2,906 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
Quantum phase-space analysis of the pendular cavity
We perform a quantum mechanical analysis of the pendular cavity, using the
positive-P representation, showing that the quantum state of the moving mirror,
a macroscopic object, has noticeable effects on the dynamics. This system has
previously been proposed as a candidate for the quantum-limited measurement of
small displacements of the mirror due to radiation pressure, for the production
of states with entanglement between the mirror and the field, and even for
superposition states of the mirror. However, when we treat the oscillating
mirror quantum mechanically, we find that it always oscillates, has no
stationary steady-state, and exhibits uncertainties in position and momentum
which are typically larger than the mean values. This means that previous
linearised fluctuation analyses which have been used to predict these highly
quantum states are of limited use. We find that the achievable accuracy in
measurement is far worse than the standard quantum limit due to thermal noise,
which, for typical experimental parameters, is overwhelming even at 2 mK.Comment: 25 pages, 6 figures To be published in Phys. Rev.
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