140 ExperimetltatTests ofBett inequalities

[78] M. Genovese, C. Novero, and E. Predazzi, Can experimental tests of Be]] inequalities 8 performed with pseudoscalar masons be definitive? Pays. Z,eff. B 513 (2001), 401. [79] M. Genovese, C. Novero, and E. Predazzi, On the conc]usive tests of ]oca] rea]ism and Bell's Theorem without Inequalities: On the pseudoscalar masons, Rou/zd.P/zys. 32 (2002), 589. [80] M. Genovese, Entanglement properties of kaons and tests of hidden-variab]e mode]s, Inception and Scope of the GHZ Theorem P/zys. Rev. A 69 (2004), 022103. [8 1] Y. Hasegawa et a]., Vio]aLion of a Bell-]ike inequa]ity in sing]e-neutron interferometry, OLIVAL FREIRE JR AND OSVALDO PESSOA JR A/afz£re425 (2003),45. [82] E. Hag]ey et a]., Generation of Einstein-Podo]sky-Rosen pairs of atoms, P/zys. Rev. Z,eff. 79, 1 (1997). [83] M. Ansmann et a]., Violation of Be]]'s inequa]ity in Josephson phase qubits, Aiarure 461 (2009),504. [84] D.L. Moehring, M.J. Madsen, B.B. B]inov, and C. Monroe, Experimenta] Be]] inequality violation with an atom and a photon, P/zys. Rev. Z,eff. 93 (2004), 090410. 8.1 Introduction [85] M.A. Rowe et a]., Experimenta] vio]ation of a Be]]'s inequality with efhcient detection, Since its inception, fifty years ago, Bell's theorem has had a long history not only of exper- /Vafure409 (2001),791. [86] D.N. Matsukevich,P. Maunz, D.L. Moehring, S. O]mschenk,and C. Monroe, Be]] imenta[ tests but a]so of theoretical deve]opments. Studying pairs of corvelated quantum- inequality violation with two remote atomic qubits, P/zys.Reu. Z,eff. 100 (2008), mechanical particles separatedin space, in a composite "entangled" state, Be]] [ 1] showed 140404 thai the joint ascription of hidden variables and locality to the system led to an inequality [87] J. Hofmann et a]., Hera]ded entang]ement between wide]y separatedatoms, Scfefzce that is violated by the predictions of quantum mechanics. Fifteen years later, experiments 337 (2012),72. confirmed the predictions of quantum mechanics,ruling out a large class of local realist [88] M. Giustina et a]., Be]] vio]ation using entang]ed photons without the fair-sampling theories. assumption, ]Vaf re 497 (2013), 227. [89] J. Larsson et a]., Be]]-inequa]ity vio]ation with entang]ed photons, free of the One of the most meaningful theoretical developmentsthat followed Bell's work was coincidence-time loophole, Pays. Rev. A 90 (2014), 032107. the Greenberger--Horne--Zeilinger (GHZ) theorem, also known as Bell's theorem without [90] B.G. Christensen et a]., Detection-]oopho]e-free test of quantum non]oca]ity, and inequalities. In 1989, the American physicists Daniel Greenberger and Michael Horne, who applications, P/zys. Rev. Z,eff. 111 (2013), 1 30406. had been working on Bell's theorem since the late 1960s, together with the Ausuian physi- [9 1] G. Au]etta (ed.), Roa/zdaffolzsand .rrzrerprefafforzsof Quczrzrm /]/echo/tics (Wor]d Sci- cist Anton Zeilinger, introduced a novelty into the testing of entanglement, extending Bell's entific,Singapore, 2000). [92] M. Giustina et a]., P/zys.Rev. ],eff. 115, 250401 (2015); Lyndon K. Sha]m et a]., Phys. theorem in a different and interesting direction. According to Franck La]oE [2], Rev. Leu. 115, 250402 (2015). For many years, everyone thought that Bell had basically exhausted the subject by considering all [93] B. Henson et a]., NZzfwre526, 682 (2015). really interesting situations, and that two-spin systemsprovided the most spectacularquantum vio- [94] A. Cabe]]o, Proposed experiment to test the bounds of quantum cone]ations, P/zys. /?ev.Z,ef£. 92(2004),060403. lations of local realism. It therefore came as a surprise to many when in 1989 Greenberger,Horne, [95] F.A. Bovino, G. Castagno]i, ].P. Degiovanni, and S. Caste]]etto, Experimenta] evidence and Zeilinger (GHZ) showed that systems containing more than two correlated particles may actually for bounds on quantum correlations, P/zys. Rev. Z,en. 92(2004), 060404. exhibit even more dramatic vio]ations of ]oca] realism The trio analyzed the Einstein, Podolsky, and Rosen 1935 argument once again and were able to write what are now called Greenberger--Horne--Zeilinger(GHZ) entangled states, involving three or four correlated spin- I/z particles, leading to conflicts between local realist theories and quantum mechanics. However, unlike Bell's theorem, the conflict now was not of a statistical nature, as was the case with Bell's theorem, insofar as measurements on a single GHZ state could lead to conflicting predictions with ]oca] rea]istic mode]s [3-5].t in this paper we present the history of the creation of this theorem and analyze its scope.

