49,855 research outputs found
Projection Measurement of the Maximally Entangled N-Photon State for a Demonstration of N-Photon de Broglie Wavelength
We construct a projection measurement process for the maximally entangled
N-photon state (the NOON-state) with only linear optical elements and
photodetectors. This measurement process will give null result for any N-photon
state that is orthogonal to the NOON state. We examine the projection process
in more detail for N=4 by applying it to a four-photon state from type-II
parametric down-conversion. This demonstrates an orthogonal projection
measurement with a null result. This null result corresponds to a dip in a
generalized Hong-Ou-Mandel interferometer for four photons. We find that the
depth of the dip in this arrangement can be used to distinguish a genuine
entangled four-photon state from two separate pairs of photons. We next apply
the NOON state projection measurement to a four-photon superposition state from
two perpendicularly oriented type-I parametric down-conversion processes. A
successful NOON state projection is demonstrated with the appearance of the
four-photon de Broglie wavelength in the interference fringe pattern.Comment: 8 pages, 3 figures, new title, some content change, replaced Fig.
The Sorting Index and Permutation Codes
In the combinatorial study of the coefficients of a bivariate polynomial that
generalizes both the length and the reflection length generating functions for
finite Coxeter groups, Petersen introduced a new Mahonian statistic ,
called the sorting index. Petersen proved that the pairs of statistics
and have the same joint distribution over
the symmetric group, and asked for a combinatorial proof of this fact. In
answer to the question of Petersen, we observe a connection between the sorting
index and the B-code of a permutation defined by Foata and Han, and we show
that the bijection of Foata and Han serves the purpose of mapping
to . We also give a type analogue of the
Foata-Han bijection, and we derive the quidistribution of and over signed
permutations. So we get a combinatorial interpretation of Petersen's
equidistribution of and . Moreover, we show that
the six pairs of set-valued statistics ,
, , ,
and are equidistributed over signed
permutations. For Coxeter groups of type , Petersen showed that the two
statistics and are equidistributed. We introduce two statistics
and for elements of and we prove that the two
pairs of statistics and are
equidistributed.Comment: 25 page
Conditions for Nondistortion Interrogation of Quantum System
Under some physical considerations, we present a universal formulation to
study the possibility of localizing a quantum object in a given region without
disturbing its unknown internal state. When the interaction between the object
and probe wave function takes place only once, we prove the necessary and
sufficient condition that the object's presence can be detected in an initial
state preserving way. Meanwhile, a conditioned optimal interrogation
probability is obtained.Comment: 5 pages, Revtex, 1 figures, Presentation improved, corollary 1 added.
To appear in Europhysics Letter
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