508 research outputs found
Space shuttle navigation analysis. Volume 2: Baseline system navigation
Studies related to the baseline navigation system for the orbiter are presented. The baseline navigation system studies include a covariance analysis of the Inertial Measurement Unit calibration and alignment procedures, postflight IMU error recovery for the approach and landing phases, on-orbit calibration of IMU instrument biases, and a covariance analysis of entry and prelaunch navigation system performance
Irreversibility in asymptotic manipulations of entanglement
We show that the process of entanglement distillation is irreversible by
showing that the entanglement cost of a bound entangled state is finite. Such
irreversibility remains even if extra pure entanglement is loaned to assist the
distillation process.Comment: RevTex, 3 pages, no figures Result on indistillability of PPT states
under pure entanglement catalytic LOCC adde
Spectral Orbits and Peak-to-Average Power Ratio of Boolean Functions with respect to the {I,H,N}^n Transform
We enumerate the inequivalent self-dual additive codes over GF(4) of
blocklength n, thereby extending the sequence A090899 in The On-Line
Encyclopedia of Integer Sequences from n = 9 to n = 12. These codes have a
well-known interpretation as quantum codes. They can also be represented by
graphs, where a simple graph operation generates the orbits of equivalent
codes. We highlight the regularity and structure of some graphs that correspond
to codes with high distance. The codes can also be interpreted as quadratic
Boolean functions, where inequivalence takes on a spectral meaning. In this
context we define PAR_IHN, peak-to-average power ratio with respect to the
{I,H,N}^n transform set. We prove that PAR_IHN of a Boolean function is
equivalent to the the size of the maximum independent set over the associated
orbit of graphs. Finally we propose a construction technique to generate
Boolean functions with low PAR_IHN and algebraic degree higher than 2.Comment: Presented at Sequences and Their Applications, SETA'04, Seoul, South
Korea, October 2004. 17 pages, 10 figure
Reversible transformations from pure to mixed states, and the unique measure of information
Transformations from pure to mixed states are usually associated with
information loss and irreversibility. Here, a protocol is demonstrated allowing
one to make these transformations reversible. The pure states are diluted with
a random noise source. Using this protocol one can study optimal
transformations between states, and from this derive the unique measure of
information. This is compared to irreversible transformations where one does
not have access to noise. The ideas presented here shed some light on attempts
to understand entanglement manipulations and the inevitable irreversibility
encountered there where one finds that mixed states can contain "bound
entanglement".Comment: 10 pages, no figures, revtex4, table added, to appear in Phys. Rev.
On a conjecture of Widom
We prove a conjecture of H.Widom stated in [W] (math/0108008) about the
reality of eigenvalues of certain infinite matrices arising in asymptotic
analysis of large Toeplitz determinants. As a byproduct we obtain a new proof
of A.Okounkov's formula for the (determinantal) correlation functions of the
Schur measures on partitions.Comment: 9 page
Output state in multiple entanglement swapping
The technique of quantum repeaters is a promising candidate for sending
quantum states over long distances through a lossy channel. The usual
discussions of this technique deals with only a finite dimensional Hilbert
space. However the qubits with which one implements this procedure will "ride"
on continuous degrees of freedom of the carrier particles. Here we analyze the
action of quantum repeaters using a model based on pulsed parametric down
conversion entanglement swapping. Our model contains some basic traits of a
real experiment. We show that the state created, after the use of any number of
parametric down converters in a series of entanglement swappings, is always an
entangled (actually distillable) state, although of a different form than the
one that is usually assumed. Furthermore, the output state always violates a
Bell inequality.Comment: 11 pages, 6 figures, RevTeX
On the Form Factor for the Unitary Group
We study the combinatorics of the contributions to the form factor of the
group U(N) in the large limit. This relates to questions about
semiclassical contributions to the form factor of quantum systems described by
the unitary ensemble.Comment: 35 page
Increasing subsequences and the hard-to-soft edge transition in matrix ensembles
Our interest is in the cumulative probabilities Pr(L(t) \le l) for the
maximum length of increasing subsequences in Poissonized ensembles of random
permutations, random fixed point free involutions and reversed random fixed
point free involutions. It is shown that these probabilities are equal to the
hard edge gap probability for matrix ensembles with unitary, orthogonal and
symplectic symmetry respectively. The gap probabilities can be written as a sum
over correlations for certain determinantal point processes. From these
expressions a proof can be given that the limiting form of Pr(L(t) \le l) in
the three cases is equal to the soft edge gap probability for matrix ensembles
with unitary, orthogonal and symplectic symmetry respectively, thereby
reclaiming theorems due to Baik-Deift-Johansson and Baik-Rains.Comment: LaTeX, 19 page
Maximally entangled mixed states of two qubits
We consider mixed states of two qubits and show under which global unitary
operations their entanglement is maximized. This leads to a class of states
that is a generalization of the Bell states. Three measures of entanglement are
considered: entanglement of formation, negativity and relative entropy of
entanglement. Surprisingly all states that maximize one measure also maximize
the others. We will give a complete characterization of these generalized Bell
states and prove that these states for fixed eigenvalues are all equivalent
under local unitary transformations. We will furthermore characterize all
nearly entangled states closest to the maximally mixed state and derive a new
lower bound on the volume of separable mixed states
On some properties of orthogonal Weingarten functions
We give a Fourier-type formula for computing the orthogonal Weingarten
formula. The Weingarten calculus was introduced as a systematic method to
compute integrals of polynomials with respect to Haar measure over classical
groups. Although a Fourier-type formula was known in the unitary case, the
orthogonal counterpart was not known. It relies on the Jack polynomial
generalization of both Schur and zonal polynomials. This formula substantially
reduces the complexity involved in the computation of Weingarten formulas. We
also describe a few more new properties of the Weingarten formula, state a
conjecture and give a table of values.Comment: 18 pages, 0 figur
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