1,616 research outputs found
Symmetric Informationally Complete Quantum Measurements
We consider the existence in arbitrary finite dimensions d of a POVM
comprised of d^2 rank-one operators all of whose operator inner products are
equal. Such a set is called a ``symmetric, informationally complete'' POVM
(SIC-POVM) and is equivalent to a set of d^2 equiangular lines in C^d.
SIC-POVMs are relevant for quantum state tomography, quantum cryptography, and
foundational issues in quantum mechanics. We construct SIC-POVMs in dimensions
two, three, and four. We further conjecture that a particular kind of
group-covariant SIC-POVM exists in arbitrary dimensions, providing numerical
results up to dimension 45 to bolster this claim.Comment: 8 page
The road to deterministic matrices with the restricted isometry property
The restricted isometry property (RIP) is a well-known matrix condition that
provides state-of-the-art reconstruction guarantees for compressed sensing.
While random matrices are known to satisfy this property with high probability,
deterministic constructions have found less success. In this paper, we consider
various techniques for demonstrating RIP deterministically, some popular and
some novel, and we evaluate their performance. In evaluating some techniques,
we apply random matrix theory and inadvertently find a simple alternative proof
that certain random matrices are RIP. Later, we propose a particular class of
matrices as candidates for being RIP, namely, equiangular tight frames (ETFs).
Using the known correspondence between real ETFs and strongly regular graphs,
we investigate certain combinatorial implications of a real ETF being RIP.
Specifically, we give probabilistic intuition for a new bound on the clique
number of Paley graphs of prime order, and we conjecture that the corresponding
ETFs are RIP in a manner similar to random matrices.Comment: 24 page
Restricted Isometries for Partial Random Circulant Matrices
In the theory of compressed sensing, restricted isometry analysis has become
a standard tool for studying how efficiently a measurement matrix acquires
information about sparse and compressible signals. Many recovery algorithms are
known to succeed when the restricted isometry constants of the sampling matrix
are small. Many potential applications of compressed sensing involve a
data-acquisition process that proceeds by convolution with a random pulse
followed by (nonrandom) subsampling. At present, the theoretical analysis of
this measurement technique is lacking. This paper demonstrates that the th
order restricted isometry constant is small when the number of samples
satisfies , where is the length of the pulse.
This bound improves on previous estimates, which exhibit quadratic scaling
Prime tight frames
We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. In particular, we show that any finite tight frame can be written as a union of prime tight frames. We then characterize all prime harmonic tight frames and use this characterization to suggest effective analysis and synthesis computation strategies for such frames. Finally, we describe all prime frames constructed from the spectral tetris method, and, as a byproduct, we obtain a characterization of when the spectral tetris construction works for redundancies below two
Search for right-handed W bosons in top quark decay
We present a measurement of the fraction f+ of right-handed W bosons produced
in top quark decays, based on a candidate sample of events in the
lepton+jets decay mode. These data correspond to an integrated luminosity of
230pb^-1, collected by the DO detector at the Fermilab Tevatron
Collider at sqrt(s)=1.96 TeV. We use a constrained fit to reconstruct the
kinematics of the and decay products, which allows for the
measurement of the leptonic decay angle for each event. By comparing
the distribution from the data with those for the expected
background and signal for various values of f+, we find
f+=0.00+-0.13(stat)+-0.07(syst). This measurement is consistent with the
standard model prediction of f+=3.6x10^-4.Comment: Submitted to Physical Review D Rapid Communications 7 pages, 3
figure
Measurement of the B0_s semileptonic branching ratio to an orbitally excited D_s** state, Br(B0_s -> Ds1(2536) mu nu)
In a data sample of approximately 1.3 fb-1 collected with the D0 detector
between 2002 and 2006, the orbitally excited charm state D_s1(2536) has been
observed with a measured mass of 2535.7 +/- 0.6 (stat) +/- 0.5 (syst) MeV via
the decay mode B0_s -> D_s1(2536) mu nu X. A first measurement is made of the
branching ratio product Br(b(bar) -> D_s1(2536) mu nu X).Br(D_s1(2536)->D*
K0_S). Assuming that D_s1(2536) production in semileptonic decay is entirely
from B0_s, an extraction of the semileptonic branching ratio Br(B0_s ->
D_s1(2536) mu nu X) is made.Comment: 7 pages, 2 figures, LaTeX, version with minor changes as accepted by
Phys. Rev. Let
Measurement of the Lifetime Difference in the B_s^0 System
We present a study of the decay B_s^0 -> J/psi phi We obtain the CP-odd
fraction in the final state at time zero, R_perp = 0.16 +/- 0.10 (stat) +/-
0.02 (syst), the average lifetime of the (B_s, B_sbar) system, tau (B_s^0)
=1.39^{+0.13}_{-0.16} (stat) ^{+0.01}_{-0.02} (syst) ps, and the relative width
difference between the heavy and light mass eigenstates, Delta Gamma/Gamma =
(Gamma_L - Gamma_H)/Gamma =0.24^{+0.28}_{-0.38} (stat) ^{+0.03}_{-0.04} (syst).
With the additional constraint from the world average of the B_s^0$lifetime
measurements using semileptonic decays, we find tau (B_s^0)= 1.39 +/- 0.06 ~ps
and Delta Gamma/\Gamma = 0.25^{+0.14}_{-0.15}. For the ratio of the B_s^0 and
B^0 lifetimes we obtain tau(B_s^0)/tau(B^0)} = 0.91 +/- 0.09 (stat) +/- 0.003
(syst).Comment: submitted to Phys. Rev. Lett. FERMILAB-PUB-05-324-
A search for W bb and W Higgs production in ppbar collisions at sqrt(s)=1.96 TeV
We present a search for W b \bar{b} production in p \bar{p} collisions at
sqrt{s}=1.96 TeV in events containing one electron, an imbalance in transverse
momentum, and two b-tagged jets. Using 174 pb-1 of integrated luminosity
accumulated by the D0 experiment at the Fermilab Tevatron collider, and the
standard-model description of such events, we set a 95% C.L. upper limit on W b
\bar{b}WH--$135
GeV.Comment: 7 pages, 4 figures, 1 table, submitted to Physical Review Letter
Study of events and limits on anomalous and couplings in ppbar collisions at TeV
We present a measurement of the Z\gamma production cross section and limits
on anomalous ZZ\gamma and Z\gamma\gamma couplings for form-factor scales of
Lambda = 750 and 1000 GeV. The measurement is based on 138 (152) candidate
events in the ee\gamma (\mu\mu\gamma) final state using 320 (290) pb^{-1} of
ppbar collisions at \sqrt{s} = 1.96 TeV. The 95% C.L. limits on real and
imaginary parts of individual anomalous couplings are |h_{10,30}^{Z}|<0.23,
|h_{20,40}^{Z}|<0.020, |h_{10,30}^{\gamma}|<0.23, and
|h_{20,40}^{\gamma}|<0.019 for Lambda = 1000 GeV.Comment: submitted to Phys. Rev. Letter
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