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	Experimental tests of Bell's inequality
		For timing in a test of Bell's inequality to be conclusive requires that we time the occurrence of a macroscopic event.
		In contrast to previous measurements with massive particles, this violation of Bell's inequality was obtained by use of a complete set of measurements.
		Bell's inequality tests necessitate major improvements of technology in order to finally, after more than 15 years, go significantly beyond the 1982 experiment of Aspect et al.
	www.mtnmath.com /whatrh/node81.html (2118 words)

	Clauser and Horne's 1974 Bell test
		Not all of the inequalities to be found in text books and popular articles have been used in practice - not all are equally general, some in fact holding true for only rather limited classes of local realist theory, typically restricted to experiments in which there are no null outcomes, the detectors being perfect.
		Special cases of the Bell inequalities apply when there is rotational invariance and the detector settings are selected with the differences all equal to either φ or 3φ for some angle φ.
		The important feature of the CH74 inequality is, as is stressed both in the 1974 paper and in the 1978 report on the Bell tests by Clauser and Shimony (Clauser, 1978), that it does not require knowledge of N, the number of emitted pairs.
	www.starrepublic.org /encyclopedia/wikipedia/c/cl/clauser_and_horne_s_1974_bell_test.html (1554 words)

	CHSH inequality - Wikipedia, the free encyclopedia
		In physics, the CHSH Bell test is an application of Bell's theorem, intended to distinguish between quantum mechanics (QM) and local hidden variable theories.
		They derived the CHSH inequality, which, as with John Bell's original one (Bell, 1964), applies to a statistical property of counts of "coincidences" in a Bell test experiment that follows from the assumption that there exist underlying local hidden variables.
		The inequality must be obeyed under local realism but can be infringed under certain conditions by the QM formula.
	en.wikipedia.org /wiki/CHSH_inequality (1366 words)

	Bell test experiments - Wikipedia, the free encyclopedia
		The term "Bell inequality" can mean any one of a number of inequalities — in practice, in real experiments, the CHSH or CH74 inequality, not the original one derived by John Bell.
		One of the main achievements of this new branch of physics is showing that violation of Bell's inequalities leads to the possibility of a secure information transfer, which utilizes the so-called quantum cryptography (involving entangled states of pairs of particles).
		The second was the first application of the CHSH inequality, the third the famous one (originally suggested by John Bell) in which the choice between the two settings on each side was made during the flight of the photons.
	en.wikipedia.org /wiki/Bell_test_loopholes (2225 words)

	CHSH inequality -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-24)
		If it is numerically greater than 2 it has infringed the CHSH inequality and the experiment is declared to have supported the QM prediction and ruled out all local hidden variable theories.
		It would appear from both these later derivations that the only assumptions really needed for the inequality itself (as opposed to the method of estimation of the test statistic) are that the distribution of the possible states of the source remains constant and the detectors on the two sides act independently.
		To obtain the CHSH test statistic S (expression (2)), all that is needed is to multiply the inequalities for which j is different from k by −1 and add these to the inequalities for which j and k are the same.
	www.absoluteastronomy.com /encyclopedia/c/ch/chsh_inequality3.htm (1380 words)

	CONK! Encyclopedia: Bell's_inequality (Site not responding. Last check: 2007-10-24)
		He showed that the assumption of local realism - that particle attributes have definite values independent of the act of observation and that physical effects have a finite propagation speed - leads to a requirement for certain types of phenomena which is not present in quantum mechanics.
		The QM predicted correlation is due to quantum entanglement of the pair, with the idea that their state is not determined until the point at which a measurement is made on one or the other.
		Bell's inequalities are tested by "coincidence counts" from a Bell test experiment such as the optical one shown in the diagram.
	www.conk.com /search/encyclopedia.cgi?q=Bell's_inequality (3057 words)

