Chaotic spin-spin entanglement on a recursive lattice

We propose an exactly solvable multisite interaction spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice for the rigorous studies of chaotic entanglement. By making use of the generalized star-triangle transformation, we map the initial model onto an effective Ising one on a Husimi lattice, which we solve then exactly by applying the recursive method. Expressing the entanglement of the Heisenberg spins, that we quantify by means of the concurrence, in terms of the magnetic quantities of the system, we demonstrate its bifurcation and chaotic behavior. Furthermore, we show that the underlying chaos may slightly enhance the amount of the entanglement, and present on the phase diagram the transition lines from the uniform to periodic and from the periodic to chaotic regimes.Comment: 12 pages, 7 figures. Updated version for publicatio

Simulating arbitrary Gaussian circuits with linear optics

Linear canonical transformations of bosonic modes correspond to Gaussian unitaries, which comprise passive linear-optical transformations as effected by a multiport passive interferometer and active Bogoliubov transformations as effected by a nonlinear amplification medium. As a consequence of the Bloch-Messiah theorem, any Gaussian unitary can be decomposed into a passive interferometer followed by a layer of single-mode squeezers and another passive interferometer. Here, it is shown how to circumvent the need for active transformations. Namely, we provide a technique to simulate sampling from the joint input and output distributions of any Gaussian circuit with passive interferometry only, provided two-mode squeezed vacuum states are available as a prior resource. At the heart of the procedure, we exploit the fact that a beam splitter under partial time reversal simulates a two-mode squeezer, which gives access to an arbitrary Gaussian circuit without any nonlinear optical medium. This yields, in particular, a procedure for simulating with linear optics an extended boson sampling experiment, where photons jointly propagate through an arbitrary multimode Gaussian circuit, followed by the detection of output photon patterns.Comment: 12 pages, 4 figure

Generation of entanglement in systems of intercoupled qubits

We consider systems of two and three qubits, mutually coupled by Heisenberg-type exchange interaction and interacting with external laser fields. We show that these systems allow one to create maximally entangled Bell states, as well as three qubit Greenberger-Horne-Zeilinger and W states. In particular, we point out that some of the target states are the eigenstates of the initial bare system. Due to this, one can create entangled states by means of pulse area and adiabatic techniques, when starting from a separable (non-entangled) ground state. On the other hand, for target states, not present initially in the eigensystem of the model, we apply the robust stimulated Raman adiabatic passage and $\pi$ pulse techniques, that create desired coherent superpositions of non-entangled eigenstates.Comment: 9 pages, 7 figures. Updated version for publicatio

A compact entanglement distillery using realistic quantum memories

We adopt the beam splitter model for losses to analyse the performance of a recent compact continuous-variable entanglement distillation protocol [Phys. Rev. Lett. 108, 060502, (2012)] implemented using realistic quantum memories. We show that the decoherence undergone by a two-mode squeezed state while stored in a quantum memory can strongly modify the results of the preparatory step of the protocol. We find that the well-known method for locally increasing entanglement, phonon subtraction, may not result in entanglement gain when losses are taken into account. Thus, we investigate the critical number $m_c$ of phonon subtraction attempts from the matter modes of the quantum memory. If the initial state is not de-Gaussified within $m_c$ attempts, the protocol should be restarted to obtain any entanglement increase. Moreover, the condition $m_c>1$ implies an additional constraint on the subtraction beam splitter interaction transmissivity, viz. it should be about 50% for a wide range of protocol parameters. Additionally, we consider the average entanglement rate, which takes into account both the unavoidable probabilistic nature of the protocol and its possible failure as a result of a large number of unsuccessful subtraction attempts. We find that a higher value of the average entanglement can be achieved by increasing the subtraction beam splitter interaction transmissivity. We conclude that the compact distillation protocol with the practical constraints coming from realistic quantum memories allows a feasible experimental realization within existing technologies.Comment: 9 pages, 8 figures. Updated version for publicatio

Direct dialling of Haar random unitary matrices

Random unitary matrices find a number of applications in quantum information science, and are central to the recently defined boson sampling algorithm for photons in linear optics. We describe an operationally simple method to directly implement Haar random unitary matrices in optical circuits, with no requirement for prior or explicit matrix calculations. Our physically-motivated and compact representation directly maps independent probability density functions for parameters in Haar random unitary matrices, to optical circuit components. We go on to extend the results to the case of random unitaries for qubits