The first paper is the original presentation of the GHZ theorem. The second paper, co-authored with Abner Shimony, contains a more detailed presentation of the theorem and its proof and suggests possible experiments, including momentum and energy coi relations among three and more photonsproduced through parametric down-conversion. The third paper presentsGreenberger's recollectionsof the backgroundof the origina! paper.On the backgroundof dle GHZ theorem,see a]so[7, pp. 23G44]

141 142 Belt's '!'heoremwithout !nequatities 8,3 Reception of the GHZ Theorem 143

8.2 The Men behind the GllZ Theorem quantum and atomic optics from scratch. Zeilinger was supported by the Austrian Sci- ence Foundation and was looking for the basics in the new field. Sometimeshe did this In the early 1980s, Greeenberger, Home, and Zeilinger began to collaborate around the through interaction with other teams, such as Leonard Mandel's in Rochester. Reasons for subject of neutron interferometry at the Massachusetts Institute of Technology (MIT), but this choice were related to his understanding that these fields offered more opportunities they came from different backgrounds concerning the research on the foundations of quan- than neutron interferometry. He was increasingly attracted by the foundations of quantum tum mechanics. As early as 1969, while doing his PhD dissertation at Boston University physics and particularly by the features of entanglement. under the supervision of Abner Shimony, Hol'ne began to work on foundations. His chal- The collaboration among the trio started with joint work involving only Zeilinger and lenge was to cain Bell's theorem to a laboratory test, in which he succeeded,but not alone. Home and concemed quantum two-particle interference. Indeed, this topic, nowadays a What is now ca]]ed the CHSH paper [6], which is the adaptation of Be]]'s origina] theorem hallmark of quantum light behavior, was independently exploited by two teams and arose to a real-life experiment, resulted from the collaboration of Shimony and Horne with John in physics through two diRerent and independent paths: on one hand, via quantum optics, Clauser, an experimental physicist who was independently working on the same subject and on the other, via scientists who were working on neutron interferometry, such as Anton at the University of California at Berkeley, and Richard Holt, who was doing his PhD at Zeilinger and Michael Home. In 1985, unaware of the achievements in the quantum optics Harvard under Francis Pipkin on the same issue. The CASH paper triggered a string of community, Zeilinger and Horne tried to combine the interferometry experiments they were experimental tests, which continue to date, leading ultimately to the wide acknowledgment doing with Bell's theorem. Then they suggesteda new experiment with Bell's theorem using of entanglement as a new physical effect. In the early 1970s, however, Home thought this light, but instead of using conflation among polarizations (internal variables) they used lin subject was dead and turned to work with neutrons while teaching at Stonehill College, near Boston. ear momenta. They concluded thai the quantum description of two-particle interferometry was comp]ete]y ana]ogous to the description of sing]et spin states used by Be]1 [10]. How- Zeilinger's interests in foundational issues nourished while he studied at the University ever, they did not know how to produce such statesin laboratories, becausethey "didn't of Vienna, and were favored by the flexible curriculum at this university at that time and by know where to get a source that would emit pairs of particles in opposite directions." When the intellectual climate of physics in Vienna -- with its mix of science and philosophy a Home read the Ghosh--Mande] paper [ 11 ], they sent their paper LOMandel, who reacted by legacy