	Bell test loopholes
		One can either argue that Bell's logic was wrong and his inequality can be infringed without implying nonlocal effects; or one may challenge the experimental evidence and the correctness of the quantum-mechanical prediction.
		If the logic of the experiments is studied in conjunction with the geometry it can be seen that, given the low detection efficiencies achieved in the actual experiments, the set of detected pairs is unlikely in general to be a fair sample of those emitted (see the "Chaotic Ball" model).
		It is the timing, locality or light cone one, whereby the violation of the inequality is supposed to be due to exchange of signals between the detectors during flight of the "photons".
	www.starrepublic.org /encyclopedia/wikipedia/b/be/bell_test_loopholes.html (844 words)

	inequality
		If the sense of the inequality is the same for all values of the variables for which its members are defined, then the inequality is called an "absolute" or "unconditonal" inequality.
		If the sense of an inequality holds only for certain values of the variables involved, but is reversed or destroyed for other values of the variables, it is called a conditional inequality.
		The sense of an inequality is not changed if both sides are increased or decreased by the same number, or if both sides are multiplied or divided by a positive number; the sense of an inequality is reversed if both members are multiplied or divided by a negative number.
	www.fact-library.com /inequality.html (355 words)

	Bell state - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-24)
		They are named after John S. Bell, as they are the subject of his famous Bell inequality.
		A Bell state is defined as a maximally entangled quantum state of two qubits.
		John S. Bell showed in his famous paper of 1964 by using simple probability theory arguments that these correlations cannot be perfect in case of "pre-agreement" stored in some hidden variables -- but that quantum mechanics predict perfect correlations.
	hartselle.us /project/wikipedia/index.php/Bell_state (556 words)

	Encyclopedia: CHSH inequality (Site not responding. Last check: 2007-10-24)
		John S. Bell (June 28, 1928 - October 1, 1990) was a physicist who became well known as the originator of Bells Theorem, regarded by some in the quantum physics community as one of the most important theorems of the 20th century.
		Bells Theorem states that a Bell inequality must be obeyed under any local hidden variable theory but is violated under quantum mechanics (QM).
		Quantum entanglement is a quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other, even though the individual objects may be spatially separated.
	www.nationmaster.com /encyclopedia/CHSH-inequality (1737 words)

	ProjectW (Site not responding. Last check: 2007-10-24)
		This is used to construct a family of Bell inequalities for bipartite quantum systems of arbitrarily high dimensionality which are strongly resistant to noise.
		John Bell’s hidden variables model, (and the inequalities used to investigate it), are at the very core of the subject of quantum non locality.
		We show that the 2 sided memory loophole allows a systematic violation of the CHSH inequality when the data are analysed in the standard way, but cannot produce a violation if a CHSH expression depending linearly on the data is used.
	atesit.phys.uniroma1.it /BristolReport.htm (560 words)

	List Of Articles (Site not responding. Last check: 2007-10-24)
		It is generally believed that Bell's inequality holds for the case of entangled states, including two correlated particles or special states of a single particle.
		Considering an extended type of Bohm's version of EPR thought experiment, we derive Bell's inequality for the case of factorizable contextual hidden variable theories which are consistent with the predictions of quantum theory.
		In the experimental verification of Bell's inequalities in real photonic experiments, it is generally believed that the so-called fair sampling assumption (which means that a small fraction of results provide a fair statistical sample) has an unavoidable role.
	theory.ipm.ac.ir /papers/shafiee.html (801 words)

	The CH74 Bell test
		“Bell inequalities” are designed to form the basis of tests for the non-local “quantum entanglement” phenomenon predicted by quantum mechanics (QM) as against “local hidden variable” theories.
		(CHSH) two-channel test is briefly discussed, then two different derivations of the single-channel inequality.
		Aspect, and, one must presume, others who are continuing to use the CHSH test, are evidently labouring under a misapprehension regarding the assumptions involved in the CH74 test.
	freespace.virgin.net /ch.thompson1/Papers/CH74/CH74assumptions.htm (2625 words)

