BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY: CHSH Bell Inequalities made simple(r): Linear functions\, loopho les\, and how to post-select data without causing one. - Dan Browne (UCL) DTSTART:20110203T141500Z DTEND:20110203T151500Z UID:TALK28120@talks.cam.ac.uk CONTACT:Ashley Montanaro DESCRIPTION:This work began as an investigation into whether the cosmetic similarities between Bell inequality experiments and measurement-based qua ntum computing might reflect a deeper connection. What we find is that the ``computational viewpoint'' is remarkably well-suited to the study of CHS H-type Bell inequalities\, and provides a very simple way of characterisin g the correlations permitted by local hidden variable (LHV) theories. Whil e mathematically equivalent to previous work (see Werner and Wolf's paper cited below for the original derivation of this set of correlations) this provides a cleaner and simpler operational definition\, which\, in particu lar\, make ''loopholes'' easy to characterise.\n\nLoopholes in Bell inequa lity experiments arise when imperfections in the experimental setup mean t hat it does not concord precisely with the assumptions under which Bell in equalities are derived. Often those flaws mean that local hidden variable theories would be able to access correlations which in a strict Bell setup would be forbidden to them\, and hence a quantum mechanical reproduction of that correlation cannot refute local hidden variable theories - a "loo phole" in the argument.\n\nThe simplicity of the characterisation of the L HV correlations in our model allow us to pin down explicit mechanisms by w hich loopholes arise. For example\, a well-known loophole is the detector loophole\, where\, due to inefficient detectors\, data must be post-selec ted - only when both detectors fire can the data be used. The origin of th e detector loophole can be cleanly understood within our framework\, and c onstructing LHV models which fake an imperfect quantum detector while maxi mally violating Bell inequalities (to the bounds previously identified by Garg and Mermin) is straightforward. We see that there are many ways in w hich post-selection of data can cause loopholes.\n\nIn addition to providi ng a simpler (and quantum information friendly) way to understand previous results (hence "for beginners")\, we can use our model for new investigat ions. For example\, we can characterise post-selection strategies where no loopholes arise - and consider the effect of this post-selection upon qua ntum correlations. We find that there is a broad family of non-loophole in ducing post-selection strategies which one can adopt. Surprisingly\, we se e that while not expanding the region of correlations accessible by LHV th eories\, such post-selection can expand the region of correlations accessi ble by quantum theories. In other words\, performing this post-selection allows quantum measurements to achieve correlations which were previously impossible\, without creating a loophole. This effect becomes apparent in the multi-partite setting (the smallest example we have is for 6 qubits)\, and does not enhance the bi-partite CHSH inequality\, therefore\, it is c urrently unclear whether this post-selection will aid current Bell inequal ity experiments. However\, the larger multi-partite region now includes ne w types of quantum correlation previously overlooked in the Bell inequalit y setting\, most notably (post-selected simulations of) the adaptive measu rements which arise in measurement-based quantum computation. We expect th at these results will give new insights into measurement-based quantum com putation and related areas and will be valuable in the search for informat ion theoretic characterisations of the set of quantum correlations which g o beyond the bi-partite setting.\n\nThese results were developed in collab oration with Matty Hoban.\n\nPrevious work in this direction:\nJ. Anders a nd D.E. Browne\, arXiv:0805.1002\;\nM. Hoban et al\, arXiv:1009.5213\n\nMa in reference for these results:\nM. Hoban and D. E. Browne\, in preparatio n (hopefully on the arxiv very soon)\n\nOther reading:\nMulti-partite Bell inequalities\, Werner and Wolf\, Phys. Rev. A 64\, 032112 (2001)\;\nDetec tor Loophole\, Garg and Mermin\, Phys. Rev. D 35\, 3831–3835 (1987) LOCATION:MR13\, Centre for Mathematical Sciences END:VEVENT END:VCALENDAR