coming from the late nineteenth century. In addition, working under the supervision saying, "This is so much simpler than the way we describe it, you should publish it." They of Helmut Rauch on neutron interferometry, he benefited from Rauch's support for research called Horne's former supervisor, Abner Shimony, and wrote the "two-particle interferom- on the foundations of quantum mechanics.2 in 1976, as a consequence of this interest shared etry" paper explaining "the fundamental ideas of the recently opened held of two-particle with Rauch, Zeilinger went to a conference in Ence, Italy, organized by John Bell, fully interferometry, which employs spatially separated,quantum mechanically entangledtwo- dedicated to the foundations of quantum mechanics. Over there, while the hottest topic was partic[e states" [12].' Bell's experiments, Zeilinger talked about neutron interferometry. He presenteda report While neutron interferometry had been the common ground of collaboration among on experiments held by Rauch's team confirming a counterintuitive quantum prediction. Zeilinger, Greenberger,and Horne, the GHZ theorem was a result that had implications This prediction states that a neutron quantum state changes its sign after a 2n rotation, far beyond their original interest. The first intuition related to the GHZ theorem came from only recovering the origina] sign after a 4z rotation [8]. Zei]inger went to Ence unaware Greenberger,who askedZeilinger and Horne, "Do you think there would be something of entanglement but came back fascinated by the subject. interesting with three particles that are entangled?Would there be any difference, some- Greenberger was a high-energy theorist working at the City College of New York when thing new to lean with a three-particle entanglement?" The work matured while he spent a he decided to move to adomain where connections between quantum mechanics and gravity sabbatical in Vienna working with Zeilinger. "I have a Bell 's theorem without inequalities,' could be revealed. He chose neutron experiments precisely to look for these connections was the manner in which he reported his results to Horne.4 and met Zei]inger and Horne at a neutron conference in Grenob]e [5]. ]n the Carty 1970s, Clifford Shull's laboratory at MIT becamethe meeting point for the GHZ trio. Shull was working on neutron scattering, which earned him the 1994 Nobel Prize. Zeilinger was there 8.3 Reception of the GHZ Theorem as a postdoctoral student and later as a visiting professor. Horne taught at Stonehill College The GHZ theorem was ready in 1986, but the result remained unpublished for three years. In and conducted researchat MTT. Greenberger was always around the lab. Basic experiments 1988 Greenberger presented the proof at a conference at George Mason University (which with neutron interferometry were the bread and butler of the trio. led to publication the following year), and in 1989 it was presentedat a conferencein Sicily For Zeilinger, the GHZ theoremwas a reward for a risky professionalchange. In the mid- 1980s he had decided to leave neutron interferometry to build a researchprogram in 3 The 1985 Horne and Zeilinger paper was preparedfor a conferencein Joensuu, Finland, dedicated to the 50th anniversary of the EPR paper. This was the first of Zeilinger's papers to deal with Bell's theorem. Interview with Michael Horne by Joan Bromberg 12 September2002, AIP. Interviewwith Anton Zeilinger by Olival FreireJr., 30 June2014, AIP. Anton Zeilinger, interviewed by Olival Freire, 30 June 2014, American Institute of Physics (AIP). For Rauch's research on 4 interview with Michael Horne by Joan Bromberg. 12 September2002, AIP. Interview with Anton Zeilinger by Ohval Freire Jr., neutron interferometry and its relation to foundational issues,see the review [9]. 30 June and 2 July 2014, AIP. ''q'H -,r