	John Stewart Bell
		In 1964 he derived an inequality that must be satisfied for there to be a local hidden-variable theory of quantum mechanics.
		In 1967 the first of many experiments that have shown a violation of Bell's Inequality was conducted.
		For more on the history and physics of Bell's theorem, see the articles on Bell's inequality and the EPR paradox.
	www.brainyencyclopedia.com /encyclopedia/j/jo/john_stewart_bell.html (425 words)

	Bell's theorem general proof
		from 8.7 by converting the equality to an inequality.
		This is called the CHSH inequality from the initials of the authors who first derived it[
		For the experiment involving magnetic spin in Section 8.4 provides a good example of how this inequality is violated.
	www.mtnmath.com /whatrh/node80.html (504 words)

	Bell's theorem (Site not responding. Last check: 2007-10-24)
		The Theorem is named after John Bell, whose ground-breaking mid-1960's papers examined both von Neumann's proof of the non-existence of hidden variables (1932) and the EPR paradox (1935) in greater detail.
		Experimental tests of Bell inequalities support the failure of local realism, and in particular, that some of unexpected correlations suggested by the EPR thought experiment do in fact occur.
		For approaches that explicitly formalize local realism, see the page on the CHSH inequality, where two derivations are given, including one by Bell (Bell, 1971).
	www.worldhistory.com /wiki/B/Bell's-theorem.htm (2392 words)

	"My bound" : citing
		1996 A. Chefles, S.M. Barnett, "Complementarity and Cirel'son's inequality." J. Phys.
		1984 A.A. Grib, "Bell's inequalities and experimental verification of quantum correlations at macroscopic distances." Soviet Phys.
		1987 L.J. Landau, "On the violation of Bell's inequality in quantum theory." Phys.
	www.tau.ac.il /~tsirel/Research/mybound/cit_a.html (1317 words)

	Bell test experiments - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-24)
		In quantum mechanics, Bell's Theorem states that a Bell inequality must be obeyed under any local hidden variable theory but can in certain circumstance be violated under quantum mechanics(QM).
		While more work needs to be done, it now appears that fair sampling is a reasonable assumption and is therefore not a loophole.
		Weihs, 1998: G. Weihs, et al., Violation of Bell’s inequality under strict Einstein locality conditions (http://arXiv.org/abs/quant-ph/9910080), Phys.
	hartselle.us /project/wikipedia/index.php/Bell_test_loopholes (1806 words)

	Stronger-than-quantum correlations
		Bell s inequality is a condition which must be fulfilled by local realistic, i.e.
		A violation of Bell's inequality by the maximum value of 4 has also been studied by Popescu and Rohrlich [8] and, for a classical system, by Aerts [16].
		Consequently a violation of Bell s inequality by the maximum value of 4 would be a two-particle analogue to the GHZ argument [17].
	tph.tuwien.ac.at /~svozil/publ/strong.htm (1897 words)

	Experimental violation of a Bell's inequality with efficient detection : Nature
		In contrast to previous measurements with massive particles, this violation of Bell's inequality was obtained by use of a complete set of measurements.
		The CHSH inequality (equation (2)) is maximally violated by quantum mechanics at certain sets of phase angles.
		Lamehi-Rachti, M. and Mittig, W. Quantum mechanics and hidden variables: a test of Bell's inequality by the measurement of the spin correlation in low-energy proton-proton scattering.
	www.nature.com /nature/journal/v409/n6822/full/409791a0.html (2993 words)

