50 research outputs found
Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements
We introduce the problem of constructing weighted complex projective
2-designs from the union of a family of orthonormal bases. If the weight
remains constant across elements of the same basis, then such designs can be
interpreted as generalizations of complete sets of mutually unbiased bases,
being equivalent whenever the design is composed of d+1 bases in dimension d.
We show that, for the purpose of quantum state determination, these designs
specify an optimal collection of orthogonal measurements. Using highly
nonlinear functions on abelian groups, we construct explicit examples from d+2
orthonormal bases whenever d+1 is a prime power, covering dimensions d=6, 10,
and 12, for example, where no complete sets of mutually unbiased bases have
thus far been found.Comment: 28 pages, to appear in J. Math. Phy
Zeroes of Gaussian Analytic Functions with Translation-Invariant Distribution
We study zeroes of Gaussian analytic functions in a strip in the complex
plane, with translation-invariant distribution. We prove that the a limiting
horizontal mean counting-measure of the zeroes exists almost surely, and that
it is non-random if and only if the spectral measure is continuous (or
degenerate). In this case, the mean zero-counting measure is computed in terms
of the spectral measure. We compare the behavior with Gaussian analytic
function with symmetry around the real axis. These results extend a work by
Norbert Wiener.Comment: 24 pages, 1 figure. Some corrections were made and presentation was
improve
Challenges in QCD matter physics - The Compressed Baryonic Matter experiment at FAIR
Substantial experimental and theoretical efforts worldwide are devoted to
explore the phase diagram of strongly interacting matter. At LHC and top RHIC
energies, QCD matter is studied at very high temperatures and nearly vanishing
net-baryon densities. There is evidence that a Quark-Gluon-Plasma (QGP) was
created at experiments at RHIC and LHC. The transition from the QGP back to the
hadron gas is found to be a smooth cross over. For larger net-baryon densities
and lower temperatures, it is expected that the QCD phase diagram exhibits a
rich structure, such as a first-order phase transition between hadronic and
partonic matter which terminates in a critical point, or exotic phases like
quarkyonic matter. The discovery of these landmarks would be a breakthrough in
our understanding of the strong interaction and is therefore in the focus of
various high-energy heavy-ion research programs. The Compressed Baryonic Matter
(CBM) experiment at FAIR will play a unique role in the exploration of the QCD
phase diagram in the region of high net-baryon densities, because it is
designed to run at unprecedented interaction rates. High-rate operation is the
key prerequisite for high-precision measurements of multi-differential
observables and of rare diagnostic probes which are sensitive to the dense
phase of the nuclear fireball. The goal of the CBM experiment at SIS100
(sqrt(s_NN) = 2.7 - 4.9 GeV) is to discover fundamental properties of QCD
matter: the phase structure at large baryon-chemical potentials (mu_B > 500
MeV), effects of chiral symmetry, and the equation-of-state at high density as
it is expected to occur in the core of neutron stars. In this article, we
review the motivation for and the physics programme of CBM, including
activities before the start of data taking in 2022, in the context of the
worldwide efforts to explore high-density QCD matter.Comment: 15 pages, 11 figures. Published in European Physical Journal