6,985 research outputs found
Non Abelian structures and the geometric phase of entangled qudits
In this work, we address some important topological and algebraic aspects of
two-qudit states evolving under local unitary operations. The projective
invariant subspaces and evolutions are connected with the common elements
characterizing the su(d) Lie algebra and their representations. In particular,
the roots and weights turn out to be natural quantities to parametrize cyclic
evolutions and fractional phases. This framework is then used to recast the
coset contribution to the geometric phase in a form that generalizes the usual
monopole-like formula for a single qubit.Comment: 22 pages, LaTe
Fractional topological phase for entangled qudits
We investigate the topological structure of entangled qudits under unitary
local operations. Different sectors are identified in the evolution, and their
geometrical and topological aspects are analyzed. The geometric phase is
explicitly calculated in terms of the concurrence. As a main result, we predict
a fractional topological phase for cyclic evolutions in the multiply connected
space of maximally entangled states.Comment: REVTex, 4 page
Scale-Invariance and the Strong Coupling Problem
The effective theory of adiabatic fluctuations around arbitrary
Friedmann-Robertson-Walker backgrounds - both expanding and contracting -
allows for more than one way to obtain scale-invariant two-point correlations.
However, as we show in this paper, it is challenging to produce scale-invariant
fluctuations that are weakly coupled over the range of wavelengths accessible
to cosmological observations. In particular, requiring the background to be a
dynamical attractor, the curvature fluctuations are scale-invariant and weakly
coupled for at least 10 e-folds only if the background is close to de Sitter
space. In this case, the time-translation invariance of the background
guarantees time-independent n-point functions. For non-attractor solutions, any
predictions depend on assumptions about the evolution of the background even
when the perturbations are outside of the horizon. For the simplest such
scenario we identify the regions of the parameter space that avoid both
classical and quantum mechanical strong coupling problems. Finally, we present
extensions of our results to backgrounds in which higher-derivative terms play
a significant role.Comment: 17 pages + appendices, 3 figures; v2: typos fixe
Phase detection at the quantum limit with multi-photon Mach-Zehnder interferometry
We study a Mach-Zehnder interferometer fed by a coherent state in one input
port and vacuum in the other. We explore a Bayesian phase estimation strategy
to demonstrate that it is possible to achieve the standard quantum limit
independently from the true value of the phase shift and specific assumptions
on the noise of the interferometer. We have been able to implement the protocol
using parallel operation of two photon-number-resolving detectors and
multiphoton coincidence logic electronics at the output ports of a
weakly-illuminated Mach-Zehnder interferometer. This protocol is unbiased and
saturates the Cramer-Rao phase uncertainty bound and, therefore, is an optimal
phase estimation strategy.Comment: 4 pages, 5 figures replaced fig. 1 to correct graphics bu
Density Perturbations in the Ekpyrotic Scenario
We study the generation of density perturbations in the ekpyrotic scenario
for the early universe, including gravitational backreaction. We expose
interesting subtleties that apply to both inflationary and ekpyrotic models.
Our analysis includes a detailed proposal of how the perturbations generated in
a contracting phase may be matched across a `bounce' to those in an expanding
hot big bang phase. For the physical conditions relevant to the ekpyrotic
scenario, we re-obtain our earlier result of a nearly scale-invariant spectrum
of energy density perturbations. We find that the perturbation amplitude is
typically small, as desired to match observation.Comment: 36 pages, compressed and RevTex file, one postscript figure file.
Minor typographical and numerical errors corrected, discussion added. This
version to appear in Physical Review
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