	[No title] (Site not responding. Last check: 2007-10-24)
		)]), [Gisin 91 a] (Bell's inequality holds for all non-product states), [Peres 92 d], [Gisin-Peres 92] (for two spin-s particles in the singlet state the violation of the CHSH inequality is constant for any s; large s is no guarantee of classical behavior) [Geng 92] (for two different spins), [Wódkiewicz 92], [Peres 93 a] (Sec.
		[Braunstein-Caves 88, 89, 90] (chained Bell's inequalities, with more than two alternative observables on each particle), [Gisin 99], [Collins-Gisin 03] (for three possible two-outcome measurements per qubit, there is only one inequality which is inequivalent to the CHSH inequality; there are states which violate it but do not violate the CHSH inequality).
		For mixed states: [Braunstein-Mann-Revzen 92] (maximum violation for mixed states), [Mann-Nakamura-Revzen 92], [Beltrametti-Maczy\'nski 93], [Horodecki-Horodecki-Horodecki 95] (necessary and sufficient condition for a mixed state to violate the CHSH inequalities), [Aravind 95].
	physmag.h1.ru /bibliography/1_1.html (1311 words)

	Tax Loophole (Site not responding. Last check: 2007-10-24)
		The "Bell inequalities" tested in actual "Bell test experiments" are not quite the original ones that Bell proposed, nor do experimental conditions necessarily comply with the assumptions on which the inequalities depend.
		It is well known that the CHSH inequality requires fair sampling, while it is perhaps less well known (though it is clear from the 1974 derivation) that the CH74 one does not.
		The majority of recent experiments (almost all since about 1985) have used the CHSH or related inequalities, amongst which is classed, for this purpose, the "visibility" test.
	www.wwwtln.com /finance/176/tax-loophole.html (1805 words)

	Quantum Cryptography with Polarization Entangled Photons (Site not responding. Last check: 2007-10-24)
		If the measured probabilities violate Wigner's inequality, then the security of the quantum channel is ascertained, and the generated keys can readily be used.
		This scheme is an improvement on the Ekert scheme which uses the CHSH inequality and requires three settings of Alice's and Bob's analyzers for testing the inequality and generating the keys.
		From the resulting nine combinations of settings, four are taken for testing the inequality, two are used for building the keys and three are omitted at all.
	www.quantum.univie.ac.at /research/photonentangle/crypto/prot_wigner.html (249 words)

	2007 May « Quantum Quandaries
		In any case, a report of an experiment on quantum foundations in Nature cannot possibly go ignored for too long on this blog.
		report on is an experiment showing violations of an inequality proposed by Leggett, aimed at ruling out a class of nonlocal hidden-variable theories, whilst simultaneously violating the CHSH inequality, so that local hidden-variable theories are also ruled out in the same experiment.
		This is of course subject to the usual caveats that apply to Bell experiments, but let’s grant the correctness of the analysis for now and take a look at the class of nonlocal hidden-variable theories that are ruled out.
	mattleifer.wordpress.com /2007/05 (336 words)

	[No title] (Site not responding. Last check: 2007-10-24)
		By exhibiting a violation of a novel form of the Bell-CHSH inequality, \.{Z}ukowski has recently established that the quantum correlations exploited in the standard perfect teleportation protocol cannot be recovered by any local hidden variables model.
		Allowing the quantum channel state in the protocol to be given by any density operator of two spin-1/2 particles, we show that a violation of a generalized form of \.{Z}ukowski's teleportation inequality can only occur if the channel state, considered by itself, violates a Bell-CHSH inequality.
		On the other hand, although it is sufficient for a teleportation process to have a nonclassical fidelity---defined as a fidelity exceeding $2/3$---that the channel state employed violate a Bell-CHSH inequality, we show that such a violation does \emph{not} imply a violation of \.{Z}ukowski's teleportation inequality or any of its generalizations.
	www.cs.odu.edu /~melmilig/maktbaelectroneya/files/00000207.dc (185 words)

	Distributing entanglement and single photons through an intra-city, free-space quantum channel
		For this experiment, our quantum channel was maintained for a total of 40 minutes during which time a coincidence lock found approximately 60000 coincident detection events.
		The polarization correlations in those events yielded a Bell parameter, S=2.27±0.019, which violates the CHSH-Bell inequality by 14 standard deviations.
		Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell's Inequality under Strict Einstein Locality Conditions,” Phys.
	www.opticsexpress.org /abstract.cfm?URI=OPEX-13-1-202 (938 words)

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