144 Belt's Theoremwittlout Ineqimlities 8.4 The Bet! !nequatily 145

Z Z This feature of rotational symmetry in the experimental outcomes implies that the quan +1 -(3 1 2 (D- +1 tum mechanical representation of the singlet state must have rotational symmetry. This & .+ e16'..> ..b appearsin the following expression: l ,(Q 0 l 'P,> . 1+:>tl-:>2 --; . l--:>il+.>z. (8.1) SGI SG2

The notation l+:>Z indicates the eigenstaLeof the z component of spin in the positive direc- Figure 8. 1 '1U'o spin-i/2 particles emitted in an entangled Slate with perfect anticorrelation. tion, associatedwith eigenvalue + 1, for particle 2. That this expression is rotationally invari ant may be verified by replacing each individual state by its representation in another basis in honor of Werner Heisenberg, attended by N. David Mermin, from the United States, and (corresponding to the eigenstales for another angle of the SG magnets). Michae[ Redhead,from England, who began to pub]icize it [ 13, 14] .5 Zei]ingel ' reca]]s when The proof that local realist theories cannot accountfor the predictions of quantum he met Bell at a conference in Amherst, in 1990, how enthusiastic Bell was about the result. mechanics for pairs of entang]ed particles was derived by Be]] in 1964 by means of an Unfortunately,Bell's untimely deathin that sameyear preventedhim from following the inequality that limits the predictions of any local realist theory, but may be violated by the subject. After this initial favorable reception, Greenberger, Horne, and Zeilinger realized the quantum mechanical predictions. The version derived by Clauser, Horne, Shimony, and subject deserved a better presentation than simply a conference paper.6 They called Abner Holt[6] is Shimony to join them in the writing of a more complete paper explaining the theorem and envisioning possible experiments. As we have seen, it was the second time Shimony was c(a, b) + c(a', h) + c(a, &') c(a', b')I $ 2. (8.2) called on by Horne and Zeilinger to further exploit and present their original ideas. If /(a) and //(&) representthe ]'esults of measurementsfor each pair of particles per- fomled with SG magnetsadjusted respectively at angles a and b, then the correlation 8.4 The Bell Inequality coeMcient c(a, b) is the mean of the products /(a) - //(b) averaged over all the pairs of particles. To understand the GHZ theorem, one might begin with the celebrated two-particle spin Bell [1] postulated the existence of a set of hidden variables X that uniquely determine singlet state, with zero total angular momentum, introduced by David Bohm in his 195 1 the values of the measurement outcomes. The general expressions for values (either I or textbook, Q fanfzt/ z TbeoW, and depicted in Fig. 8. 1. -- 1) predicted by the realist hidden variables theory are /(a, &, X) and /J'(a, b, A,). In order Stern Gerlach (SG) magnets separatethe beams in such a way that, for each particle, the to impose the property of /oca/i in these models, Bell dropped the dependence of a mea- probability of measuring each of the two possible outcomes is I/z. The observable being surement outcome on the far-away SG magnet; as a result of this factorizability condition, measuredis the z-component of spin, with the two possible eigenvalues (outcomes) conven- the values of outcomes are written simply as /(a, X) and //(b, X). With this, Bell was able tionally chosen as +l and 1, as shown in the figure.The singlet state is such that in ideal to derive hisinequality. experimental situations, in which both SG magnets point in the same angle (the "superclas- Quantum mechanics predicts that the correlation function for the singlet state is given sica[" case, according to [3]), one measures perfect anticorre]ation, meaning that if partic]e by I is measured with the value of the spin component / = + 1, particle 2 will necessarily be measured with the value // = -- 1, and vice versa. cw:(a, h) = --cos(a -- Z,). (8.3) The experiment shown in Fig. 8. I could be readily explained by a local realist theory: one One may find values for a, a', b, and b' for which the values obtained in (8.3) violate inequal- could supposethat the spin particles are emitted with dehnite and opposite spin components ity (8.2) in the z direction. What such a local realist theory cannot do is explain the fact that perfect One notes in this inequality that its experimental verification must involve four experi- anticonelation would occurlor a/zya/zg/e of the SG magnets,assuming that both magnets mental runs, with four pairs of angles of the magnets. This introduces additional hypotheses and pairs of detectors are quickly rotated at the same angle, right after the emission of the of fair sampling in the experimental test of local realist theories. pair of particles. If an experimental test could be done with a single setup, this would reduce the additional assumptions used to rule out local realist theories. The first derivation of a version of Bell 's Gilder [15] theorem without inequa]ities was done by Heywood and Redhead [ 16], based on simplihed 6 in fact, there already was some competition over the most general proof of the theorem between Greenberger,Horne, and versions of the Kochen--Speckertheorem. A simpler and more testable approach was that of Zeilinger, on one hand, and Clifton, Redhead,and Butterfield, on the other. This competition is recordedin the paper by Clifton ef cz/.[14] in a "note added in proof" on p. 182. Greenberger, Horne, and Zei]inger [3] , who derived a proof involving four spin-i/2 particles. ''l'H'='rr