Generation and sampling of quantum states of light in a silicon chip

Implementing large instances of quantum algorithms requires the processing of many quantum information carriers in a hardware platform that supports the integration of different components. While established semiconductor fabrication processes can integrate many photonic components, the generation and algorithmic processing of many photons has been a bottleneck in integrated photonics. Here we report the on-chip generation and processing of quantum states of light with up to eight photons in quantum sampling algorithms. Switching between different optical pumping regimes, we implement the Scattershot, Gaussian and standard boson sampling protocols in the same silicon chip, which integrates linear and nonlinear photonic circuitry. We use these results to benchmark a quantum algorithm for calculating molecular vibronic spectra. Our techniques can be readily scaled for the on-chip implementation of specialised quantum algorithms with tens of photons, pointing the way to efficiency advantages over conventional computers

Etats intriqués et interaction cohérente dans les milieux résonants

The entanglement features of some solid state materials, as well as of particular systems of interacting atoms and fields are analyzed. A detailed investigation of the rich phase structure of low dimensional spin models, describing the natural mineral azurite and copper based coordination compounds, has revealed regimes with the most robust entanglement behavior. Using the dynamical system approach, the phase structure of some classical models on hierarchical (recursive) lattices has been also studied and, for the first time, the transition between chaotic and periodic regimes by means of tangent bifurcation has been detected.A detailed description of entanglement properties of three atoms trapped in a cavity within the dispersive limit is presented. A relatively simple tunability of the atomic interaction strength of the above system and its close relation to the problems of frustrated magnetism is shown. Furthermore, the propagation effects of two intense laser pulses in a medium of [lambda] atoms with unequal oscillator strengths are investigated. Obtained results are crucial in some problems of quantum information theory, as, e.g., in the analysis of population transfer mechanism in media possessing the above properties. Finally, the dissipation effects in a recently proposed compact continuous-variable entanglement distillation protocol have been analyzed. Despite additional constraints on the parameters of the protocol, the discussed entanglement distillation scheme in quantum memories is still possible to implement within emerging technologies.Nous analysons les caractéristiques d'intrication de quelques matériaux à l'état solide ainsi que des systèmes particuliers d'atomes et de champs en interaction. Une étude détaillée de la riche structure de phase des modèles de spins de basse dimension, décrivant le minéral naturel d'azurite et les composés de coordination à base de cuivre, a révélé des régimes à comportement d'intrication des plus robustes. En utilisant l'approche des systèmes dynamiques, la structure de phase de certains modèles classiques en réseaux hiérarchiques (récursifs) a aussi été étudiée et, pour la première fois, la transition entre régime chaotique et régime périodique au moyen de la bifurcation tangente a été détectée.Nous présentons une description détaillée des propriétés d'intrication de trois atomes piégés dans la limite dispersive. Une relativement simple accordabilité de la force atomique d'interaction de ce système et son étroite relation aux problèmes de frustration magnétique est démontrée. Les effets de propagation de pulses laser intenses dans un système atomique de type [lambda] avec des forces d'oscillateurs différentes sont analysés. Les résultats obtenus sont d'extrême importance dans des problèmes d'information quantique, comme par exemple, dans l'analyse du mécanisme de transfert de population dans des milieux ayant les propriétés définies ci-avant. Enfin, nous avons analysé les effets dissipatifs dans un protocole de distillation de l'intrication à variable continue récemment proposé. Malgré des contraintes additionnelles sur les paramètres du protocole, il est encore possible d'implémenter ce schéma de distillation évoqué ci-avant dans les technologies émergentes

Boson sampling with Gaussian measurements

We develop an alternative boson sampling model operating on single-photon states followed by linear interferometry and Gaussian measurements. The hardness proof for simulating such continuous-outcome measurements is established in two main steps, making use of the symmetry of quantum evolution under time reversal. Namely, we first construct a time-symmetric version of scattershot boson sampling in which, as opposed to the original proposal, both legs of a collection of two-mode squeezed vacuum states undergo parallel linear-optical transformations. This time-symmetric scattershot model yields, as a corollary, an instance of boson sampling from Gaussian states where photon counting is hard to simulate. Then, a time-reversed setup is used to develop a boson sampling model in which the simulation of Gaussian measurements − namely the outcome of unbalanced heterodyne detection − is proven to be computationally hard. These results illustrate how time symmetry may serve as a tool for analyzing the computational complexity of novel physically-motivated computational problems.SCOPUS: ar.jinfo:eu-repo/semantics/publishe