Multipartite table methods

International audienceA unified view of most previous table-lookup-and-addition methods (bipartite tables, SBTM, STAM, and multipartite methods) is presented. This unified view allows a more accurate computation of the error entailed by these methods, which enables a wider design space exploration, leading to tables smaller than the best previously published ones by up to 50 percent. The synthesis of these multipartite architectures on Virtex FPGAs is also discussed. Compared to other methods involving multipliers, the multipartite approach offers the best speed/area tradeoff for precisions up to 16 bits. A reference implementation is available at www.ens-lyon.fr/LIP/Arenaire/

Low Precision Table Based Complex Reciprocal Approximation

International audienceA recently proposed complex valued division algorithm designed for efficient hardware implementations requires a prescaling step by a constant factor. Techniques for obtaining this prescaling factor have been mentioned by the authors, which serves to justify the feasibility of the algorithm but is inadequate for obtaining efficient implementations. Table based solutions are formulated in this paper for obtaining the prescaling factor, a low precision reciprocal approximation for a complex value, using techniques adopted from univariate function approximations. Two separate designs are proposed, one using a single table (a reference design) and another using generalized multipartite tables. The main contribution of this work is the extension of generalized multipartite table methods to a function of two variables. The multipartite tables derived were up to 67% more memory efficient than their single table counterparts

Experimental certification of millions of genuinely entangled atoms in a solid

Quantum theory predicts that entanglement can also persist in macroscopic physical systems, albeit difficulties to demonstrate it experimentally remain. Recently, significant progress has been achieved and genuine entanglement between up to 2900 atoms was reported. Here we demonstrate 16 million genuinely entangled atoms in a solid-state quantum memory prepared by the heralded absorption of a single photon. We develop an entanglement witness for quantifying the number of genuinely entangled particles based on the collective effect of directed emission combined with the nonclassical nature of the emitted light. The method is applicable to a wide range of physical systems and is effective even in situations with significant losses. Our results clarify the role of multipartite entanglement in ensemble-based quantum memories as a necessary prerequisite to achieve a high single-photon process fidelity crucial for future quantum networks. On a more fundamental level, our results reveal the robustness of certain classes of multipartite entangled states, contrary to, e.g., Schr\"odinger-cat states, and that the depth of entanglement can be experimentally certified at unprecedented scales.Comment: 11 pages incl. Methods and Suppl. Info., 4 figures, 1 table. v2: close to published version. See also parallel submission by Zarkeshian et al (1703.04709

Feynman graphs and the large dimensional limit of multipartite entanglement

We are interested in the properties of multipartite entanglement of a system composed by $n$ $d$-level parties (qudits). Focussing our attention on pure states we want to tackle the problem of the maximization of the entanglement for such systems. In particular we effort the problem trying to minimize the purity of the system. It has been shown that not for all systems this function can reach its lower bound, however it can be proved that for all values of $n$ a $d$ can always be found such that the lower bound can be reached. In this paper we examine the high-temperature expansion of the distribution function of the bipartite purity over all balanced bipartition considering its optimization problem as a problem of statistical mechanics. In particular we prove that the series characterizing the expansion converges and we analyze the behavior of each term of the series as $d\to \infty$.Comment: 29 pages, 11 figure

Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks

The Einstein-Podolsky-Rosen (EPR) paradox established a link between entanglement and nonlocality in quantum mechanics. EPR steering is the nonlocality associated with the EPR paradox and has traditionally only been investigated between two parties. Here, we present the first experimental observations of multipartite EPR steering, and of the genuine tripartite continuous variable entanglement of three mesoscopic optical systems. We explore different linear optics networks - each one with optimised asymmetries - that create multipartite steerable states containing different numbers of quantised optical modes (qumodes). By introducing asymmetric loss on a 7-qumode state, we characterize 8 regimes of directional steering, showing that N + 1 regimes exist for an N-qumode state. Further, we reveal the directional monogamy of steering, and experimentally demonstrate continuous variable one-sided semi device-independent quantum secret sharing. Our methods establish principles for the development of multiparty quantum communication protocols with asymmetric observers, and can be extended to qubits, whether photonic, atomic, superconducting, or otherwise.Comment: 7 pages, 4 figures. Comments are most welcome. Edited version to appear Jan 2015 in peer-reviewed journa