7,136 research outputs found
Nonlocality and entanglement in qubit systems
Nonlocality and quantum entanglement constitute two special aspects of the
quantum correlations existing in quantum systems, which are of paramount
importance in quantum-information theory. Traditionally, they have been
regarded as identical (equivalent, in fact, for pure two qubit states, that is,
{\it Gisin's Theorem}), yet they constitute different resources. Describing
nonlocality by means of the violation of several Bell inequalities, we obtain
by direct optimization those states of two qubits that maximally violate a Bell
inequality, in terms of their degree of mixture as measured by either their
participation ratio or their maximum eigenvalue
. This optimum value is obtained as well, which coincides with
previous results. Comparison with entanglement is performed too. An example of
an application is given in the XY model. In this novel approximation, we also
concentrate on the nonlocality for linear combinations of pure states of two
qubits, providing a closed form for their maximal nonlocality measure. The case
of Bell diagonal mixed states of two qubits is also extensively studied.
Special attention concerning the connection between nonlocality and
entanglement for mixed states of two qubits is paid to the so called maximally
entangled mixed states. Additional aspects for the case of two qubits are also
described in detail. Since we deal with qubit systems, we will perform an
analogous study for three qubits, employing similar tools. Relation between
distillability and nonlocality is explored quantitatively for the whole space
of states of three qubits. We finally extend our analysis to four qubit
systems, where nonlocality for generalized Greenberger-Horne-Zeilinger states
of arbitrary number of parties is computed.Comment: 16 pages, 3 figure
Triple Cohomology of Lie-Rinehart Algebras and the Canonical Class of Associative Algebras
We introduce a bicomplex which computes the triple cohomology of
Lie--Rinehart algebras. We prove that the triple cohomology is isomorphic to
the Rinehart cohomology \cite{Ri} provided the Lie--Rinehart algebra is
projective over the corresponding commutative algebra. As an application we
construct a canonical class in the third dimensional cohomology corresponding
to an associative algebra
Maximally correlated multipartite quantum states
We investigate quantum states that posses both maximum entanglement and
maximum discord between the pertinent parties. Since entanglement (discord) is
defined only for bipartite (two qubit) systems, we shall introduce an
appropriate sum over of all bi-partitions as the associated measure. The
ensuing definition --not new for entanglement-- is thus extended here to
quantum discord. Also, additional dimensions within the parties are considered
({\it qudits}). We also discuss nonlocality (in the form of maximum violation
of a Bell inequality) for all multiqubit systems. The emergence of more
nonlocal states than local ones, all of them possessing maximum entanglement,
will be linked, surprisingly enough, to whether quantum mechanics is defined
over the fields of real or complex numbers.Comment: 13 pages, 5 figures, 2 table
The 750 GeV Diphoton Excess as a First Light on Supersymmetry Breaking
One of the most exciting explanations advanced for the recent diphoton excess
found by ATLAS and CMS is in terms of sgoldstino decays: a signal of low-energy
supersymmetry-breaking scenarios. The sgoldstino, a scalar, couples directly to
gluons and photons, with strength related to gaugino masses, that can be of the
right magnitude to explain the excess. However, fitting the suggested resonance
width, Gamma ~ 45 GeV, is not so easy. In this paper we explore efficient
possibilities to enhance the sgoldstino width, via the decay into two Higgses,
two Higgsinos and through mixing between the sgoldstino and the Higgs boson. In
addition, we present an alternative and more efficient mechanism to generate a
mass splitting between the scalar and pseudoscalar components of the
sgoldstino, which has been suggested as an interesting alternative explanation
to the apparent width of the resonance.Comment: 14 pages, 3 figure
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