36,585 research outputs found

### Bell's inequality and the coincidence-time loophole

This paper analyzes effects of time-dependence in the Bell inequality. A
generalized inequality is derived for the case when coincidence and
non-coincidence [and hence whether or not a pair contributes to the actual
data] is controlled by timing that depends on the detector settings. Needless
to say, this inequality is violated by quantum mechanics and could be violated
by experimental data provided that the loss of measurement pairs through
failure of coincidence is small enough, but the quantitative bound is more
restrictive in this case than in the previously analyzed "efficiency loophole."Comment: revtex4, 3 figures, v2: epl document class, reformatted w slight
change

### On an Argument of David Deutsch

We analyse an argument of Deutsch, which purports to show that the
deterministic part of classical quantum theory together with deterministic
axioms of classical decision theory, together imply that a rational decision
maker behaves as if the probabilistic part of quantum theory (Born's law) is
true. We uncover two missing assumptions in the argument, and show that the
argument also works for an instrumentalist who is prepared to accept that the
outcome of a quantum measurement is random in the frequentist sense: Born's law
is a consequence of functional and unitary invariance principles belonging to
the deterministic part of quantum mechanics. Unfortunately, it turns out that
after the necessary corrections we have done no more than give an easier proof
of Gleason's theorem under stronger assumptions. However, for some special
cases the proof method gives positive results while using different assumptions
to Gleason. This leads to the conjecture that the proof could be improved to
give the same conclusion as Gleason under unitary invariance together with a
much weaker functional invariance condition.Comment: Revision 28-7-03: added reference Final revision 28-05-04. To appear
in proceedings of "Quantum Probability and Infinite Dimensional Analysis",
Greifswald, 2003; World Scientifi

### Teleportation into Quantum Statistics

The paper is a tutorial introduction to quantum information theory,
developing the basic model and emphasizing the role of statistics and
probability.Comment: Been waiting 3 years for math.S

### Better Bell inequalities (passion at a distance)

I explain so-called quantum nonlocality experiments and discuss how to
optimize them. Statistical tools from missing data maximum likelihood are
crucial. New results are given on CGLMP, CH and ladder inequalities. Open
problems are also discussed.Comment: Published at http://dx.doi.org/10.1214/074921707000000328 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org

### Pearle's Hidden-Variable Model Revisited

Pearle (1970) gave an example of a local hidden variables model which exactly
reproduced the singlet correlations of quantum theory, through the device of
data-rejection: particles can fail to be detected in a way which depends on the
hidden variables carried by the particles and on the measurement settings. If
the experimenter computes correlations between measurement outcomes of particle
pairs for which both particles are detected, he is actually looking at a
subsample of particle pairs, determined by interaction involving both
measurement settings and the hidden variables carried in the particles. We
correct a mistake in Pearle's formulas (a normalization error) and more
importantly show that the model is more simple than first appears. We
illustrate with visualisations of the model and with a small simulation
experiment, with code in the statistical programming language R included in the
paper. Open problems are discussed.Comment: 19pp. This is now arXiv version 4 = final revision for journa

### No probability loophole in the CHSH

Geurdes (2014, Results in Physics) outlines a probabilistic construction of a
counterexample to Bell's theorem. He gives a procedure to repeatedly sample
from a specially constructed "pool" of local hidden variable models (depending
on a table of numerically calculated parameters) and select from the results
one LHV model, determining a random value S of the usual CHSH combination of
four (theoretical) correlation values. He claims Prob(|S| > 2) > 0. We expose a
fatal flaw in the analysis: the procedure generates a non-local hidden variable
model.
To disprove this claim, Geurdes should program his procedure and generate
random LHV's till he finds one violating the CHSH inequality.Comment: version 3: major revision, new analysis, identification of main erro

- …