Generalized Intelligent States for an Arbitrary Quantum System

Generalized Intelligent States (coherent and squeezed states) are derived for an arbitrary quantum system by using the minimization of the so-called Robertson-Schr\"odinger uncertainty relation. The Fock-Bargmann representation is also considered. As a direct illustration of our construction, the P\"oschl-Teller potentials of trigonometric type will be shosen. We will show the advantage of the Fock-Bargmann representation in obtaining the generalized intelligent states in an analytical way. Many properties of these states are studied

Quantum protocols for anonymous voting and surveying

We describe quantum protocols for voting and surveying. A key feature of our schemes is the use of entangled states to ensure that the votes are anonymous and to allow the votes to be tallied. The entanglement is distributed over separated sites; the physical inaccessibility of any one site is sufficient to guarantee the anonymity of the votes. The security of these protocols with respect to various kinds of attack is discussed. We also discuss classical schemes and show that our quantum voting protocol represents a N-fold reduction in computational complexity, where N is the number of voters.Comment: 8 pages. V2 includes the modifications made for the published versio

Stochastic diffusion model of multistep activation in a voltage-dependent K channel

The energy barrier to the activated state for the S4 voltage sensor of a K channel is dependent on the electrostatic force between positively charged S4 residues and negatively charged groups on neighboring segments, the potential difference across the membrane, and the dielectric boundary force on the charged residues near the interface between the solvent and the low dielectric region of the membrane gating pore. The variation of the potential function with transverse displacement and rotation of the S4 sensor across the membrane may be derived from a solution of Poisson’s equation for the electrostatic potential. By approximating the energy of an S4 sensor along a path between stationary states by a piecewise linear function of the transverse displacement, the dynamics of slow activation, in the millisecond range, may be described by the lowest frequency component of an analytical solution of interacting diffusion equations of Fokker–Planck type for resting and barrier regions. The solution of the Smoluchowski equations for an S4 sensor in an energy landscape with several barriers is in accord with an empirical master equation for multistep activation in a voltage-dependent K channel.S. R. Vaccar

The resource theory of quantum reference frames: manipulations and monotones

Every restriction on quantum operations defines a resource theory, determining how quantum states that cannot be prepared under the restriction may be manipulated and used to circumvent the restriction. A superselection rule is a restriction that arises through the lack of a classical reference frame and the states that circumvent it (the resource) are quantum reference frames. We consider the resource theories that arise from three types of superselection rule, associated respectively with lacking: (i) a phase reference, (ii) a frame for chirality, and (iii) a frame for spatial orientation. Focussing on pure unipartite quantum states (and in some cases restricting our attention even further to subsets of these), we explore single-copy and asymptotic manipulations. In particular, we identify the necessary and sufficient conditions for a deterministic transformation between two resource states to be possible and, when these conditions are not met, the maximum probability with which the transformation can be achieved. We also determine when a particular transformation can be achieved reversibly in the limit of arbitrarily many copies and find the maximum rate of conversion. A comparison of the three resource theories demonstrates that the extent to which resources can be interconverted decreases as the strength of the restriction increases. Along the way, we introduce several measures of frameness and prove that these are monotonically nonincreasing under various classes of operations that are permitted by the superselection rule.Comment: 37 pages, 4 figures, Published Versio

On the squeezed states for n observables

Three basic properties (eigenstate, orbit and intelligence) of the canonical squeezed states (SS) are extended to the case of arbitrary n observables. The SS for n observables X_i can be constructed as eigenstates of their linear complex combinations or as states which minimize the Robertson uncertainty relation. When X_i close a Lie algebra L the generalized SS could also be introduced as orbit of Aut(L^C). It is shown that for the nilpotent algebra h_N the three generalizations are equivalent. For the simple su(1,1) the family of eigenstates of uK_- + vK_+ (K_\pm being lowering and raising operators) is a family of ideal K_1-K_2 SS, but it cannot be represented as an Aut(su^C(1,1)) orbit although the SU(1,1) group related coherent states (CS) with symmetry are contained in it. Eigenstates |z,u,v,w;k> of general combination uK_- + vK_+ + wK_3 of the three generators K_j of SU(1,1) in the representations with Bargman index k = 1/2,1, ..., and k = 1/4,3/4 are constructed and discussed in greater detail. These are ideal SS for K_{1,2,3}. In the case of the one mode realization of su(1,1) the nonclassical properties (sub-Poissonian statistics, quadrature squeezing) of the generalized even CS |z,u,v;+> are demonstrated. The states |z,u,v,w;k=1/4,3/4> can exhibit strong both linear and quadratic squeezing.Comment: 25 pages, LaTex, 4 .pic and .ps figures. Improvements in text, discussion on generation scheme added. To appear in Phys. Script

Atom Lasers, Coherent States, and Coherence:II. Maximally Robust Ensembles of Pure States

