Enhancement of entanglement in one-dimensional disordered systems

The pairwise quantum entanglement of sites in disordered electronic one-dimensional systems (rings) is studied. We focus on the effect of diagonal and off diagonal disorder on the concurrence $C_{ij}$ between electrons on neighbor and non neighbor sites $i,j$ as a function of band filling. In the case of diagonal disorder, increasing the degree of disorder leads to a decrease of the concurrence with respect to the ordered case. However, off-diagonal disorder produces a surprisingly strong enhancement of entanglement. This remarkable effect occurs near half filling, where the concurrence becomes up to 15% larger than in the ordered system.Comment: 21 pages, 9 figure

Entanglement Distillation Protocols and Number Theory

We show that the analysis of entanglement distillation protocols for qudits of arbitrary dimension $D$ benefits from applying basic concepts from number theory, since the set \zdn associated to Bell diagonal states is a module rather than a vector space. We find that a partition of \zdn into divisor classes characterizes the invariant properties of mixed Bell diagonal states under local permutations. We construct a very general class of recursion protocols by means of unitary operations implementing these local permutations. We study these distillation protocols depending on whether we use twirling operations in the intermediate steps or not, and we study them both analitically and numerically with Monte Carlo methods. In the absence of twirling operations, we construct extensions of the quantum privacy algorithms valid for secure communications with qudits of any dimension $D$. When $D$ is a prime number, we show that distillation protocols are optimal both qualitatively and quantitatively.Comment: REVTEX4 file, 7 color figures, 2 table

Thresholds for Linear Optics Quantum Computing with Photon Loss at the Detectors

We calculate the error threshold for the linear optics quantum computing proposal by Knill, Laflamme and Milburn [Nature 409, pp. 46--52 (2001)] under an error model where photon detectors have efficiency <100% but all other components -- such as single photon sources, beam splitters and phase shifters -- are perfect and introduce no errors. We make use of the fact that the error model induced by the lossy hardware is that of an erasure channel, i.e., the error locations are always known. Using a method based on a Markov chain description of the error correction procedure, our calculations show that, with the 7 qubit CSS quantum code, the gate error threshold for fault tolerant quantum computation is bounded below by a value between 1.78% and 11.5% depending on the construction of the entangling gates.Comment: 7 pages, 6 figure

The Bravyi-Kitaev transformation for quantum computation of electronic structure

Quantum simulation is an important application of future quantum computers with applications in quantum chemistry, condensed matter, and beyond. Quantum simulation of fermionic systems presents a specific challenge. The Jordan-Wigner transformation allows for representation of a fermionic operator by O(n) qubit operations. Here we develop an alternative method of simulating fermions with qubits, first proposed by Bravyi and Kitaev [S. B. Bravyi, A.Yu. Kitaev, Annals of Physics 298, 210-226 (2002)], that reduces the simulation cost to O(log n) qubit operations for one fermionic operation. We apply this new Bravyi-Kitaev transformation to the task of simulating quantum chemical Hamiltonians, and give a detailed example for the simplest possible case of molecular hydrogen in a minimal basis. We show that the quantum circuit for simulating a single Trotter time-step of the Bravyi-Kitaev derived Hamiltonian for H2 requires fewer gate applications than the equivalent circuit derived from the Jordan-Wigner transformation. Since the scaling of the Bravyi-Kitaev method is asymptotically better than the Jordan-Wigner method, this result for molecular hydrogen in a minimal basis demonstrates the superior efficiency of the Bravyi-Kitaev method for all quantum computations of electronic structure

Entanglement of two qubits mediated by one-dimensional plasmonic waveguides

We investigate qubit-qubit entanglement mediated by plasmons supported by one-dimensional waveguides. We explore both the situation of spontaneous formation of entanglement from an unentangled state and the emergence of driven steady-state entanglement under continuous pumping. In both cases, we show that large values for the concurrence are attainable for qubit-qubit distances larger than the operating wavelength by using plasmonic waveguides that are currently available.Comment: 4 pages, 4 figures. Minor Changes. Journal Reference added. Highlighted in Physic

Spin noise and Bell inequalities in a realistic superconductor-quantum dot entangler

Charge and spin current correlations are analyzed in a source of spin-entangled electrons built from a superconductor and two quantum dots in parallel. In addition to the ideal (crossed Andreev) channel, parasitic channels (direct Andreev and cotunneling) and spin flip processes are fully described in a density matrix framework. The way they reduce both the efficiency and the fidelity of the entangler is quantitatively described by analyzing the zero-frequency noise correlations of charge current as well as spin current in the two output branches. Spin current noise is characterized by a spin Fano factor, equal to 0 (total current noise) and -1 (crossed correlations) for an ideal entangler. The violation of the Bell inequalities, as a test of non-locality (entanglement) of split pairs, is formulated in terms of the correlations of electron charge and spin numbers counted in a specific time window $\tau$. The efficiency of the test is analyzed, comparing $\tau$ to the various time scales in the entangler operation.Comment: 8 pages, 5 figures, references added, to appear in Phys. Rev.

Influence of static electric fields on an optical ion trap

We recently reported on a proof-of-principle experiment demonstrating optical trapping of an ion in a single-beam dipole trap superimposed by a static electric potential [Nat. Photonics 4, 772--775 (2010)]. Here, we first discuss the experimental procedures focussing on the influence and consequences of the static electric potential. These potentials can easily prevent successful optical trapping, if their configuration is not chosen carefully. Afterwards, we analyse the dipole trap experiments with different analytic models, in which different approximations are applied. According to these models the experimental results agree with recoil heating as the relevant heating effect. In addition, a Monte-Carlo simulation has been developed to refine the analysis. It reveals a large impact of the static electric potential on the dipole trap experiments in general. While it supports the results of the analytic models for the parameters used in the experiments, the analytic models cease their validity for significantly different parameters. Finally, we propose technical improvements for future realizations of experiments with optically trapped ions.Comment: 16 pages, 16 figure

N II 5668-5712, a New Class of Spectral Features in Eta Carinae

We report on the N II 5668-5712 emission and absorption lines in the spectrum of Eta Carinae. Spectral lines of the stellar wind regions can be classified into four physically distinct categories: 1) low-excitation emission such as H I and Fe II, 2) higher excitation He I features, 3) the N II lines discussed in this paper, and 4) He II emission. These categories have different combinations of radial velocity behavior, excitation processes, and dependences on the secondary star. The N II lines are the only known features that originate in "normal" undisturbed zones of the primary wind but depend primarily on the location of the hot secondary star. N II probably excludes some proposed models, such as those where He I lines originate in the secondary star's wind or in an accretion disk.Comment: 4 figures, 1 tabl

Multiqubit symmetric states with high geometric entanglement

We propose a detailed study of the geometric entanglement properties of pure symmetric N-qubit states, focusing more particularly on the identification of symmetric states with a high geometric entanglement and how their entanglement behaves asymptotically for large N. We show that much higher geometric entanglement with improved asymptotical behavior can be obtained in comparison with the highly entangled balanced Dicke states studied previously. We also derive an upper bound for the geometric measure of entanglement of symmetric states. The connection with the quantumness of a state is discussed