40 research outputs found
The minimum-error discrimination via Helstrom family of ensembles and Convex Optimization
Using the convex optimization method and Helstrom family of ensembles
introduced in Ref. [1], we have discussed optimal ambiguous discrimination in
qubit systems. We have analyzed the problem of the optimal discrimination of N
known quantum states and have obtained maximum success probability and optimal
measurement for N known quantum states with equiprobable prior probabilities
and equidistant from center of the Bloch ball, not all of which are on the one
half of the Bloch ball and all of the conjugate states are pure. An exact
solution has also been given for arbitrary three known quantum states. The
given examples which use our method include: 1. Diagonal N mixed states; 2. N
equiprobable states and equidistant from center of the Bloch ball which their
corresponding Bloch vectors are inclined at the equal angle from z axis; 3.
Three mirror-symmetric states; 4. States that have been prepared with equal
prior probabilities on vertices of a Platonic solid.
Keywords: minimum-error discrimination, success probability, measurement,
POVM elements, Helstrom family of ensembles, convex optimization, conjugate
states PACS Nos: 03.67.Hk, 03.65.TaComment: 15 page
Constructing Entanglement Witness Via Real Skew-Symmetric Operators
In this work, new types of EWs are introduced. They are constructed by using
real skew-symmetric operators defined on a single party subsystem of a
bipartite dxd system and a maximal entangled state in that system. A canonical
form for these witnesses is proposed which is called canonical EW in
corresponding to canonical real skew-symmetric operator. Also for each possible
partition of the canonical real skew-symmetric operator corresponding EW is
obtained. The method used for dxd case is extended to d1xd2 systems. It is
shown that there exist Cd2xd1 distinct possibilities to construct EWs for a
given d1xd2 Hilbert space. The optimality and nd-optimality problem is studied
for each type of EWs. In each step, a large class of quantum PPT states is
introduced. It is shown that among them there exist entangled PPT states which
are detected by the constructed witnesses. Also the idea of canonical EWs is
extended to obtain other EWs with greater PPT entanglement detection power.Comment: 40 page
Restoration of Macroscopic Isotropy on -Simplex Fractal Conductor Networks
Restoration of macroscopic isotropy has been investigated in (d+1)-simplex
fractal conductor networks via exact real space renormalization group
transformations. Using some theorems of fixed point theory, it has been shown
very rigoroursly that the macroscopic conductivity becomes isotropic for large
scales and anisotropy vanishes with a scaling exponent which is computed
exactly for arbitrary values of d and decimation numbers b=2,3,4 and
5.Comment: 27 Pages, 3 Figure
Relativistic entanglement in single-particle quantum states using Non-Linear entanglement witnesses
In this study, the spin-momentum correlation of one massive spin-1/2 and
spin-1 particle states, which are made based on projection of a relativistic
spin operator into timelike direction is investigated. It is shown that by
using Non-Linear entanglement witnesses (NLEWs), the effect of Lorentz
transformation would decrease both the amount and the region of entanglement.Comment: 16 pages, 2 figures; to be published in Quantum Inf Process,
10.1007/s11128-011-0289-z (2011
Poisson-Lie T-Duality and Bianchi Type Algebras
All Bianchi bialgebras have been obtained. By introducing a non-degenerate
adjoint invariant inner product over these bialgebras the associated Drinfeld
doubles have been constructed, then by calculating the coupling matrices for
these bialgebras several sigma-models with Poisson-Lie symmetry have been
obtained. Two simple examples as prototypes of Poisson-Lie dual models have
been given.Comment: 16 pages, Latex; Some comments to the concluding section added,
references adde
Hierarchy of Chaotic Maps with an Invariant Measure
We give hierarchy of one-parameter family F(a,x) of maps of the interval
[0,1] with an invariant measure. Using the measure, we calculate
Kolmogorov-Sinai entropy, or equivalently Lyapunov characteristic exponent, of
these maps analytically, where the results thus obtained have been approved
with numerical simulation. In contrary to the usual one-parameter family of
maps such as logistic and tent maps, these maps do not possess period doubling
or period-n-tupling cascade bifurcation to chaos, but they have single fixed
point attractor at certain parameter values, where they bifurcate directly to
chaos without having period-n-tupling scenario exactly at these values of
parameter whose Lyapunov characteristic exponent begins to be positive.Comment: 18 pages (Latex), 7 figure
Shape invariant hypergeometric type operators with application to quantum mechanics
A hypergeometric type equation satisfying certain conditions defines either a
finite or an infinite system of orthogonal polynomials. The associated special
functions are eigenfunctions of some shape invariant operators. These operators
can be analysed together and the mathematical formalism we use can be extended
in order to define other shape invariant operators. All the considered shape
invariant operators are directly related to Schrodinger type equations.Comment: More applications available at http://fpcm5.fizica.unibuc.ro/~ncotfa
Quantum central limit theorem for continuous-time quantum walks on odd graphs in quantum probability theory
The method of the quantum probability theory only requires simple structural
data of graph and allows us to avoid a heavy combinational argument often
necessary to obtain full description of spectrum of the adjacency matrix. In
the present paper, by using the idea of calculation of the probability
amplitudes for continuous-time quantum walk in terms of the quantum probability
theory, we investigate quantum central limit theorem for continuous-time
quantum walks on odd graphs.Comment: 19 page, 1 figure
Investigation of continuous-time quantum walk on root lattice and honeycomb lattice
The continuous-time quantum walk (CTQW) on root lattice (known as
hexagonal lattice for ) and honeycomb one is investigated by using
spectral distribution method. To this aim, some association schemes are
constructed from abelian group and two copies of finite
hexagonal lattices, such that their underlying graphs tend to root lattice
and honeycomb one, as the size of the underlying graphs grows to
infinity. The CTQW on these underlying graphs is investigated by using the
spectral distribution method and stratification of the graphs based on
Terwilliger algebra, where we get the required results for root lattice
and honeycomb one, from large enough underlying graphs. Moreover, by using the
stationary phase method, the long time behavior of CTQW on infinite graphs is
approximated with finite ones. Also it is shown that the Bose-Mesner algebras
of our constructed association schemes (called -variable -polynomial) can
be generated by commuting generators, where raising, flat and lowering
operators (as elements of Terwilliger algebra) are associated with each
generator. A system of -variable orthogonal polynomials which are special
cases of \textit{generalized} Gegenbauer polynomials is constructed, where the
probability amplitudes are given by integrals over these polynomials or their
linear combinations. Finally the suppersymmetric structure of finite honeycomb
lattices is revealed. Keywords: underlying graphs of association schemes,
continuous-time quantum walk, orthogonal polynomials, spectral distribution.
PACs Index: 03.65.UdComment: 41 pages, 4 figure
Effects of polydispersity on the phase coexistence diagrams in multiblock copolymers with Laser block length distribution
Phase behavior of AB-multiblock copolymer melts which consists of chains with
Laser distribution of A and B blocks have been investigated in the framework of
the mean-field theory, where the polydispersity of copolymer is a function of
two parameters K and M. The influence of the Laser distribution on higher order
correlation functions (up to sixth order) are computed for various values of K
and M, and their contributions on the phase diagrams and phase coexistence are
presented. It is shown that, with increasing polydispersity (decreasing K and
increasing M) the transition lines of all phases shift upwards, consequently
polydispersity destabilize the system.Comment: 15 pages, Late