Generalized qudit Choi maps

Following the linear programming prescription of Ref. \cite{PRA72}, the $d\otimes d$ Bell diagonal entanglement witnesses are provided. By using Jamiolkowski isomorphism, it is shown that the corresponding positive maps are the generalized qudit Choi maps. Also by manipulating particular $d\otimes d$ Bell diagonal separable states and constructing corresponding bound entangled states, it is shown that thus obtained $d\otimes d$ BDEW's (consequently qudit Choi maps) are non-decomposable in certain range of their parameters.Comment: 22 page

Supersonic quantum communication

When locally exciting a quantum lattice model, the excitation will propagate through the lattice. The effect is responsible for a wealth of non-equilibrium phenomena, and has been exploited to transmit quantum information through spin chains. It is a commonly expressed belief that for local Hamiltonians, any such propagation happens at a finite "speed of sound". Indeed, the Lieb-Robinson theorem states that in spin models, all effects caused by a perturbation are limited to a causal cone defined by a constant speed, up to exponentially small corrections. In this work we show that for translationally invariant bosonic models with nearest-neighbor interactions, this belief is incorrect: We prove that one can encounter excitations which accelerate under the natural dynamics of the lattice and allow for reliable transmission of information faster than any finite speed of sound. The effect is only limited by the model's range of validity (eventually by relativity). It also implies that in non-equilibrium dynamics of strongly correlated bosonic models far-away regions may become quickly entangled, suggesting that their simulation may be much harder than that of spin chains even in the low energy sector.Comment: 4+3 pages, 1 figure, some material added, typographic error fixe

Effects of self-phase modulation on weak nonlinear optical quantum gates

A possible two-qubit gate for optical quantum computing is the parity gate based on the weak Kerr effect. Two photonic qubits modulate the phase of a coherent state, and a quadrature measurement of the coherent state reveals the parity of the two qubits without destroying the photons. This can be used to create so-called cluster states, a universal resource for quantum computing. Here, the effect of self-phase modulation on the parity gate is studied, introducing generating functions for the Wigner function of a modulated coherent state. For materials with non-EIT-based Kerr nonlinearities, there is typically a self-phase modulation that is half the magnitude of the cross-phase modulation. Therefore, this effect cannot be ignored. It is shown that for a large class of physical implementations of the phase modulation, the quadrature measurement cannot distinguish between odd and even parity. Consequently, weak nonlinear parity gates must be implemented with physical systems where the self-phase modulation is negligable.Comment: 7 pages, 4 figure

Scalable reconstruction of density matrices

Recent contributions in the field of quantum state tomography have shown that, despite the exponential growth of Hilbert space with the number of subsystems, tomography of one-dimensional quantum systems may still be performed efficiently by tailored reconstruction schemes. Here, we discuss a scalable method to reconstruct mixed states that are well approximated by matrix product operators. The reconstruction scheme only requires local information about the state, giving rise to a reconstruction technique that is scalable in the system size. It is based on a constructive proof that generic matrix product operators are fully determined by their local reductions. We discuss applications of this scheme for simulated data and experimental data obtained in an ion trap experiment.Comment: 9 pages, 5 figures, replaced with published versio

Bubble Growth in Superfluid 3-He: The Dynamics of the Curved A-B Interface

We study the hydrodynamics of the A-B interface with finite curvature. The interface tension is shown to enhance both the transition velocity and the amplitudes of second sound. In addition, the magnetic signals emitted by the growing bubble are calculated, and the interaction between many growing bubbles is considered.Comment: 20 pages, 3 figures, LaTeX, ITP-UH 11/9

Population structures in the SARA and SARB reference collections of Salmonella enterica according to MLST, MLEE and microarray hybridization

In the 1980's and 1990's, population genetic analyses based on Multilocus Enzyme Electrophoresis (MLEE) provided an initial overview of the genetic diversity of multiple bacterial species, including Salmonella enterica. The genetic diversity within S. enterica subspecies enterica according to MLEE is represented by the SARA and SARB reference collections, each consisting of 72 isolates, which have been extensively used for comparative analyses. MLEE has subsequently been replaced by Multilocus Sequence Typing (MLST). Our initial MLST results indicated that some strains within the SARB collection differed from their published descriptions. We therefore performed MLST on four versions of the SARB collection from different sources and one collection of SARA, and found that multiple isolates in SARB and SARA differ in serovar from their original description, and other SARB isolates differed between different sources. Comparisons with a global MLST database allowed a plausible reconstruction of the serovars of the original collection. MLEE, MLST and microarrays were largely concordant at recognizing closely related strains. MLST was particularly effective at recognizing discrete population genetic groupings while the two other methods provided hints of higher order relationships. However, quantitative pair-wise phylogenetic distances differed considerably between all three methods. Our results provide a translation dictionary from MLEE to MLST for the extant SARA and SARB collections which can facilitate genomic comparisons based on archival insights from MLEE

Quantum lost property: a possible operational meaning for the Hilbert-Schmidt product

Minimum error state discrimination between two mixed states \rho and \sigma can be aided by the receipt of "classical side information" specifying which states from some convex decompositions of \rho and \sigma apply in each run. We quantify this phenomena by the average trace distance, and give lower and upper bounds on this quantity as functions of \rho and \sigma. The lower bound is simply the trace distance between \rho and \sigma, trivially seen to be tight. The upper bound is \sqrt{1 - tr(\rho\sigma)}, and we conjecture that this is also tight. We reformulate this conjecture in terms of the existence of a pair of "unbiased decompositions", which may be of independent interest, and prove it for a few special cases. Finally, we point towards a link with a notion of non-classicality known as preparation contextuality.Comment: 3 pages, 1 figure. v2: Less typos in text and less punctuation in titl

Dynamic Energy Management

We present a unified method, based on convex optimization, for managing the power produced and consumed by a network of devices over time. We start with the simple setting of optimizing power flows in a static network, and then proceed to the case of optimizing dynamic power flows, i.e., power flows that change with time over a horizon. We leverage this to develop a real-time control strategy, model predictive control, which at each time step solves a dynamic power flow optimization problem, using forecasts of future quantities such as demands, capacities, or prices, to choose the current power flow values. Finally, we consider a useful extension of model predictive control that explicitly accounts for uncertainty in the forecasts. We mirror our framework with an object-oriented software implementation, an open-source Python library for planning and controlling power flows at any scale. We demonstrate our method with various examples. Appendices give more detail about the package, and describe some basic but very effective methods for constructing forecasts from historical data.Comment: 63 pages, 15 figures, accompanying open source librar