700 research outputs found
Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries
The operator-Schmidt decomposition is useful in quantum information theory
for quantifying the nonlocality of bipartite unitary operations. We construct a
family of unitary operators on C^n tensor C^n whose operator-Schmidt
decompositions are computed using the discrete Fourier transform. As a
corollary, we produce unitaries on C^3 tensor C^3 with operator-Schmidt number
S for every S in {1,...,9}. This corollary was unexpected, since it
contradicted reasonable conjectures of Nielsen et al [Phys. Rev. A 67 (2003)
052301] based on intuition from a striking result in the two-qubit case. By the
results of Dur, Vidal, and Cirac [Phys. Rev. Lett. 89 (2002) 057901
quant-ph/0112124], who also considered the two-qubit case, our result implies
that there are nine equivalence classes of unitaries on C^3 tensor C^3 which
are probabilistically interconvertible by (stochastic) local operations and
classical communication. As another corollary, a prescription is produced for
constructing maximally-entangled operators from biunimodular functions.
Reversing tact, we state a generalized operator-Schmidt decomposition of the
quantum Fourier transform considered as an operator C^M_1 tensor C^M_2 -->
C^N_1 tensor C^N_2, with M_1 x M_2 = N_1 x N_2. This decomposition shows (by
Nielsen's bound) that the communication cost of the QFT remains maximal when a
net transfer of qudits is permitted. In an appendix, a canonical procedure is
given for removing basis-dependence for results and proofs depending on the
"magic basis" introduced in [S. Hill and W. Wootters, "Entanglement of a pair
of quantum bits," Phys Rev. Lett 78 (1997) 5022-5025, quant-ph/9703041 (and
quant-ph/9709029)].Comment: More formal version of my talk at the Simons Conference on Quantum
and Reversible Computation at Stony Brook May 31, 2003. The talk slides and
audio are available at
http://www.physics.sunysb.edu/itp/conf/simons-qcomputation.html. Fixed typos
and minor cosmetic
Unbiased bases (Hadamards) for 6-level systems: Four ways from Fourier
In quantum mechanics some properties are maximally incompatible, such as the
position and momentum of a particle or the vertical and horizontal projections
of a 2-level spin. Given any definite state of one property the other property
is completely random, or unbiased. For N-level systems, the 6-level ones are
the smallest for which a tomographically efficient set of N+1 mutually unbiased
bases (MUBs) has not been found. To facilitate the search, we numerically
extend the classification of unbiased bases, or Hadamards, by incrementally
adjusting relative phases in a standard basis. We consider the non-unitarity
caused by small adjustments with a second order Taylor expansion, and choose
incremental steps within the 4-dimensional nullspace of the curvature. In this
way we prescribe a numerical integration of a 4-parameter set of Hadamards of
order 6.Comment: 5 pages, 2 figure
Constructing Mutually Unbiased Bases in Dimension Six
The density matrix of a qudit may be reconstructed with optimal efficiency if
the expectation values of a specific set of observables are known. In dimension
six, the required observables only exist if it is possible to identify six
mutually unbiased complex 6x6 Hadamard matrices. Prescribing a first Hadamard
matrix, we construct all others mutually unbiased to it, using algebraic
computations performed by a computer program. We repeat this calculation many
times, sampling all known complex Hadamard matrices, and we never find more
than two that are mutually unbiased. This result adds considerable support to
the conjecture that no seven mutually unbiased bases exist in dimension six.Comment: As published version. Added discussion of the impact of numerical
approximations and corrected the number of triples existing for non-affine
families (cf Table 3
Constructive updating/downdating of oblique projectors: a generalization of the Gram-Schmidt process
A generalization of the Gram-Schmidt procedure is achieved by providing
equations for updating and downdating oblique projectors. The work is motivated
by the problem of adaptive signal representation outside the orthogonal basis
setting. The proposed techniques are shown to be relevant to the problem of
discriminating signals produced by different phenomena when the order of the
signal model needs to be adjusted.Comment: As it will appear in Journal of Physics A: Mathematical and
Theoretical (2007
Exotic complex Hadamard matrices, and their equivalence
In this paper we use a design theoretical approach to construct new,
previously unknown complex Hadamard matrices. Our methods generalize and extend
the earlier results of de la Harpe--Jones and Munemasa--Watatani and offer a
theoretical explanation for the existence of some sporadic examples of complex
Hadamard matrices in the existing literature. As it is increasingly difficult
to distinguish inequivalent matrices from each other, we propose a new
invariant, the fingerprint of complex Hadamard matrices. As a side result, we
refute a conjecture of Koukouvinos et al. on (n-8)x(n-8) minors of real
Hadamard matrices.Comment: 10 pages. To appear in Cryptography and Communications: Discrete
Structures, Boolean Functions and Sequence
Editor's Choice: Contemporary treatment of popliteal artery aneurysm in eight countries: A Report from the Vascunet collaboration of registries.
