9,465 research outputs found
Closed formula for the relative entropy of entanglement
The long-standing problem of finding a closed formula for the relative
entropy of entanglement (REE) for two qubits is addressed. A compact-form
solution to the inverse problem, which characterizes an entangled state for a
given closest separable state, is obtained. Analysis of the formula for a large
class of entangled states strongly suggests that a compact analytical solution
of the original problem, which corresponds to finding the closest separable
state for a given entangled state, can be given only in some special cases. A
few applications of the compact-form formula are given to show additivity of
the REE, to relate the REE with the Rains upper bound for distillable
entanglement, and to show that a Bell state does not have a unique closest
separable state.Comment: 7 pages, the title was modified as suggested by the PRA editor
A closed formula for the number of convex permutominoes
In this paper we determine a closed formula for the number of convex
permutominoes of size n. We reach this goal by providing a recursive generation
of all convex permutominoes of size n+1 from the objects of size n, according
to the ECO method, and then translating this construction into a system of
functional equations satisfied by the generating function of convex
permutominoes. As a consequence we easily obtain also the enumeration of some
classes of convex polyominoes, including stack and directed convex
permutominoes
A Closed Formula for the Product in Simple Integral Extensions
Let be an algebraic number and let . An
explicit formula for the coordinates of the product is given in
terms of the coordinates of and and the companion matrix of
the minimal polynomial of . The formula as well as its proof extend to
fairly general simple integral extensions
A Note on the generating function of p-Bernoulli numbers
We use analytic combinatorics to give a direct proof of the closed formula
for the generating function of -Bernoulli numbers.Comment: 6 page
A Closed Formula for the Barrier Transmission Coefficient in Quaternionic Quantum mechanics
In this paper, we analyze, by using a matrix approach, the dynamics of a
non-relativistic particle in presence of a quaternionic potential barrier. The
matrix method used to solve the quaternionic Schrodinger equation allows to
obtain a closed formula for the transmission coefficient. Up to now, in
quaternionic quantum mechanics, almost every discussion on the dynamics of
non-relativistic particle was motived by or evolved from numerical studies. A
closed formula for the transmission coefficient stimulates an analysis of
qualitative differences between complex and quaternionic quantum mechanics,
and, by using the stationary phase method, gives the possibility to discuss
transmission times.Comment: 10 pages, 2 figure
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