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CATEGORIES:CQIF Seminar
SUMMARY: CHSH Bell Inequalities made simple(r): Linear fu
nctions\, loopholes\, and how to post-select data
without causing one. - Dan Browne (UCL)
DTSTART;TZID=Europe/London:20110203T141500
DTEND;TZID=Europe/London:20110203T151500
UID:TALK28120AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/28120
DESCRIPTION:This work began as an investigation into whether t
he cosmetic similarities between Bell inequality e
xperiments and measurement-based quantum computing
might reflect a deeper connection. What we find i
s that the ``computational viewpoint'' is remarkab
ly well-suited to the study of CHSH-type Bell ineq
ualities\, and provides a very simple way of chara
cterising the correlations permitted by local hidd
en variable (LHV) theories. While mathematically e
quivalent to previous work (see Werner and Wolf's
paper cited below for the original derivation of t
his set of correlations) this provides a cleaner a
nd simpler operational definition\, which\, in par
ticular\, make ''loopholes'' easy to characterise.
\n\nLoopholes in Bell inequality experiments arise
when imperfections in the experimental setup mean
that it does not concord precisely with the assum
ptions under which Bell inequalities are derived.
Often those flaws mean that local hidden variable
theories would be able to access correlations whic
h in a strict Bell setup would be forbidden to the
m\, and hence a quantum mechanical reproduction of
that correlation cannot refute local hidden vari
able theories - a "loophole" in the argument.\n\nT
he simplicity of the characterisation of the LHV c
orrelations in our model allow us to pin down expl
icit mechanisms by which loopholes arise. For exam
ple\, a well-known loophole is the detector loopho
le\, where\, due to inefficient detectors\, data m
ust be post-selected - only when both detectors f
ire can the data be used. The origin of the detect
or loophole can be cleanly understood within our f
ramework\, and constructing LHV models which fake
an imperfect quantum detector while maximally viol
ating Bell inequalities (to the bounds previously
identified by Garg and Mermin) is straightforward
. We see that there are many ways in which post-se
lection of data can cause loopholes.\n\nIn additio
n to providing a simpler (and quantum information
friendly) way to understand previous results (henc
e "for beginners")\, we can use our model for new
investigations. For example\, we can characterise
post-selection strategies where no loopholes arise
- and consider the effect of this post-selection
upon quantum correlations. We find that there is a
broad family of non-loophole inducing post-select
ion strategies which one can adopt. Surprisingly\,
we see that while not expanding the region of cor
relations accessible by LHV theories\, such post-s
election can expand the region of correlations acc
essible by quantum theories. In other words\, per
forming this post-selection allows quantum measure
ments to achieve correlations which were previousl
y impossible\, without creating a loophole. This e
ffect becomes apparent in the multi-partite settin
g (the smallest example we have is for 6 qubits)\,
and does not enhance the bi-partite CHSH inequali
ty\, therefore\, it is currently unclear whether t
his post-selection will aid current Bell inequalit
y experiments. However\, the larger multi-partite
region now includes new types of quantum correlati
on previously overlooked in the Bell inequality se
tting\, most notably (post-selected simulations of
) the adaptive measurements which arise in measure
ment-based quantum computation. We expect that the
se results will give new insights into measurement
-based quantum computation and related areas and w
ill be valuable in the search for information theo
retic characterisations of the set of quantum corr
elations which go beyond the bi-partite setting.\n
\nThese results were developed in collaboration wi
th Matty Hoban.\n\nPrevious work in this direction
:\nJ. Anders and D.E. Browne\, arXiv:0805.1002\;\n
M. Hoban et al\, arXiv:1009.5213\n\nMain reference
for these results:\nM. Hoban and D. E. Browne\, i
n preparation (hopefully on the arxiv very soon)\n
\nOther reading:\nMulti-partite Bell inequalities\
, Werner and Wolf\, Phys. Rev. A 64\, 032112 (2001
)\;\nDetector Loophole\, Garg and Mermin\, Phys. R
ev. D 35\, 3831–3835 (1987)
LOCATION:MR13\, Centre for Mathematical Sciences
CONTACT:Ashley Montanaro
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