46 research outputs found
Weakly-entangled states are dense and robust
Motivated by the mathematical definition of entanglement we undertake a
rigorous analysis of the separability and non-distillability properties in the
neighborhood of those three-qubit mixed states which are entangled and
completely bi-separable. Our results are not only restricted to this class of
quantum states, since they rest upon very general properties of mixed states
and Unextendible Product Bases for any possible number of parties. Robustness
against noise of the relevant properties of these states implies the
significance of their possible experimental realization, therefore being of
physical -and not exclusively mathematical- interest.Comment: 4 pages, final version, accepted for publication in PR
Speed of Light in Non--Trivial Vacua
We unify all existing results on the change of the speed of low--energy
photons due to modifications of the vacuum, finding that it is given by a
universal constant times the quotient of the difference of energy densities
between the usual and modified vacua over the mass of the electron to the
fourth power. Whether photons move faster or slower than depends only on
the lower or higher energy density of the modified vacuum, respectively.
Physically, a higher energy density is characterized by the presence of
additional particles (real or virtual) in the vacuum whereas a lower one stems
from the absence of some virtual modes. We then carry out a systematic study of
the speed of propagation of massless particles for several field theories up to
two loops on a thermal vacuum. Only low--energy massless particles
corresponding to a massive theory show genuine modifications of their speed
while remaining massless. All other modifications are mass-related, or running
mass-related. We also develop a formalism for the Casimir vacuum which
parallels the thermal one and check that photons travel faster than between
plates.Comment: 24 p., plain te
Mode dependent field renormalization and triviality
We critically analyze the introduction of an independent zero momentum mode
field renormalization for Phi4. It leads to an infrared divergent effective
action. It does not achieve its purpose: triviality still gives massless
particles in the broken phase in the continuum limit. It leads to an effective
potential which is not the low energy limit of the effective action.Comment: 14 pages, no figures, TeX fil