Entangling power and operator entanglement in qudit systems

We establish the entangling power of a unitary operator on a general finite-dimensional bipartite quantum system with and without ancillas, and give relations between the entangling power based on the von Neumann entropy and the entangling power based on the linear entropy. Significantly, we demonstrate that the entangling power of a general controlled unitary operator acting on two equal-dimensional qudits is proportional to the corresponding operator entanglement if linear entropy is adopted as the quantity representing the degree of entanglement. We discuss the entangling power and operator entanglement of three representative quantum gates on qudits: the SUM, double SUM, and SWAP gates.Comment: 8 pages, 1 figure. Version 3: Figure was improved and the MS was a bit shortene

Protecting Quantum Information with Entanglement and Noisy Optical Modes

We incorporate active and passive quantum error-correcting techniques to protect a set of optical information modes of a continuous-variable quantum information system. Our method uses ancilla modes, entangled modes, and gauge modes (modes in a mixed state) to help correct errors on a set of information modes. A linear-optical encoding circuit consisting of offline squeezers, passive optical devices, feedforward control, conditional modulation, and homodyne measurements performs the encoding. The result is that we extend the entanglement-assisted operator stabilizer formalism for discrete variables to continuous-variable quantum information processing.Comment: 7 pages, 1 figur

Generation of atom-photon entangled states in atomic Bose-Einstein condensate via electromagnetically induced transparency

In this paper, we present a method to generate continuous-variable-type entangled states between photons and atoms in atomic Bose-Einstein condensate (BEC). The proposed method involves an atomic BEC with three internal states, a weak quantized probe laser and a strong classical coupling laser, which form a three-level Lambda-shaped BEC system. We consider a situation where the BEC is in electromagnetically induced transparency (EIT) with the coupling laser being much stronger than the probe laser. In this case, the upper and intermediate levels are unpopulated, so that their adiabatic elimination enables an effective two-mode model involving only the atomic field at the lowest internal level and the quantized probe laser field. Atom-photon quantum entanglement is created through laser-atom and inter-atomic interactions, and two-photon detuning. We show how to generate atom-photon entangled coherent states and entangled states between photon (atom) coherent states and atom-(photon-) macroscopic quantum superposition (MQS) states, and between photon-MQS and atom-MQS states.Comment: 9 pages, 1 figur

Exponential Decay of Correlations Implies Area Law

We prove that a finite correlation length, i.e. exponential decay of correlations, implies an area law for the entanglement entropy of quantum states defined on a line. The entropy bound is exponential in the correlation length of the state, thus reproducing as a particular case Hastings proof of an area law for groundstates of 1D gapped Hamiltonians. As a consequence, we show that 1D quantum states with exponential decay of correlations have an efficient classical approximate description as a matrix product state of polynomial bond dimension, thus giving an equivalence between injective matrix product states and states with a finite correlation length. The result can be seen as a rigorous justification, in one dimension, of the intuition that states with exponential decay of correlations, usually associated with non-critical phases of matter, are simple to describe. It also has implications for quantum computing: It shows that unless a pure state quantum computation involves states with long-range correlations, decaying at most algebraically with the distance, it can be efficiently simulated classically. The proof relies on several previous tools from quantum information theory - including entanglement distillation protocols achieving the hashing bound, properties of single-shot smooth entropies, and the quantum substate theorem - and also on some newly developed ones. In particular we derive a new bound on correlations established by local random measurements, and we give a generalization to the max-entropy of a result of Hastings concerning the saturation of mutual information in multiparticle systems. The proof can also be interpreted as providing a limitation on the phenomenon of data hiding in quantum states.Comment: 35 pages, 6 figures; v2 minor corrections; v3 published versio

Quantitative Treatment of Decoherence

We outline different approaches to define and quantify decoherence. We argue that a measure based on a properly defined norm of deviation of the density matrix is appropriate for quantifying decoherence in quantum registers. For a semiconductor double quantum dot qubit, evaluation of this measure is reviewed. For a general class of decoherence processes, including those occurring in semiconductor qubits, we argue that this measure is additive: It scales linearly with the number of qubits.Comment: Revised version, 26 pages, in LaTeX, 3 EPS figure

Driving non-Gaussian to Gaussian states with linear optics

Published versio

Novel genetic loci associated with hippocampal volume

The hippocampal formation is a brain structure integrally involved in episodic memory, spatial navigation, cognition and stress responsiveness. Structural abnormalities in hippocampal volume and shape are found in several common neuropsychiatric disorders. To identify the genetic underpinnings of hippocampal structure here we perform a genome-wide association study (GWAS) of 33,536 individuals and discover six independent loci significantly associated with hippocampal volume, four of them novel. Of the novel loci, three lie within genes (ASTN2, DPP4 and MAST4) and one is found 200 kb upstream of SHH. A hippocampal subfield analysis shows that a locus within the MSRB3 gene shows evidence of a localized effect along the dentate gyrus, subiculum, CA1 and fissure. Further, we show that genetic variants associated with decreased hippocampal volume are also associated with increased risk for Alzheimer's disease (rg =-0.155). Our findings suggest novel biological pathways through which human genetic variation influences hippocampal volume and risk for neuropsychiatric illness

Serum magnesium and calcium levels in relation to ischemic stroke : Mendelian randomization study

ObjectiveTo determine whether serum magnesium and calcium concentrations are causally associated with ischemic stroke or any of its subtypes using the mendelian randomization approach.MethodsAnalyses were conducted using summary statistics data for 13 single-nucleotide polymorphisms robustly associated with serum magnesium (n = 6) or serum calcium (n = 7) concentrations. The corresponding data for ischemic stroke were obtained from the MEGASTROKE consortium (34,217 cases and 404,630 noncases).ResultsIn standard mendelian randomization analysis, the odds ratios for each 0.1 mmol/L (about 1 SD) increase in genetically predicted serum magnesium concentrations were 0.78 (95% confidence interval [CI] 0.69-0.89; p = 1.3 7 10-4) for all ischemic stroke, 0.63 (95% CI 0.50-0.80; p = 1.6 7 10-4) for cardioembolic stroke, and 0.60 (95% CI 0.44-0.82; p = 0.001) for large artery stroke; there was no association with small vessel stroke (odds ratio 0.90, 95% CI 0.67-1.20; p = 0.46). Only the association with cardioembolic stroke was robust in sensitivity analyses. There was no association of genetically predicted serum calcium concentrations with all ischemic stroke (per 0.5 mg/dL [about 1 SD] increase in serum calcium: odds ratio 1.03, 95% CI 0.88-1.21) or with any subtype.ConclusionsThis study found that genetically higher serum magnesium concentrations are associated with a reduced risk of cardioembolic stroke but found no significant association of genetically higher serum calcium concentrations with any ischemic stroke subtype