574 research outputs found
Hard Properties with (Very) Short PCPPs and Their Applications
We show that there exist properties that are maximally hard for testing, while still admitting PCPPs with a proof size very close to linear. Specifically, for every fixed ?, we construct a property P^(?)? {0,1}^n satisfying the following: Any testing algorithm for P^(?) requires ?(n) many queries, and yet P^(?) has a constant query PCPP whose proof size is O(n?log^(?)n), where log^(?) denotes the ? times iterated log function (e.g., log^(2)n = log log n). The best previously known upper bound on the PCPP proof size for a maximally hard to test property was O(n?polylog(n)).
As an immediate application, we obtain stronger separations between the standard testing model and both the tolerant testing model and the erasure-resilient testing model: for every fixed ?, we construct a property that has a constant-query tester, but requires ?(n/log^(?)(n)) queries for every tolerant or erasure-resilient tester
Compatibility and noncontextuality for sequential measurements
A basic assumption behind the inequalities used for testing noncontextual
hidden variable models is that the observables measured on the same individual
system are perfectly compatible. However, compatibility is not perfect in
actual experiments using sequential measurements. We discuss the resulting
"compatibility loophole" and present several methods to rule out certain hidden
variable models which obey a kind of extended noncontextuality. Finally, we
present a detailed analysis of experimental imperfections in a recent trapped
ion experiment and apply our analysis to that case.Comment: 15 pages, 2 figures, v2: problem with latex solve
Enforceability of labor law : evidence from a labor court in Mexico
The authors analyze lawsuits involving publicly-appointed lawyers in a labor court in Mexico to study how a rigid law is enforced. They show that, even after a judge has awarded something to a worker alleging unjust dismissal, the award goes uncollected 56 percent of the time. Workers who are dismissed after working more than seven years, however, do not leave these awards uncollected because their legally-mandated severance payments are larger. A simple theoretical model is used to generate predictions on how lawsuit outcomes should depend on the information available to the worker and on the worker's cost of collecting an award after trial, both of which are determined in part by the worker's lawyer. Differences in outcomes across lawyers are consistent with the hypothesis that firms take advantage both of workers who are poorly informed and of workers who find it more costly to collect an award after winning at trial.Public Sector Corruption&Anticorruption Measures,Information Security&Privacy,Legal Products,Microfinance,Bankruptcy and Resolution of Financial Distress
Proposed test of macroscopic quantum contextuality
We show that, for any system with a number of levels which can be identified
with n qubits, there is an inequality for the correlations between three
compatible dichotomic measurements which must be satisfied by any noncontextual
theory, but is violated by any quantum state. Remarkably, the violation grows
exponentially with n, and the tolerated error per correlation also increases
with n, showing that state-independent quantum contextuality is experimentally
observable in complex systems.Comment: REVTeX4, 5 pages, 1 figur
A Strong Composition Theorem for Junta Complexity and the Boosting of Property Testers
We prove a strong composition theorem for junta complexity and show how such
theorems can be used to generically boost the performance of property testers.
The -approximate junta complexity of a function is the
smallest integer such that is -close to a function that
depends only on variables. A strong composition theorem states that if
has large -approximate junta complexity, then has even
larger -approximate junta complexity, even for . We develop a fairly complete understanding of this behavior,
proving that the junta complexity of is characterized by that of
along with the multivariate noise sensitivity of . For the important
case of symmetric functions , we relate their multivariate noise sensitivity
to the simpler and well-studied case of univariate noise sensitivity.
We then show how strong composition theorems yield boosting algorithms for
property testers: with a strong composition theorem for any class of functions,
a large-distance tester for that class is immediately upgraded into one for
small distances. Combining our contributions yields a booster for junta
testers, and with it new implications for junta testing. This is the first
boosting-type result in property testing, and we hope that the connection to
composition theorems adds compelling motivation to the study of both topics.Comment: 44 pages, 1 figure, FOCS 202
Bell non-locality and Kochen-Specker contextuality: How are they connected?
Bell non-locality and Kochen-Specker (KS) contextuality are logically
independent concepts, fuel different protocols with quantum vs classical
advantage, and have distinct classical simulation costs. A natural question is
what are the relations between these concepts, advantages, and costs. To
address this question, it is useful to have a map that captures all the
connections between Bell non-locality and KS contextuality in quantum theory.
The aim of this work is to introduce such a map. After defining the
theory-independent notions of Bell non-locality and KS contextuality for ideal
measurements, we show that, in quantum theory, due to Neumark's dilation
theorem, every matrix of quantum Bell non-local correlations can be mapped to
an identical matrix of KS contextual correlations produced in a scenario with
identical relations of compatibility but where measurements are ideal and no
space-like separation is required. A more difficult problem is identifying
connections in the opposite direction. We show that there are "one-to-one" and
partial connections between KS contextual correlations and Bell non-local
correlations for some KS contextuality scenarios, but not for all of them.
However, there is also a method that transforms any matrix of KS contextual
correlations for quantum systems of dimension into a matrix of Bell
non-local correlations between two quantum subsystems each of them of dimension
. We collect all these connections in map and list some problems which can
benefit from this map.Comment: 13 pages, 2 figure
Necessary and sufficient detection efficiency for the Mermin inequalities
We prove that the threshold detection efficiency for a loophole-free Bell
experiment using an -qubit Greenberger-Horne-Zeilinger state and the
correlations appearing in the -partite Mermin inequality is . If
the detection efficiency is equal to or lower than this value, there are local
hidden variable models that can simulate all the quantum predictions. If the
detection efficiency is above this value, there is no local hidden variable
model that can simulate all the quantum predictions.Comment: REVTeX4, 5 pages, 1 figur
Renormalization Group Constraints on New Top Interactions from Electroweak Precision Data
Anomalous interactions involving the top quark contribute to some of the most
difficult observables to directly access experimentally. They can give however
a sizeable correction to very precisely measured observables at the loop level.
Using a model-independent effective Lagrangian approach, we present the leading
indirect constraints on dimension-six effective operators involving the top
quark from electroweak precision data. They represent the most stringent
constraints on these interactions, some of which may be directly testable in
future colliders.Comment: 14 pages, 1 Table, 1 Figure. Minor changes, references added. Matches
published versio
Candidate nomination procedures andpolitical selection: evidence from LatinAmerican parties
This paper explores empirically the role of nomination procedures on politicalselection and the determinants for adopting contestable selection methods such asprimaries. Using data from Latin American parties, I find evidence that politicalcompetition increases probability of primary adoption. Moreover, primarynominated candidates obtained larger vote shares and during their mandatecountries experienced improvements in several measures of quality of government.The results exploit within party variation and are robust to relevant identificationconcerns. Together, these findings suggest that nomination procedures matter forpolitical selection and that the quality differences are significant enough to influenceelectoral and economic outcomes.Primaries, political selection, political competition, quality of politicians.
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