Entangled symmetric states of N qubits with all positive partial transpositions

From both theoretical and experimental points of view symmetric states constitute an important class of multipartite states. Still, entanglement properties of these states, in particular those with positive partial transposition (PPT), lack a systematic study. Aiming at filling in this gap, we have recently affirmatively answered the open question of existence of four-qubit entangled symmetric states with positive partial transposition and thoroughly characterized entanglement properties of such states [J. Tura et al., Phys. Rev. A 85, 060302(R) (2012)] With the present contribution we continue on characterizing PPT entangled symmetric states. On the one hand, we present all the results of our previous work in a detailed way. On the other hand, we generalize them to systems consisting of arbitrary number of qubits. In particular, we provide criteria for separability of such states formulated in terms of their ranks. Interestingly, for most of the cases, the symmetric states are either separable or typically separable. Then, edge states in these systems are studied, showing in particular that to characterize generic PPT entangled states with four and five qubits, it is enough to study only those that assume few (respectively, two and three) specific configurations of ranks. Finally, we numerically search for extremal PPT entangled states in such systems consisting of up to 23 qubits. One can clearly notice regularity behind the ranks of such extremal states, and, in particular, for systems composed of odd number of qubits we find a single configuration of ranks for which there are extremal states.Comment: 16 pages, typos corrected, some other improvements, extension of arXiv:1203.371

Four-qubit entangled symmetric states with positive partial transpositions

We solve the open question of the existence of four-qubit entangled symmetric states with positive partial transpositions (PPT states). We reach this goal with two different approaches. First, we propose a half-analytical-half-numerical method that allows to construct multipartite PPT entangled symmetric states (PPTESS) from the qubit-qudit PPT entangled states. Second, we adapt the algorithm allowing to search for extremal elements in the convex set of bipartite PPT states [J. M. Leinaas, J. Myrheim, and E. Ovrum, Phys. Rev. A 76, 034304 (2007)] to the multipartite scenario. With its aid we search for extremal four-qubit PPTESS and show that generically they have ranks (5,7,8). Finally, we provide an exhaustive characterization of these states with respect to their separability properties.Comment: 5+4 pages, improved version, title slightly modifie

Local Unitary Classification of Arbitrary Dimensional Multipartite Pure States

We propose a practical entanglement classification scheme for general multipartite pure states in arbitrary dimensions under local unitary equivalence by exploiting the high order singular value decomposition technique and local symmetries of the states. By virtue of this scheme, the method of determining the local unitary equivalence of $n$-qubit states proposed by Kraus is extended to the case for arbitrary dimensional multipartite states.Comment: 10 pages; published in Phys. Rev. Let

Entanglement classes of symmetric Werner states

The symmetric Werner states for $n$ qubits, important in the study of quantum nonlocality and useful for applications in quantum information, have a surprisingly simple and elegant structure in terms of tensor products of Pauli matrices. Further, each of these states forms a unique local unitary equivalence class, that is, no two of these states are interconvertible by local unitary operations.Comment: 4 pages, 1 table, additional references in version 2, revised abstract and introduction in version 3, small clarifications for published version in version

An artificial retina processor for track reconstruction at the LHC crossing rate

The goal of the INFN-RETINA R&D project is to develop and implement a computational methodology that allows to reconstruct events with a large number (> 100) of charged-particle tracks in pixel and silicon strip detectors at 40 MHz, thus matching the requirements for processing LHC events at the full bunch-crossing frequency. Our approach relies on a parallel pattern-recognition algorithm, dubbed artificial retina, inspired by the early stages of image processing by the brain. In order to demonstrate that a track-processing system based on this algorithm is feasible, we built a sizable prototype of a tracking processor tuned to 3 000 patterns, based on already existing readout boards equipped with Altera Stratix III FPGAs. The detailed geometry and charged-particle activity of a large tracking detector currently in operation are used to assess its performances. We report on the test results with such a prototype

Cell type-specific plasticity of striatal projection neurons in parkinsonism and L-DOPA-induced dyskinesia

The striatum is widely viewed as the fulcrum of pathophysiology in Parkinson’s disease (PD) and L-DOPA-induced dyskinesia (LID). In these disease states, the balance in activity of striatal direct pathway spiny projection neurons (dSPNs) and indirect pathway spiny projection neurons (iSPNs) is disrupted, leading to aberrant action selection. However, it is unclear whether countervailing mechanisms are engaged in these states. Here we report that iSPN intrinsic excitability and excitatory corticostriatal synaptic connectivity were lower in PD models than normal; ​L-DOPA treatment restored these properties. Conversely, dSPN intrinsic excitability was elevated in tissue from PD models and suppressed in LID models. Although the synaptic connectivity of dSPNs did not change in PD models, it fell with ​L-DOPA treatment. In neither case, however, was the strength of corticostriatal connections globally scaled. Thus, SPNs manifested homeostatic adaptations in intrinsic excitability and in the number but not strength of excitatory corticostriatal synapses

Transcriptomic analysis of resistant and susceptible banana corms in response to infection by Fusarium oxysporum f. sp. cubense tropical race 4

Fusarium wilt disease, caused by Fusarium oxysporum f. sp. cubense, especially by tropical race 4 (Foc TR4), is threatening the global banana industry. Musa acuminata Pahang, a wild diploid banana that displays strong resistance to Foc TR4, holds great potential to understand the underlying resistance mechanisms. Microscopic examination reports that, in a wounding inoculation system, the Foc TR4 infection processes in roots of Pahang (resistant) and a triploid cultivar Brazilian (susceptible) were similar by 7 days post inoculation (dpi), but significant differences were observed in corms of both genotypes at 14 dpi. We compare transcriptomic responses in the corms of Pahang and Brazilian, and show that Pahang exhibited constitutive defense responses before Foc TR4 infection and inducible defense responses prior to Brazilian at the initial Foc TR4 infection stage. Most key enzymatic genes in the phenylalanine metabolism pathway were up-regulated in Brazilian, suggesting that lignin and phytotoxin may be triggered during later stages of Foc TR4 infection. This study unravels a few potential resistance candidate genes whose expression patterns were assessed by RT-qPCR assay and improves our understanding the defense mechanisms of Pahang response to Foc TR4