9,284 research outputs found
A New Approximate Min-Max Theorem with Applications in Cryptography
We propose a novel proof technique that can be applied to attack a broad
class of problems in computational complexity, when switching the order of
universal and existential quantifiers is helpful. Our approach combines the
standard min-max theorem and convex approximation techniques, offering
quantitative improvements over the standard way of using min-max theorems as
well as more concise and elegant proofs
Galois correspondence for counting quantifiers
We introduce a new type of closure operator on the set of relations,
max-implementation, and its weaker analog max-quantification. Then we show that
approximation preserving reductions between counting constraint satisfaction
problems (#CSPs) are preserved by these two types of closure operators.
Together with some previous results this means that the approximation
complexity of counting CSPs is determined by partial clones of relations that
additionally closed under these new types of closure operators. Galois
correspondence of various kind have proved to be quite helpful in the study of
the complexity of the CSP. While we were unable to identify a Galois
correspondence for partial clones closed under max-implementation and
max-quantification, we obtain such results for slightly different type of
closure operators, k-existential quantification. This type of quantifiers are
known as counting quantifiers in model theory, and often used to enhance first
order logic languages. We characterize partial clones of relations closed under
k-existential quantification as sets of relations invariant under a set of
partial functions that satisfy the condition of k-subset surjectivity. Finally,
we give a description of Boolean max-co-clones, that is, sets of relations on
{0,1} closed under max-implementations.Comment: 28 pages, 2 figure
Dependence Logic with Generalized Quantifiers: Axiomatizations
We prove two completeness results, one for the extension of dependence logic
by a monotone generalized quantifier Q with weak interpretation, weak in the
meaning that the interpretation of Q varies with the structures. The second
result considers the extension of dependence logic where Q is interpreted as
"there exists uncountable many." Both of the axiomatizations are shown to be
sound and complete for FO(Q) consequences.Comment: 17 page
Estimating entanglement in teleportation experiments
Quantum state teleportation is a protocol where a shared entangled state is
used as a quantum channel to transmit quantum information between distinct
locations. Here we consider the task of estimating entanglement in
teleportation experiments. We show that the data accessible in a teleportation
experiment allows to put a lower bound on some entanglement measures, such as
entanglement negativity and robustness. Furthermore, we show cases in which the
lower bounds are tight. The introduced lower bounds can also be interpreted as
quantifiers of the nonclassicality of a teleportation experiment. Thus, our
findings provide a quantitative relation between teleportation and
entanglement.Comment: The title is changed and the manuscript is significantly
restructured. Codes available at
https://github.com/paulskrzypczyk/nonclassicalteleportation/blob/master/Quantifying%20teleportation.ipyn
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