758 research outputs found
On the Impossibility to Extend Triples of Mutually Unbiased Product Bases in Dimension Six
An analytic proof is given which shows that it is impossible to extend any
triple of mutually unbiased (MU) product bases in dimension six by a single MU
vector. Furthermore, the 16 states obtained by removing two orthogonal states
from any MU product triple cannot figure in a (hypothetical) complete set of
seven MU bases. These results follow from exploiting the structure of MU
product bases in a novel fashion, and they are among the strongest ones
obtained for MU bases in dimension six without recourse to computer algebra.Comment: 12 pages, identical to published versio
Universal quantum computation on a semiconductor quantum wire network
Universal quantum computation (UQC) using Majorana fermions on a 2D
topological superconducting (TS) medium remains an outstanding open problem.
This is because the quantum gate set that can be generated by braiding of the
Majorana fermions does not include \emph{any} two-qubit gate and also the
single-qubit phase gate. In principle, it is possible to create these
crucial extra gates using quantum interference of Majorana fermion currents.
However, it is not clear if the motion of the various order parameter defects
(vortices, domain walls, \emph{etc.}), to which the Majorana fermions are bound
in a TS medium, can be quantum coherent. We show that these obstacles can be
overcome using a semiconductor quantum wire network in the vicinity of an
-wave superconductor, by constructing topologically protected two-qubit
gates and any arbitrary single-qubit phase gate in a topologically unprotected
manner, which can be error corrected using magic state distillation. Thus our
strategy, using a judicious combination of topologically protected and
unprotected gate operations, realizes UQC on a quantum wire network with a
remarkably high error threshold of as compared to to
in ordinary unprotected quantum computation.Comment: 7 pages, 2 figure
Let Your CyberAlter Ego Share Information and Manage Spam
Almost all of us have multiple cyberspace identities, and these {\em
cyber}alter egos are networked together to form a vast cyberspace social
network. This network is distinct from the world-wide-web (WWW), which is being
queried and mined to the tune of billions of dollars everyday, and until
recently, has gone largely unexplored. Empirically, the cyberspace social
networks have been found to possess many of the same complex features that
characterize its real counterparts, including scale-free degree distributions,
low diameter, and extensive connectivity. We show that these topological
features make the latent networks particularly suitable for explorations and
management via local-only messaging protocols. {\em Cyber}alter egos can
communicate via their direct links (i.e., using only their own address books)
and set up a highly decentralized and scalable message passing network that can
allow large-scale sharing of information and data. As one particular example of
such collaborative systems, we provide a design of a spam filtering system, and
our large-scale simulations show that the system achieves a spam detection rate
close to 100%, while the false positive rate is kept around zero. This system
has several advantages over other recent proposals (i) It uses an already
existing network, created by the same social dynamics that govern our daily
lives, and no dedicated peer-to-peer (P2P) systems or centralized server-based
systems need be constructed; (ii) It utilizes a percolation search algorithm
that makes the query-generated traffic scalable; (iii) The network has a built
in trust system (just as in social networks) that can be used to thwart
malicious attacks; iv) It can be implemented right now as a plugin to popular
email programs, such as MS Outlook, Eudora, and Sendmail.Comment: 13 pages, 10 figure
Optical matrix elements in tight-binding models with overlap
We investigate the effect of orbital overlap on optical matrix elements in
empirical tight-binding models. Empirical tight-binding models assume an
orthogonal basis of (atomiclike) states and a diagonal coordinate operator
which neglects the intra-atomic part. It is shown that, starting with an atomic
basis which is not orthogonal, the orthogonalization process induces
intra-atomic matrix elements of the coordinate operator and extends the range
of the effective Hamiltonian. We analyze simple tight-binding models and show
that non-orthogonality plays an important role in optical matrix elements. In
addition, the procedure gives formal justification to the nearest-neighbor
spin-orbit interaction introduced by Boykin [Phys. Rev \textbf{B} 57, 1620
(1998)] in order to describe the Dresselahaus term which is neglected in
empirical tight-binding models.Comment: 16 pages 6 figures, to appear in Phys. Rev.
Tight-binding study of interface states in semiconductor heterojunctions
Localized interface states in abrupt semiconductor heterojunctions are
studied within a tight-binding model. The intention is to provide a microscopic
foundation for the results of similar studies which were based upon the
two-band model within the envelope function approximation. In a two-dimensional
description, the tight-binding Hamiltonian is constructed such that the
Dirac-like bulk spectrum of the two-band model is recovered in the continuum
limit. Localized states in heterojunctions are shown to occur under conditions
equivalent to those of the two-band model. In particular, shallow interface
states are identified in non-inverted junctions with intersecting bulk
dispersion curves. As a specific example, the GaSb-AlSb heterojunction is
considered. The matching conditions of the envelope function approximation are
analyzed within the tight-binding description.Comment: RevTeX, 11 pages, 3 figures, to appear in Phys. Rev.
Conduction band tight-binding description for silicon applied to phosphorous donors
A tight-binding parametrization for silicon, optimized to correctly reproduce
effective masses as well as the reciprocal space positions of the
conduction-band minima, is presented. The reliability of the proposed
parametrization is assessed by performing systematic comparisons between the
descriptions of donor impurities in Si using this parametrization and
previously reported ones. The spectral decomposition of the donor wavefunction
demonstrates the importance of incorporating full band effects for a reliable
representation, and that an incomplete real space description results from a
truncated reciprocal space expansion as proposed within the effective mass
theory.Comment: 4 pages, 3 figure
Information-Disturbance Theorem for Mutually Unbiased Observables
We derive a novel version of information-disturbance theorems for mutually
unbiased observables. We show that the information gain by Eve inevitably makes
the outcomes by Bob in the conjugate basis not only erroneous but random
Improved magic states distillation for quantum universality
Given stabilizer operations and the ability to repeatedly prepare a
single-qubit mixed state rho, can we do universal quantum computation? As
motivation for this question, "magic state" distillation procedures can reduce
the general fault-tolerance problem to that of performing fault-tolerant
stabilizer circuits.
We improve the procedures of Bravyi and Kitaev in the Hadamard "magic"
direction of the Bloch sphere to achieve a sharp threshold between those rho
allowing universal quantum computation, and those for which any calculation can
be efficiently classically simulated. As a corollary, the ability to repeatedly
prepare any pure state which is not a stabilizer state (e.g., any single-qubit
pure state which is not a Pauli eigenstate), together with stabilizer
operations, gives quantum universality. It remains open whether there is also a
tight separation in the so-called T direction.Comment: 6 pages, 5 figure
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