146 Belt's Tlleoremwithout }neqttatities 8.6 Epilogue: GHZ ExpeRments 147

Z components of spin. As in the derivation of Bell's theorem, the factorizability condition has

+1 -(B l been imposed, which expressesthe locality of the model. The value of each /(a, X), . . . , is either I or -- I. ,(9 3 Expressions (8.6) may be rewritten taking into account that, in the superclassical cases of strict correlation or anticorrelation, the product /(a) - //(&) . ///(c) . /V(d) is equal to the SGI SGa +.deli...>.+ correlation coefhcient cuss: Z Z 0 If a+&--c d=O, then/(a,X)-//(&,A,) ///(c,A,) /y(d,X)= --1; ,..~ +] 2 4 l -(3 ©- If a+b-- c --d = z, then /(a,X) -//(&, X) . ///(c,X) ./\''(d,A.) = 1. l ,(9 l GHZ were able to show that these two expressions lead to a contradiction. Starting with SG2 SG4 the first expression, one may derive four special cases, where @is an arbitrary angle: /(o, x) //(o, A,). .r//(o, x) . .rv(o, x) = -i, Figure 8.2 Expert mental setup for four entangled spin- l72 particles, proposed by GHZ, with every SG /(d', x) . //(o, x) . ///(d, x) . /v(o, i.) = - ] ,. magnet pointing at the same angle z. 8) /(@,A.) //(0, X) ///(0, A.). /V(@,A,) = -1, 8.5 Scope of the GHZ Theorem /(2@,X) . //(0, X) . ///(#, X) . /}''(+, A.)= - 1.

