1,362 research outputs found
The power of random measurements: measuring Tr(\rho^n) on single copies of \rho
While it is known that Tr(\rho^n) can be measured directly (i.e., without
first reconstructing the density matrix) by performing joint measurements on n
copies of the same state rho, it is shown here that random measurements on
single copies suffice, too. Averaging over the random measurements directly
yields estimates of Tr(\rho^n), even when it is not known what measurements
were actually performed (so that one cannot reconstruct \rho)
A new correlator in quantum spin chains
We propose a new correlator in one-dimensional quantum spin chains, the
Emptiness Formation Probability (EFP). This is a natural generalization
of the Emptiness Formation Probability (EFP), which is the probability that the
first spins of the chain are all aligned downwards. In the EFP we let
the spins in question be separated by sites. The usual EFP corresponds to
the special case when , and taking allows us to quantify non-local
correlations. We express the EFP for the anisotropic XY model in a
transverse magnetic field, a system with both critical and non-critical
regimes, in terms of a Toeplitz determinant. For the isotropic XY model we find
that the magnetic field induces an interesting length scale.Comment: 6 pages, 1 figur
Optical study of the vibrational and dielectric properties of BiMnO3
BiMnO3 (BMO), ferromagnetic (FM) below Tc = 100 K, was believed to be also
ferroelectric (FE) due to a non-centro-symmetric C2 structure, until
diffraction data indicated that its space group is the centro-symmetric C2/c.
Here we present infrared phonon spectra of BMO, taken on a mosaic of single
crystals, which are consistent with C2/c at any T > 10 K, as well as
room-temperature Raman data which strongly support this conclusion. We also
find that the infrared intensity of several phonons increases steadily for
decreasing T, causing the relative permittivity of BMO to vary from 18.5 at 300
K to 45 at 10 K. At variance with FE materials of displacive type, no
appreciable softening has been found in the infrared phonons. Both their
frequencies and intensities, moreover, appear insensitive to the FM transition
at Tc
Statistical properties of determinantal point processes in high-dimensional Euclidean spaces
The goal of this paper is to quantitatively describe some statistical
properties of higher-dimensional determinantal point processes with a primary
focus on the nearest-neighbor distribution functions. Toward this end, we
express these functions as determinants of matrices and then
extrapolate to . This formulation allows for a quick and accurate
numerical evaluation of these quantities for point processes in Euclidean
spaces of dimension . We also implement an algorithm due to Hough \emph{et.
al.} \cite{hough2006dpa} for generating configurations of determinantal point
processes in arbitrary Euclidean spaces, and we utilize this algorithm in
conjunction with the aforementioned numerical results to characterize the
statistical properties of what we call the Fermi-sphere point process for to 4. This homogeneous, isotropic determinantal point process, discussed
also in a companion paper \cite{ToScZa08}, is the high-dimensional
generalization of the distribution of eigenvalues on the unit circle of a
random matrix from the circular unitary ensemble (CUE). In addition to the
nearest-neighbor probability distribution, we are able to calculate Voronoi
cells and nearest-neighbor extrema statistics for the Fermi-sphere point
process and discuss these as the dimension is varied. The results in this
paper accompany and complement analytical properties of higher-dimensional
determinantal point processes developed in \cite{ToScZa08}.Comment: 42 pages, 17 figure
Quantum state tomography by continuous measurement and compressed sensing
The need to perform quantum state tomography on ever larger systems has
spurred a search for methods that yield good estimates from incomplete data. We
study the performance of compressed sensing (CS) and least squares (LS)
estimators in a fast protocol based on continuous measurement on an ensemble of
cesium atomic spins. Both efficiently reconstruct nearly pure states in the
16-dimensional ground manifold, reaching average fidelities FCS = 0.92 and FLS
= 0.88 using similar amounts of incomplete data. Surprisingly, the main
advantage of CS in our protocol is an increased robustness to experimental
imperfections
Roots of the derivative of the Riemann zeta function and of characteristic polynomials
We investigate the horizontal distribution of zeros of the derivative of the
Riemann zeta function and compare this to the radial distribution of zeros of
the derivative of the characteristic polynomial of a random unitary matrix.
Both cases show a surprising bimodal distribution which has yet to be
explained. We show by example that the bimodality is a general phenomenon. For
the unitary matrix case we prove a conjecture of Mezzadri concerning the
leading order behavior, and we show that the same follows from the random
matrix conjectures for the zeros of the zeta function.Comment: 24 pages, 6 figure
Singling out the effect of quenched disorder in the phase diagram of cuprates
We investigate the specific influence of structural disorder on the
suppression of antiferromagnetic order and on the emergence of cuprate
superconductivity. We single out pure disorder, by focusing on a series of
YEuBaCuO samples at fixed oxygen content
, in the range . The gradual Y/Eu isovalent substitution
smoothly drives the system through the Mott-insulator to superconductor
transition from a full antiferromagnet with N\'eel transition K at
to a bulk superconductor with superconducting critical temperature
K at , YBaCuO. The electronic properties are
finely tuned by gradual lattice deformations induced by the different cationic
radii of the two lanthanides, inducing a continuous change of the basal Cu(1)-O
chain length, as well as a controlled amount of disorder in the active
Cu(2)O bilayers. We check that internal charge transfer from the basal to
the active plane is entirely responsible for the doping of the latter and we
show that superconductivity emerges with orthorhombicity. By comparing
transition temperatures with those of the isoelectronic clean system we
deterime the influence of pure structural disorder connected with the Y/Eu
alloy.Comment: 10 pages 11 figures, submitted to Journal of Physics: Condensed
Matter, Special Issue in memory of Prof. Sandro Massid
Rate of convergence of linear functions on the unitary group
We study the rate of convergence to a normal random variable of the real and
imaginary parts of Tr(AU), where U is an N x N random unitary matrix and A is a
deterministic complex matrix. We show that the rate of convergence is O(N^{-2 +
b}), with 0 <= b < 1, depending only on the asymptotic behaviour of the
singular values of A; for example, if the singular values are non-degenerate,
different from zero and O(1) as N -> infinity, then b=0. The proof uses a
Berry-Esse'en inequality for linear combinations of eigenvalues of random
unitary, matrices, and so appropriate for strongly dependent random variables.Comment: 34 pages, 1 figure; corrected typos, added remark 3.3, added 3
reference
On the multiplicativity of quantum cat maps
The quantum mechanical propagators of the linear automorphisms of the
two-torus (cat maps) determine a projective unitary representation of the theta
group, known as Weil's representation. We prove that there exists an
appropriate choice of phases in the propagators that defines a proper
representation of the theta group. We also give explicit formulae for the
propagators in this representation.Comment: Revised version: proof of the main theorem simplified. 21 page
Calculation of the unitary part of the Bures measure for N-level quantum systems
We use the canonical coset parameterization and provide a formula with the
unitary part of the Bures measure for non-degenerate systems in terms of the
product of even Euclidean balls. This formula is shown to be consistent with
the sampling of random states through the generation of random unitary
matrices
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