181 research outputs found
Fast rate estimation of an unitary operation in SU(d)
We give an explicit procedure based on entangled input states for estimating
a operation with rate of convergence when sending
particles through the device. We prove that this rate is optimal. We also
evaluate the constant such that the asymptotic risk is . However
other strategies might yield a better const ant .Comment: 8 pages, 1 figure Rewritten version, accepted for publication in
Phys. Rev. A. The introduction is richer, the "tool section" on group
representations has been suppressed, and a section proving that the 1/N^2
rate is optimum has been adde
Eigenvalue enclosures and exclosures for non-self-adjoint problems in hydrodynamics
In this paper we present computer-assisted proofs of a number of results in theoretical fluid dynamics and in quantum mechanics. An algorithm based on interval arithmetic yields provably correct eigenvalue enclosures and exclosures for non-self-adjoint boundary eigenvalue problems, the eigenvalues of which are highly sensitive to perturbations. We apply the algorithm to: the Orr-Sommerfeld equation with Poiseuille profile to prove the existence of an eigenvalue in the classically unstable region for Reynolds number R=5772.221818; the Orr-Sommerfeld equation with Couette profile to prove upper bounds for the imaginary parts of all eigenvalues for fixed R and wave number α; the problem of natural oscillations of an incompressible inviscid fluid in the neighbourhood of an elliptical flow to obtain information about the unstable part of the spectrum off the imaginary axis; Squire's problem from hydrodynamics; and resonances of one-dimensional Schrödinger operators
All maximally entangling unitary gates
We characterize all maximally entangling bipartite unitary operators, acting
on systems of arbitrary finite dimensions , when use of
ancillary systems by both parties is allowed. Several useful and interesting
consequences of this characterization are discussed, including an understanding
of why the entangling and disentangling capacities of a given (maximally
entangling) unitary can differ and a proof that these capacities must be equal
when .Comment: 7 pages, no figure
Longest increasing subsequence as expectation of a simple nonlinear stochastic PDE with a low noise intensity
We report some new observation concerning the statistics of Longest
Increasing Subsequences (LIS). We show that the expectation of LIS, its
variance, and apparently the full distribution function appears in statistical
analysis of some simple nonlinear stochastic partial differential equation
(SPDE) in the limit of very low noise intensity.Comment: 6 pages, 4 figures, reference adde
Classic and mirabolic Robinson-Schensted-Knuth correspondence for partial flags
In this paper we first generalize to the case of partial flags a result
proved both by Spaltenstein and by Steinberg that relates the relative position
of two complete flags and the irreducible components of the flag variety in
which they lie, using the Robinson-Schensted-Knuth correspondence. Then we use
this result to generalize the mirabolic Robinson-Schensted-Knuth correspondence
defined by Travkin, to the case of two partial flags and a line.Comment: 27 pages, slightly rewritten to combine two papers into one and
clarify some section
Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues
We consider the polynuclear growth (PNG) model in 1+1 dimension with flat
initial condition and no extra constraints. Through the
Robinson-Schensted-Knuth (RSK) construction, one obtains the multilayer PNG
model, which consists of a stack of non-intersecting lines, the top one being
the PNG height. The statistics of the lines is translation invariant and at a
fixed position the lines define a point process. We prove that for large times
the edge of this point process, suitably scaled, has a limit. This limit is a
Pfaffian point process and identical to the one obtained from the edge scaling
of Gaussian orthogonal ensemble (GOE) of random matrices. Our results give
further insight to the universality structure within the KPZ class of 1+1
dimensional growth models.Comment: 40 pages, 6 figures, LaTeX; Section 4 is substantially modifie
Hermitian Young Operators
Starting from conventional Young operators we construct Hermitian operators
which project orthogonally onto irreducible representations of the (special)
unitary group.Comment: 15 page
Combinatorial R matrices for a family of crystals : B^{(1)}_n, D^{(1)}_n, A^{(2)}_{2n} and D^{(2)}_{n+1} cases
For coherent families of crystals of affine Lie algebras of type B^{(1)}_n,
D^{(1)}_n, A^{(2)}_{2n} and D^{(2)}_{n+1} we describe the combinatorial R
matrix using column insertion algorithms for B,C,D Young tableaux.Comment: 39 pages, LaTeX. This is a continuation of the authors' work appeared
in "Physical Combinatorics", ed. M.Kashiwara and T.Miwa, Birkha"user, Boston,
200
Optimizing local protocols implementing nonlocal quantum gates
We present a method of optimizing recently designed protocols for
implementing an arbitrary nonlocal unitary gate acting on a bipartite system.
These protocols use only local operations and classical communication with the
assistance of entanglement, and are deterministic while also being "one-shot",
in that they use only one copy of an entangled resource state. The optimization
is in the sense of minimizing the amount of entanglement used, and it is often
the case that less entanglement is needed than with an alternative protocol
using two-way teleportation.Comment: 11 pages, 1 figure. This is a companion paper to arXiv:1001.546
Solution of the infinite range t-J model
The t-J model with constant t and J between any pair of sites is studied by
exploiting the symmetry of the Hamiltonian with respect to site permutations.
For a given number of electrons and a given total spin the exchange term simply
yields an additive constant. Therefore the real problem is to diagonalize the
"t- model", or equivalently the infinite U Hubbard Hamiltonian. Using
extensively the properties of the permutation group, we are able to find
explicitly both the energy eigenvalues and eigenstates, labeled according to
spin quantum numbers and Young diagrams. As a corollary we also obtain the
degenerate ground states of the finite Hubbard model with infinite range
hopping -t>0.Comment: 15 pages, 2 figure
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