To access publisher's full text version of this article, please click on the hyperlink in Additional Links field or click on the hyperlink at the top of the page marked Files.
This article is open access.To study contemporary popliteal artery aneurysm (PA) repair.Vascunet is a collaboration of population-based registries in 10 countries: eight had data on PA repair (Australia, Finland, Hungary, Iceland, New Zealand, Norway, Sweden, and Switzerland).From January 2009 until June 2012, 1,471 PA repairs were registered. There were 9.59 operations per million person years, varying from 3.4 in Hungary to 17.6 in Sweden. Median age was 70 years, ranging from 66 years in Switzerland and Iceland to 74 years in Australia and New Zealand; 95.6% were men and 44% were active smokers. Elective surgery dominated, comprising 72% of all cases, but only 26.2% in Hungary and 39.7% in Finland, (p < .0001). The proportion of endovascular PA repair was 22.2%, varying from 34.7% in Australia, to zero in Switzerland, Finland, and Iceland (p < .0001). Endovascular repair was performed in 12.2% of patients with acute thrombosis and 24.1% of elective cases (p < .0001). A vein graft was used in 87.2% of open repairs, a synthetic or composite graft in 12.7%. Follow-up was until discharge or 30 days. Amputation rate was 2.0% overall: 6.5% after acute thrombosis, 1.0% after endovascular, 1.8% after open repair, and 26.3% after hybrid repair (p < .0001). Mortality was 0.7% overall: 0.1% after elective repair, 1.6% after acute thrombosis, and 11.1% after rupture.Great variability between countries in incidence of operations, indications for surgery, and choice of surgical technique was found, possibly a result of surgical tradition rather than differences in case mix. Comparative studies with longer follow-up data are warranted
Generalized Mutual Subspace Based Methods for Image Set Classification
Abstract. The subspace-based methods are effectively applied to classify sets of feature vectors by modeling them as subspaces. It is, however, difficult to appropriately determine the subspace dimensionality in advance for better performance. For alleviating such issue, we present a generalized mutual subspace method by introducing soft weighting across the basis vectors of the subspace. The bases are effectively combined via the soft weights to measure the subspace similarities (angles) without definitely setting the subspace dimensionality. By using the soft weighting, we consequently propose a novel mutual subspace-based method to construct the discriminative space which renders more discriminative subspace similarities. In the experiments on 3D object recognition using image sets, the proposed methods exhibit stably favorable performances compared to the other subspace-based methods.
On linear combinations of generalized involutive matrices
Let X(dagger) denotes the Moore-Penrose pseudoinverse of a matrix X. We study a number of situations when (aA + bB)(dagger) = aA + bB provided a, b is an element of C\{0} and A, B are n x n complex matrices such that A(dagger) = A and B(dagger) = B. (C) 2011 Taylor & FrancisLiu, X.; Wu, L.; Benítez López, J. (2011). On linear combinations of generalized involutive matrices. Linear and Multilinear Algebra. 59(11):1221-1236. doi:10.1080/03081087.2010.496111S12211236591
Validation of the Reflux Symptom Questionnaire Electronic Diary in Partial Responders to Proton Pump Inhibitor Therapy
Chronostratigraphy of the sedimentary record of Limnopolar Lake, Byers Peninsula, Livingston Island, Antarctica
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