The four-partic]e entang]ed state proposed by Greenberger ef a/. [3] is written as fo]]ows: Multiplying the first thi'ee equations of (8.8), and recalling that the values /, //, ///, and /V are either I or --l, one obtains q';;> = --E . l+:>t +:>2l--:>sl :>4 -- --x - l--:>i l--:>2 +.l3l+:>4. (8.4) /(0, X) . //(0, X) . ///(#, A,). JV'(@,A.) = - 1. (8.9) This state may be prepared in a way similar to the two-particle system of Fig. 8. 1, assum- Comparing this with the last equation of (8.8), one concludes that /(2@, X) = /(0, X), ing that each of the two entangled particles has spin 1, and that each of them decays into i.e., /(@, A.)has a constantvalue for all V'. That would be very strange,for if @= a, one two spin-l/2 particles. This is representedin Fig. 8.2. expects that the value of / will have a negative sign in relation to the value for V' = 0 One notices again strict anticorrelation between measurementson the left side of the For this to constitute a mathematical contradiction, one may take the second expression picture and on the right, as in Fig. 8.1. The situation imagined by GHZ to test local real of (8.7) and derive the following special case: ist theories involves magnets at different angles, respectively a, h, c, d, so that the suict anticorre[ation of the superc]assica] case w i]] not occur. /(@+ a, A.) - //(0, X) . ///(@, A,) . /V(0, A.) = 1.(8.10) The quantum mechanical correlation function associated with these measurements is Together with the second of equations(8.8), one concludes that /(d+ z, i.) = /(@, A.), similar to the two-particle case, and gives which contradicts the previous assertion that /(@, X) will have a constant value for all @. cw;;(a, b, c, d) = --cos(a + h -- c -- d). (8.5) Therefore, the assumption that quantum mechanics can be formulated as a realist hidden variable theory leads 10a contradiction, without the use of inequalitiesl Onecan now considera caseof strict anticorre]ation(cuss = -- ] ), of which the setupof Fig. 8.2 is a specialcase, and also a caseof strict correlation(cW.s = I ): 8.6 Epilogue: GHZ Experiments If a+h--c--d::O, thencuss = --1; r86\ If a+Zl--c--d::z, thencuss = 1. ~'''' The production of GHZ statesin laboratories was neither an easyjob nor a quick achieve- ment. It took a decade. Tn fact, from 1990 on, Bell's reaction, in particular, motivated These situations have the property that if one measures the spin components of three Zeilinger to think immediately about taking this theorem to the laboratory benches. particles, one knows for sure (in an ideal experimental situation) the value of the fourth one The road to experiments, however, was dependent on both conceptual and experimental (in the special case depicted in Fig. 8.2, a single measurement is sufficient, as indicated in advances.Zeilinger considers it the most challenging experiment he has ever carried out. Eq. (8.4)). This is ana]ogous, as pointed out by Greenberger ef a/. [3], to what happens in The quest for the required expertise, however, brought important preliminary results and the Einstein, Podolsky, and Rosen argument, which is based on counterfactual strict anti- spinoffs, such as the concept of "entanglement swapping" and the experiment on telepor- correlation measurements. tation [17, 18].7 The twentieth century c]osed with Zeilinger successfully obtaining the Let us now postulate the existence of hidden variables A, that uniquely determine the measurement outcomes /(a, X), //(b, X), ///(c, X), and /V(d, X) of the respective 7 Anton Zeilinger.interviewed by Olival Freire Jr., ibid 148 neil's Theoremwithout !nequatities experimental production of GHZ states that are in agreement with quantum theory and in Partlll disagreement with ]oca] rea]istic theories [ 19]. Nonlocality: Illusion or Reality? References

