2,143 research outputs found
On Logical Depth and the Running Time of Shortest Programs
The logical depth with significance of a finite binary string is the
shortest running time of a binary program for that can be compressed by at
most bits. There is another definition of logical depth. We give two
theorems about the quantitative relation between these versions: the first
theorem concerns a variation of a known fact with a new proof, the second
theorem and its proof are new. We select the above version of logical depth and
show the following. There is an infinite sequence of strings of increasing
length such that for each there is a such that the logical depth of the
th string as a function of is incomputable (it rises faster than any
computable function) but with replaced by the resuling function is
computable. Hence the maximal gap between the logical depths resulting from
incrementing appropriate 's by 1 rises faster than any computable function.
All functions mentioned are upper bounded by the Busy Beaver function. Since
for every string its logical depth is nonincreasing in , the minimal
computation time of the shortest programs for the sequence of strings as a
function of rises faster than any computable function but not so fast as
the Busy Beaver function.Comment: 12 pages LaTex (this supercedes arXiv:1301.4451
Theoretical investigation of moir\'e patterns in quantum images
Moir\'e patterns are produced when two periodic structures with different
spatial frequencies are superposed. The transmission of the resulting structure
gives rise to spatial beatings which are called moir\'e fringes. In classical
optics, the interest in moir\'e fringes comes from the fact that the spatial
beating given by the frequency difference gives information about details(high
spatial frequency) of a given spatial structure. We show that moir\'e fringes
can also arise in the spatial distribution of the coincidence count rate of
twin photons from the parametric down-conversion, when spatial structures with
different frequencies are placed in the path of each one of the twin beams. In
other words,we demonstrate how moir\'e fringes can arise from quantum images
Experimental Observation of Environment-induced Sudden Death of Entanglement
We demonstrate the difference between local, single-particle dynamics and
global dynamics of entangled quantum systems coupled to independent
environments. Using an all-optical experimental setup, we show that, while the
environment-induced decay of each system is asymptotic, quantum entanglement
may suddenly disappear. This "sudden death" constitutes yet another distinct
and counter-intuitive trait of entanglement.Comment: 4 pages, 4 figure
Experimental investigation of quantum key distribution with position and momentum of photon pairs
We investigate the utility of Einstein-Podolsky-Rosen correlations of the
position and momentum of photon pairs from parametric down-conversion in the
implementation of a secure quantum key distribution protocol. We show that
security is guaranteed by the entanglement between downconverted pairs, and can
be checked by either direct comparison of Alice and Bob's measurement results
or evaluation of an inequality of the sort proposed by Mancini et al. (Phys.
Rev. Lett. 88, 120401 (2002)).Comment: 6 pages, 6 figures, subimitted for publicatio
Production of optical phase space vortices with non-locally distributed mode converters
Optical vortices have been observed in a wide variety of optical systems.
They can be observed directly in the wavefront of optical beams, or in the
correlations between pairs of entangled photons. We present a novel optical
vortex which appears in a non-local plane of the two-photon phase space,
composed of a single degree of freedom of each photon of an entangled pair. The
preparation of this vortex can be viewed as a "non-local" or distributed mode
converter. We show how these novel optical vortices of arbitrary order can be
prepared in the spatial degrees of freedom of entangled photons.Comment: To appear in upcoming special issue "Orbital Angular Momentum" of the
Journal of Optic
- …