On using Greenberger-Horne-Zeilinger three-particle states for superluminal communication

Transcription

1 On ung Greenberger-Horne-Zelnger three-partcle tate for uperlumnal communcaton Raymond W. Jenen Abtract. Ung a three-partcle entangled ytem (trple), t poble n prncple to tranmt gnal fater than the peed of lght from ender to recever n the followng manner: From an emtter, for every trple, partcle and are ent to the recever and 3 to the ender. The ender gven the choce of whether or not to meaure polarzaton of partcle 3. Meanwhle the recever meaure partcle correlaton v. relatve polarzaton angle for the polarzer of partcle and. The partcle and correlaton tattc depend on whether or not partcle 3 polarzaton wa meaured, ntantaneouly. Th dependence a ba for fater-than-lght communcaton. Introducton. In th artcle, t propoed that a three-partcle entangled quantum tate, or Greenberger-Horne-Zelnger (GHZ) tate, enable fater-than-lght or uperlumnal communcaton (FTLC). The dea mple: for every entangled trple of partcle, partcle, e.g. photon, are ent to one of two oberver, labeled the recever. The other partcle of the trple ent to the oberver labeled a the ender. Thee ne for the oberver orgnate from the fact that the ender wll attempt to end nformaton, and the recever, receve nformaton, ntantaneouly, ung the 3-photon entangled tate. The ender end nformaton by the ablty to chooe between one of two operaton done on the photon ent to t end: (a) meaurng the photon polarty or path nformaton wth polarmeter or be pltter or (b) erang path nformaton. On the recever end, there are two photon receved, and the recever meaure polarty for both. The two be pltter on the recever end are held at varou relatve angle wth repect to one another, and the recever record the correlaton, a n a normal two-photon correlaton experment a wa done by Apect and co-worker []. See fgure. Snce the two recever photon may not travel along a common ax a n the two-photon cae, t neceary to defne what meant by the relatve angle between the two recever be pltter. Th can be done by choong a normal vector N n the plane of propagaton of the two photon and defnng the abolute angle of the two polarmeter a the relatve angle to N. Agan, refer to fgure. For the et-up hown n fgure, we chooe the GHZ tate [ 3 3 ] ψ. () For the equaton or tate vector (), the numberng refer to the number of a gven photon n the three-way tate, where and go to the recever and 3 to the ender. lu and mnu ymbol refer to the polarty of each photon. Now n order to

2 communcate between ender and recever, many GHZ trple wll need to be ent, even for the tranmon of a ngle bt of nformaton. For a gven populaton of trple ent out for the tranmon of a ngle bt, the recever wll record the correlaton between the data of the two receved photon, and th depend on whether or not the ender chooe to meaure polarzaton of the ender photon. The procedure for th wll be outlned n more detal below. Fgure. The FTLC devce propoed n the text, hown n two confguraton, top and bottom. There are trple of entangled photon emtted by the ource S, and they propagate n the plane wth normal N hown. The ender on the rght and recever on the left. For every trple, the ender get one photon and gven the choce of meaurng the photon polarzaton (top) or erang the nformaton (bottom). The recever meanwhle get two photon and perform a concdence or Apect-type experment between the photon. The top confguraton wll yeld concdence data fttng equaton (), and the bottom, (3). The dfference n the tattc a ba for FTLC. Now, we cl that when the ender chooe to meaure polarzaton nformaton, (top of fgure ) the correlaton tattc for the recever are co θ 4 8 n θ. 4 8 () The plu and mnu ymbol agan refer to the polarty of the recever photon..g. mean that both recever photon have polarty, accordng to the polarzer meaurement.

3 Now t alo cled that when the ender chooe to erae path nformaton, (bottom of fgure ), the tattc () change to: co n θ θ. (3) The tattc (3) are the e a thoe dcovered by Apect and co-worker [] and o volate Bell nequalty. On the other hand, the tattc () do not volate Bell nequalty; o clearly thee tattc are dtnguhable by the recever. Now berhard and Ro (R) [] cl mpoblty of tranmon of FTLC and n partcular, for three-way ytem uch a that decrbed by () ung the et-up n fgure. Snce they do not explctly how ther calculaton n ther artcle, ther argument demontrated n the followng ecton. In the ecton followng the next, t then hown how th argument can be crcumvented by conderng an operaton whch defned here a eraure. In a later ecton, expermental evdence revewed, whch demontrate that the type of operaton R conder n ther analy nuffcent. berhard and Ro argument for no FTLC. It ha been cled by R [] that for a gven quantum ytem, t mpoble for an oberver (.e. the ender), pacelke eparated from another (.e. the recever), to nfluence egenvalue correlaton between two or more meaurement done by the latter. Snce ther proof not carred out explctly n ther artcle, we contruct t here. In the ecton followng, t then hown that R do not conder a partcular acton whch may be done by the ender; nely eraure of path nformaton of the ender partcle. Then t hown that the R argument doe not hold for when the ender allowed to perform eraure. Meanng, eraure change the recever egenvalue correlaton a compared to when the ender perform an egenvalue meaurement or take no acton. And agan, latly, we argue on the ba of expermental evdence for eraure. To begn, we conder a general quantum ytem Q repreented by the tme-dependent V A V B V C A V B, and tate equaton or wavefuncton ( t ) ( ) ( ) ( ) where V ( ), ( ) ( C) V are Hlbert pace; the egenpace of three repectve operator A, B, and C. A an operator whch correpond to an operaton whch may be done by the ender, wherea the latter two correpond to operaton whch are alway done by the recever. Let the et of egenvalue of operator A, B, and C be { a, a, }, { b, b, }, and { c, c, } repectvely. Conder the cae where the recever meaure egenvalue b and c. We wh to frt calculate the ont probablty of th occurrence when the ender take no acton;.e. make no meaurement. By defnton the operator aocated to th (n)acton the dentty operator I. Sender take no acton 3

