Homalg: A meta-package for homological algebra

The central notion of this work is that of a functor between categories of finitely presented modules over so-called computable rings, i.e. rings R where one can algorithmically solve inhomogeneous linear equations with coefficients in R. The paper describes a way allowing one to realize such functors, e.g. Hom, tensor product, Ext, Tor, as a mathematical object in a computer algebra system. Once this is achieved, one can compose and derive functors and even iterate this process without the need of any specific knowledge of these functors. These ideas are realized in the ring independent package homalg. It is designed to extend any computer algebra software implementing the arithmetics of a computable ring R, as soon as the latter contains algorithms to solve inhomogeneous linear equations with coefficients in R. Beside explaining how this suffices, the paper describes the nature of the extensions provided by homalg.Comment: clarified some points, added references and more interesting example

Entanglement measure for general pure multipartite quantum states

We propose an explicit formula for an entanglement measure of pure multipartite quantum states, then study a general pure tripartite state in detail, and at end we give some simple but illustrative examples on four-qubits and m-qubits states.Comment: 5 page

Simultaneous minimum-uncertainty measurement of discrete-valued complementary observables

We have made the first experimental demonstration of the simultaneous minimum uncertainty product between two complementary observables for a two-state system (a qubit). A partially entangled two-photon state was used to perform such measurements. Each of the photons carries (partial) information of the initial state thus leaving a room for measurements of two complementary observables on every member in an ensemble.Comment: 4 pages, 4 figures, REVTeX, submitted to PR

The role of illness perceptions in adherence to surveillance in patients with familial adenomatous polyposis (FAP)

Objective The aim of the study was to examine patients' beliefs about having familial adenomatous polyposis (FAP), a hereditary colorectal cancer syndrome, and how these beliefs are associated with adherence to endoscopic surveillance. Methods Adult patients diagnosed with FAP on the national Swedish polyposis register who had undergone prophylactic colorectal surgery (n 209, response rate 76%) completed the Illness Perception Questionnaire (IPQ). Logistic regression analysis was used to investigate the relationships between illness perceptions and adherence, when controlling for demographic and clinical factors. Results FAP was less distressing in men and those with fewer symptoms, reporting less serious consequences and more coherent understanding of FAP. Non-adherence (14%) to surveillance was associated with being older, having undergone surgery less recently and no history of malignancy. Patients' beliefs about their FAP were able to explain unique variance in non-adherence, in particular those who believed FAP was less distressing. Conclusions Patients who were non-adherent to endoscopic surveillance had more positive perceptions about their FAP and, in particular, were less emotionally affected compared to those who adhered. As non-adherence implies a greater risk of future malignancies, special efforts are required to effectively prevent cancer in all patients with FAP. Those who have lived with the condition for a long time, and are not troubled by gastrointestinal symptoms or worried about their FAP, may be in need of specific information and support. Further prospective research is required to examine emotional predictors and consequences of non-adherence

Certainty relations between local and nonlocal observables

We demonstrate that for an arbitrary number of identical particles, each defined on a Hilbert-space of arbitrary dimension, there exists a whole ladder of relations of complementarity between local, and every conceivable kind of joint (or nonlocal) measurements. E.g., the more accurate we can know (by a measurement) some joint property of three qubits (projecting the state onto a tripartite entangled state), the less accurate some other property, local to the three qubits, become. We also show that the corresponding complementarity relations are particularly tight for particles defined on prime dimensional Hilbert spaces.Comment: 4 pages, no figure

Hamiltonian Formalism in Quantum Mechanics

Heisenberg motion equations in Quantum mechanics can be put into the Hamilton form. The difference between the commutator and its principal part, the Poisson bracket, can be accounted for exactly. Canonical transformations in Quantum mechanics are not, or at least not what they appear to be; their properties are formulated in a series of Conjectures

Imaging a 1-electron InAs quantum dot in an InAs/InP nanowire

Nanowire heterostructures define high-quality few-electron quantum dots for nanoelectronics, spintronics and quantum information processing. We use a cooled scanning probe microscope (SPM) to image and control an InAs quantum dot in an InAs/InP nanowire, using the tip as a movable gate. Images of dot conductance vs. tip position at T = 4.2 K show concentric rings as electrons are added, starting with the first electron. The SPM can locate a dot along a nanowire and individually tune its charge, abilities that will be very useful for the control of coupled nanowire dots

Maximal entanglement of squeezed vacuum states via swapping with number-phase measurement

We propose a method to refine entanglement via swapping from a pair of squeezed vacuum states by performing the Bell measurement of number sum and phase difference. The resultant states are maximally entangled by adjusting the two squeezing parameters to the same value. We then describe the teleportation of number states by using the entangled states prepared in this way.Comment: 4 pages, 1 PS figure, RevTe

Entangled-State Lithography: Tailoring any Pattern with a Single State

We demonstrate a systematic approach to Heisenberg-limited lithographic image formation using four-mode reciprocal binominal states. By controlling the exposure pattern with a simple bank of birefringent plates, any pixel pattern on a $(N+1) \times (N+1)$ grid, occupying a square with the side half a wavelength long, can be generated from a $2 N$-photon state.Comment: 4 pages, 4 figure

Superradiance of low density Frenkel excitons in a crystal slab of three-level atoms: Quantum interference effect

We systematically study the fluorescence of low density Frenkel excitons in a crystal slab containing $N_T$ V-type three-level atoms. Based on symmetric quasi-spin realization of SU(3) in large $N$ limit, the two-mode exciton operators are invoked to depict various collective excitations of the collection of these V-type atoms starting from their ground state. By making use of the rotating wave approximation, the light intensity of radiation for the single lattice layer is investigated in detail. As a quantum coherence effect, the quantum beat phenomenon is discussed in detail for different initial excitonic states. We also test the above results analytically without the consideration of the rotating wave approximation and the self-interaction of radiance field is also included.Comment: 18pages, 17 figures. Resubmit to Phys. Rev.