As discussed in Wiseman and Vaccaro [quant-ph/9906125], the stationary state of an optical or atom laser far above threshold is a mixture of coherent field states with random phase, or, equivalently, a Poissonian mixture of number states. We are interested in which, if either, of these descriptions of $\rho_{ss}$, is more natural. In the preceding paper we concentrated upon whether descriptions such as these are physically realizable (PR). In this paper we investigate another relevant aspect of these ensembles, their robustness. A robust ensemble is one for which the pure states that comprise it survive relatively unchanged for a long time under the system evolution. We determine numerically the most robust ensembles as a function of the parameters in the laser model: the self-energy $\chi$ of the bosons in the laser mode, and the excess phase noise $\nu$. We find that these most robust ensembles are PR ensembles, or similar to PR ensembles, for all values of these parameters. In the ideal laser limit ($\nu=\chi=0$), the most robust states are coherent states. As the phase noise $\nu$ or phase dispersion $\chi$ is increased, the most robust states become increasingly amplitude-squeezed. We find scaling laws for these states. As the phase diffusion or dispersion becomes so large that the laser output is no longer quantum coherent, the most robust states become so squeezed that they cease to have a well-defined coherent amplitude. That is, the quantum coherence of the laser output is manifest in the most robust PR states having a well-defined coherent amplitude. This lends support to the idea that robust PR ensembles are the most natural description of the state of the laser mode. It also has interesting implications for atom lasers in particular, for which phase dispersion due to self-interactions is expected to be large.Comment: 16 pages, 9 figures included. To be published in Phys. Rev. A, as Part II of a two-part paper. The original version of quant-ph/9906125 is shortly to be replaced by a new version which is Part I of the two-part paper. This paper (Part II) also contains some material from the original version of quant-ph/990612

Remote control of restricted sets of operations: Teleportation of angles

Published versio

Anatomical relationships of the anterior blood vessels to the lower lumbar intervertebral discs: analysis based on magnetic resonance imaging of patients in the prone position.

BACKGROUND: Intra-abdominal vascular injuries are rare during posterior lumbar spinal surgery, but they can result in major morbidity or mortality when they do occur. We are aware of no prior studies that have used prone patient positioning during magnetic resonance imaging for the purpose of characterizing the retroperitoneal iliac vasculature with respect to the intervertebral disc. The purpose of this study was to define the vascular anatomy adjacent to the lower lumbar spine with use of supine and prone magnetic resonance imaging. METHODS: A prospective observational study included thirty patients without spinal abnormality who underwent supine and prone magnetic resonance imaging without abdominal compression. The spinal levels of the aortic bifurcation and confluence of the common iliac veins were identified. The proximity of the anterior iliac vessels to the anterior and posterior aspects of the anulus fibrosus in sagittal and coronal planes was measured by two observers, and interobserver reliability was calculated. RESULTS: The aortic bifurcation and confluence of the common iliac veins were most commonly at the level of the L4 vertebral body and migrated cranially with prone positioning. The common iliac vessels were closer to the anterior aspect of the intervertebral disc and to the midline at L4-L5 as compared with L5-S1, consistent with the bifurcation at the L4 vertebral body. Prone positioning resulted in greater distances between the disc and iliac vessels at L4-L5 and L5-S1 by an average of 3 mm. The position of the anterior aspect of the anulus with respect to each iliac vessel demonstrated substantial variation between subjects. The intraclass correlation coefficient for measurement of vessel position exceeded 0.9, demonstrating excellent interobserver reliability. CONCLUSIONS: This study confirmed the L4 level of the aortic bifurcation and iliac vein coalescence but also demonstrated substantial mobility of the great vessels with positioning. Supine magnetic resonance imaging will underestimate the proximity of the vessels to the intervertebral disc. Large interindividual variation in the location of vasculature was noted, emphasizing the importance of careful study of the location of the retroperitoneal vessels on a case-by-case basis. CLINICAL RELEVANCE: Anatomic relationships between vessels and intervertebral discs on supine magnetic resonance imaging may differ from relationships during surgery with the patient in a prone position

An organ culture system to model early degenerative changes of the intervertebral disc

ABSTRACT: INTRODUCTION: Back pain, a significant source of morbidity in our society, is related to the degenerative changes of the intervertebral disc. At present, the treatment of disc disease consists of therapies that are aimed at symptomatic relief. This shortcoming stems in large part from our lack of understanding of the biochemical and molecular events that drive the disease process. The goal of this study is to develop a model of early disc degeneration using an organ culture. This approach is based on our previous studies that indicate that organ culture closely models molecular events that occur in vivo in an ex vivo setting. METHODS: To mimic a degenerative insult, discs were cultured under low oxygen tension in the presence of TNF-α, IL-1β and serum limiting conditions. RESULTS: Treatment resulted in compromised cell survival and changes in cellular morphology reminiscent of degeneration. There was strong suppression in the expression of matrix proteins including collagen types 1, 2, 6 and 9, proteoglycans, aggrecan and fibromodulin. Moreover, a strong induction in expression of catabolic matrix metalloproteinases (MMP) 3, 9 and 13 with a concomitant increase in aggrecan degradation was seen. An inductive effect on NGF expression was also noticed. Although similar, nucleus pulposus and annulus fibrosus tissues showed some differences in their response to the treatment. CONCLUSIONS: Results of this study show that perturbations in microenvironmental factors result in anatomical and gene expression change within the intervertebral disc that may ultimately compromise cell function and induce pathological deficits. This system would be a valuable screening tool to investigate interventional strategies aimed at restoring disc cell function