160 research outputs found
Fifty years of similarity relations: a survey of foundations and applications
On the occasion of the 50th anniversary of the publication of Zadeh's significant paper Similarity Relations and Fuzzy Orderings, an account of the development of similarity relations during this time will be given. Moreover, the main topics related to these fuzzy relations will be reviewed.Peer ReviewedPostprint (author's final draft
Quantum Correlations in Systems of Indistinguishable Particles
We discuss quantum correlations in systems of indistinguishable particles in
relation to entanglement in composite quantum systems consisting of well
separated subsystems. Our studies are motivated by recent experiments and
theoretical investigations on quantum dots and neutral atoms in microtraps as
tools for quantum information processing. We present analogies between
distinguishable particles, bosons and fermions in low-dimensional Hilbert
spaces. We introduce the notion of Slater rank for pure states of pairs of
fermions and bosons in analogy to the Schmidt rank for pairs of distinguishable
particles. This concept is generalized to mixed states and provides a
correlation measure for indistinguishable particles. Then we generalize these
notions to pure fermionic and bosonic states in higher-dimensional Hilbert
spaces and also to the multi-particle case. We review the results on quantum
correlations in mixed fermionic states and discuss the concept of fermionic
Slater witnesses. Then the theory of quantum correlations in mixed bosonic
states and of bosonic Slater witnesses is formulated. In both cases we provide
methods of constructing optimal Slater witnesses that detect the degree of
quantum correlations in mixed fermionic and bosonic states.Comment: 46 pages, 4 eps figure
Is mereology empirical? Composition for fermions
How best to think about quantum systems under permutation invariance is a
question that has received a great deal of attention in the literature. But
very little attention has been paid to taking seriously the proposal that
permutation invariance reflects a representational redundancy in the formalism.
Under such a proposal, it is far from obvious how a constituent quantum system
is represented. Consequently, it is also far from obvious how quantum systems
compose to form assemblies, i.e. what is the formal structure of their
relations of parthood, overlap and fusion.
In this paper, I explore one proposal for the case of fermions and their
assemblies. According to this proposal, fermionic assemblies which are not
entangled -- in some heterodox, but natural sense of 'entangled' -- provide a
prima facie counterexample to classical mereology. This result is puzzling;
but, I argue, no more intolerable than any other available interpretative
option.Comment: 24 pages, 1 figur
GHZ and W Entanglement Witnesses for the Non-interacting Fermi gas
The existence and nature of tripartite entanglement of a noninteracting Fermi
gas (NIFG) is investigated. Three new classes of parameterized entanglement
witnesses (EWs) are introduced with the aim of detecting genuine tripartite
entanglement in the three-body reduced density matrix and discriminating
between the presence of the two types of genuine tripartite entanglement, W\B
and GHZ\W. By choosing appropriate EW operators, the problem of finding GHZ and
W EWs is reduced to linear programming. Specifically, we devise new W EWs based
on a spin-chain model with periodic boundary conditions, and we construct a
class of parametrized GHZ EWs by linearly combining projection operators
corresponding to all the different state-vector types arising for a
three-fermion system. A third class of EWs is provided by a GHZ stabilizer
operator capable of distinguishing W\B from GHZ\B entanglement, which is not
possible with EWs. Implementing these classes of EWs, it is found that all
states containing genuine tripartite entanglement are of W type, and hence
states containing GHZ\W genuine tripartite entanglement do not arise. Some
genuine tripartite entangled states that have a positive partial transpose
(PPT) with respect to some bipartition are detected. Finally, it is
demonstrated that a NIFG does not exhibit "pure" W\B genuine tripartite
entanglement: three-party entanglement without any separable or biseparable
admixture does not occur.Comment: 15 pages, 7 figures, minor changes, to appear in Physical Review
An algorithm to compute the transitive closure, a transitive approximation and a transitive opening of a proximity
A method to get the transitive closure, a transitive opening and a transitive approximation of a reflexive and symmetric fuzzy relation is presented. The method builds at the same time a binary partition tree for the output similarities.Peer ReviewedPreprin
Photon engineering for quantum information processing
We study distinguishing information in the context of quantum interference
involving more than one parametric downconversion (PDC) source and in the
context of polarization-entangled photon pairs based on PDC. We arrive at
specific design criteria for two-photon sources so that when used as part of
complex optical systems, such as photon-based quantum information processing
schemes, distinguishing information between the photons is eliminated
guaranteeing high visibility interference. We propose practical techniques
which lead to suitably engineered two-photon states that can be realistically
implemented with available technology. Finally, we study an implementation of
the nonlinear-sign shift (NS) logic gate with PDC sources and show the effect
of distinguishing information on the performance of the gate.Comment: 23 pages, 13 figures. submitted to Quantum Information & Computatio
Computing a T-transitive lower approximation or opening of a proximity relation
Fuzzy Sets and Systems. IMPACT FACTOR: 1,181. Fuzzy Sets and Systems. IMPACT FACTOR: 1,181. Since transitivity is quite often violated even by decision makers that accept transitivity in their preferences as a condition for consistency, a standard approach to deal with intransitive preference elicitations is the search for a close enough transitive preference relation, assuming that such a violation is mainly due to decision maker estimation errors. In some way, the more number of elicitations, the more probable inconsistency is. This is mostly the case within a fuzzy framework, even when the number of alternatives or object to be classified is relatively small. In this paper we propose a fast method to compute a T-indistinguishability from a reflexive and symmetric fuzzy relation, being T any left-continuous t-norm. The computed approximation we propose will take O(n3) time complexity, where n is the number of elements under consideration, and is expected to produce a T-transitive opening. To the authorsÂż knowledge, there are no other proposed algorithm that computes T-transitive lower approximations or openings while preserving the reflexivity and symmetry properties
An algorithm to compute the transitive closure, a transitive approximation and a transitive opening of a fuzzy proximity
A method to compute the transitive closure, a transitive opening and a transitive approximation of a reflexive and symmetric fuzzy relation is given. Other previous methods in literature compute just the transitive closure, some transitive approximations or some transitive openings. The proposed algorithm computes the three different similarities that approximate a proximity for the computational cost of computing just one. The shape of the binary partition tree for the three output similarities are the same.Peer ReviewedPostprint (published version
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