffusion of atomic and colloidal systems: asymptotic laws

We present a general derivation of the non-Fickian behavior for the self-diffusion of identically interacting particle systems with excluded mutual passage. We show that the conditional probability distribution of finding a particle at position x(t) after time t, when the particle was located at x(0) at t=0, follows a Gaussian distribution in the long-time limit, with variance 2W(t) approximately t(1/2) for overdamped systems and with variance 2W(t) approximately t for classical systems. The asymptotic behavior of the mean-squared displacement, W(t), is shown to be independent of the nature of interactions for homogeneous systems in the fluid state. Moreover, the long-time behavior of self-diffusion is determined by short-time and large-scale collective density fluctuations.     

Scheme for Implementing Assisted Cloning of an Unknown d-Dimension Equatorial Quantum State by Remote State Preparation

In this paper, we propose a protocol that can produce perfect copy of an unknown d-dimensional equatorial quantum state with assistance from a state preparer. In this protocol, the maximally and non-maximally entangled bipartite d-dimensional of states are used as the quantum channels, respectively. The first stage of the protocol requires usual teleportation. In the second stage of the protocol, with the assistance of the preparer, the perfect copy of an original unknown state can be produced.     

Quantum state reconstruction by entangled measurements

We address quantum state reconstruction for d-dimensional systems based on measuring, on the system of interest and a probe, of a single entangled observable defined on the bipartite system/probe Hilbert space. We show that the statistics of the measurement and the knowledge of the probe preparation suffice to reliably reconstruct the density matrix of the system, as well as the expectation value of any desired operator, including those not corresponding to observable quantities. The statistical robustness of the reconstruction is examined and a method is developed to minimize statistical errors by tuning the probe preparation. Numerical simulations of the whole reconstruction procedure are also presented for qubit systems.     

Multiparty-controlled Joint Remote Preparation of an Arbitrary m-qudit State with d-dimensional Greenberger-Horne-Zeilinger States

We present a scheme for multiparty-controlled joint remote preparation of an arbitrary m-qudit state by using d-dimensional Greenberger-Horne-Zeilinger (GHZ) states as the quantum channel. An arbitrary m-qudit state can be transmitted from two senders to a remote receiver in a quantum communication network under the controller’s control. The senders perform m-qudit measurements according to their information of prepared state, the controllers only need perform single-particle projective measurements. The receiver can prepare the original state on his quantum system by performing corresponding unitary operation according the measurement results of the senders and controllers. It is shown that an arbitrary m-qudit state in general form can be controlled joint remote prepared if and only if the receiver cooperates with all the senders and controllers.     

Multiparty-controlled teleportation of an arbitrary GHZ-class state by using a d-dimensional (N+2)-particle nonmaximally entangled state as the quantum channel

We present a scheme for multiparty-controlled teleportation of an arbitrary high-dimensional GHZ-class state with a d-dimensional (N+2)-particle GHZ state following some ideas from the teleportation (Chinese Physics B, 2007, 16: 2867). This scheme has the advantage of transmitting much fewer particles for controlled teleportation of an arbitrary multiparticle GHZ-class state. Moreover,we discuss the application of this scheme by using a nonmaximally entangled state as its quantum channel.