[1] Bell, J.S. 1964, On the Einstein--Podolsky--Rosen paradox, P/zysics 1, 195--200. [2] LaloE, F. 2012, Z)o WeRea/Zy U/zdersra/zd Qtzanfum /b/ec/zarzfcs? (Cambridge Univer- sity Press, Cambridge). [3] Greenberger, D., Horne, M., and Zei]inger, A. ]989, Going beyond Bell's theorem. In: Kafatos,M.C. (eds.),Be//'s T%eorem,Q cz/zfm TheoD' a/zd Co/zcepr/Offsof f/ze U/zfverse(Kluwcr, Dordrecht), pp. 69--72. [4] Greenberger, D.M., Horne, M.A., Shimony, A., and Zeilinger, A. 1990, Bell's theorem without inequalities, 4/ zerlca/zJourlza/ ofP/zys/cs 58(12), 1131--43. [5] Greenberger, D. 2002, The history of the GHZ paper, in R.A. Bertlmann and A. Zeilinger (eds.). <2uarzfnz (Urz)speakah/es. Fro/m Be// to anf /7z/ndormariorz Berlin: Springer, pp. 281-6. [6] C[auser, J.F., Horne, M.A., Shimony, A., and Ho]t, R.A. ]969, Proposed experiment to test local hidden-variable theories, Physfca/ Review Z,offers 23( 15), 880 84. [7] Whitaker, A. 2012, T%eNew <2ua/zrm .4ge (Oxford University Press, Oxford). [8] Rauch, H., Zeilinger, A., Badurek, G., Willing, A., Bauspiess,W., and Bonse, U. 1975, Verihcation of coherent spinor rotation of fermions, Physics Z,offersA 54(6), 425--7. [9] Rauch, H. 2012, Quantum physics with neutrons: From spinor symmetry to Kochen Speaker phenomena, Ro zdafions ofP/zysfcs 42(1), 153--72. [lO] Horne, M.A. and Zeilinger, A. 1985, A Bell-type EPR experiment using linear momenta, in P. Lahti and P. Mittelstaedt (eds.), Symposizl/ o z fhe Roundaffons of Modern Physics: 50 Years oj the Einstein--Podotsky Rosen Gedanken Experiment (WorldScientific, Singapore), pp. 435 9. [ 11 ] Ghosh, R. and Mandel, L. 1987, Observation of nonclassical effects in the interference of two photons, P/zysica/ Review I,erfers 59(17), 1903-5 . []2] Horne, M.A., Shimony, A., and Zeilinger, A. 1989, Two-particle interferometry, Physfca/ Review I,offers 62( 19), 2209--12. [13] Mermin, N.D. 1990, What's wrong with these elements of reality? Physics today 43(6),9-11. [14] Clifton, R.K., Redhead, M.L.G., and Butterfield, J.N. 1991, Generalization of the Greenberger-Horne-Zeilinger algebraic proof of nonlocality, Rou/zdaffoFzsofP/zyslcs 21(2),14984. [15] Gilder, L. 2008, T%eAge of flzrang/enzenf Whe/zQzzcznfz£m P/zysfcs Was Rebar/z (Knopf, New York). [16] Heywood, P. and Redhead, M.L.G. ]983, Nonlocality and the Kochen--Speaker paradox, Xourzdaf/o/zs of P/zysfcs 13: 48 1--99. [17] Zukowski, M., Zeilingcr, A., Horne, M.A., and Ekert, A.1(. 1993, "Event-ready- deLectors" Bell experiment via entanglement swapping, P/zysica/ Review I,offers 71(26),4287-90. [18] Bouwmeester, D., Pan, J.W., Mantle, K., Eibl, M., Weinfurter, H., and Zeilinger, A. 1997, Experimental quantum Leleportation, /Vafure 39, 575--9. [19] Bouwmeester, D., Pan, J.W., Daniell, M., Weinfurter, H., and Zeilinger, A. 1999, Observation of three-photon Greenberger--Horne--Zeilinger entanglement, Phys£ca/ Review Z,offers 82(7), 1345--9. H renty-six original essayswritten by an impressiveline-up of 0 physicists and philosophers of physics, this anthology -reflectssome = oughts by leading experts on the influence of Bell's Theorem on Q.

D 0 m John Bell's character and background, through studies of his to more speculative ideas, addressing the controversies surrounding nvestigating the theorem's meaning and its deep implications for hysical reality. Combined, they presenta powerful comment on the Quantum Nonlocality nificance of Bell's Theorem for the development of ideas in quantum -epast 50 years. and Reality rounding the assumptions and significance of Bell's work still 50 Years of Bell's Theorem ion in field of quantum physics. Adding to this with a theoretical cal perspective, this balanced anthology is an indispensable volume Edited by Mary Bell and Shan Gao .d researchersinterested in the philosophy of physics and the fquantum mechanics physicist and the widow of John Bell, with whom she frequently he held severalpositions working on particle acceleration design :heAtomic Energy ResearchEstablishment in Harwell, Oxfordshire, celerator divisions at CERN n Associate Professor at the Institute for the History of Natural .eseAcademy of Sciences.He is the founder and managing editor of JozzrnaZof Quart um Fozzndafions.He is the author of several books of the recent anthology Profecfive .A4easurementand Quantum a Nbw Undersealaing ofQuantum .Acfec;zanlcs.His research foundations of quantum mechanics and history of modern physics

irtesy of CERN BRIDGE UNIVERSI'l'YPRESS www.cambridge.org ISBN978-1-107-10434-1

9 "781107"104341">