4 Suppoe then at tme t, b meaured, at tme t, c meaured by the recever upon applyng t operaton B and C repectvely, and wthout lo of generalty, t < t n the fre of reference of the recever. Up to t, the wavefuncton of Q gven by ( ) U ( t) ( ) t (4) where U () t the evoluton operator between tme and t, wth the ubcrpt gnfyng that the ender doe not change the Hltonan operator for Q n between meaurement. We wrte the Hermtan conugate of the evoluton operator a U () t. At tme t, collape of () t occur; and after a hort tme ε where t ε < t the wavefuncton become, by the ffth potulate [3] ( t ) ε U ( t ) b ( t ) ( ) (5) ( b ) where ( b ) the probablty of b occurrng, gven by the fourth potulate [3] b t and ( ) where ( ) ( ) ( t ) ( ) b b (6) the proecton operator aocated to obtanng egenvalue b at t : In (8) the thee k (7) b b ( t ) U ( t ) ( t ) U ( t ) N ( t ) k k b k B B. (8) B k are the N -fold degenerate egenvector aocated to egenvalue b, and V B {cf. (5) wth (5) n R []}. At tme t, the B form the tandard ba for ( ) recever meaure c, and o the condtonal probablty ( ) that b wa meaured where c b of th occurrng gven ( c b ) ( t ε ) U ( t ) U ( t ) ( t ) U ( t ) U ( t ) ( t ε ) ( t ε ) U ( t ) ( t ) U ( t ) ( t ε ) ; c c (9) 4

5 c ( t ) U ( t ) ( t ) U ( t ) c U t C C U t N l l l ( ) ( ) ; () cf. (6) n R []. The C l n () are the N -fold degenerate egenvector aocated to egenvalue c whch gve a tandard ba for V ( C). In (9), we note that the combned operator U ( t ) U ( ) functon a the evoluton operator of between tme t and t. t Combnng (5) and (9), we get ( c b ) ( ) b ( t ) ( t ) ( t ) ( ) ; c b () ( b ) thu the ont probablty ( correlaton probablty ) of the recever obtanng egenvalue b and c, ung the defnton of condtonal probablty, Sender perform a meaurement ( c b ) ( ) ( t ) ( t ) ( t ) ( ) & b c b. () Next, uppoe the ender perform an egenvalue meaurement and meaure egenvalue a m, at tme t >. We wh to agan calculate the ont probablty that the recever obtan egenvalue b and c however, gven the condton that a m meaured by the ender; that, ( c & b ). Ung the reaonng gven n the prevou ubecton, t not dffcult to ee that th condtonal probablty, gven t < t < t, ( & m) c b a ( & & m) ( ) c b a ( ) a m b c b a m a m ( ) ( t ) ( t ) ( t ) ( t ) ( t ) ( ). (3) Now by aumpton the recever ha no way of knowng whch partcular egenvalue meaured by the ender; thu we um over all a m ung Baye formula, to get the ont probablty ( c & b ) gven that the ender ha performed a meaurement: ( & b ) ( c & b ) ( ) c ( ) ( t ) ( t ) ( t ) ( t ) ( t ) ( ) ( ) ( t ) ( t ) ( t ) ( t ) ( t ) ( ). b b c c b b (4) 5

6 The goal here to how that equaton () and (4) are the e. To do th, t uffcent to nvoke the followng axom, a done n R []: (I) Suppoe a and b are two proecton operator correpondng to meaurement done on a quantum ytem Q at repectve pont a and b n pace-tme whch are pacelke eparated. Then and commute. a b Th a reaonable axom, n partcular when the theory of relatvty taken nto account; nce t a matter of one own reference fre a to the order of operaton, and further, all oberver hould agree on the outcome of the operaton. Th would not be o f the operator dd not commute! Now by aumpton, the ender and recever are pacelke eparated between the tme they perform meaurement. That, gven that the ender perform a meaurement at a pont [ (, t )] n pacetme and the recever perform the two meaurement at pont r [ (r, t )] and r [ (r, t )], then and r are pacelke eparated, and o are and r. From (I) then, the operator n (4) whch correpond to pacelke-eparated pont commute, and o ( & b ) ( ) b ( t ) ( ) ( ) ( ) ( ) c t b t a t m c ( ) ( t ) ( t ) ( t ) ( t ) ( ) b where we ued the dempotent property of proecton operator n the econd tep. Now, by the fourth potulate [3], c b ( a m ) ( ) ( t ) ( ) (5). (6) m a Summng equaton (6) over all a m and ung the property of conervaton of probablty, we have ( a ) m ( ) ( t ) ( ) ( ) ( ). (7) Thu ( ) a t m the dentty, o from (7), (4) become ( c & b ) ( ) ( t ) ( t ) ( t ) ( ) ( c & b ). b c b (8) 6

7 Thu by (8) we have equalty between () and (4);.e., there no dfference n the correlaton tattc of the recever between the cae where the ender () take no acton and () make a meaurement. But are thee acton condered by R the only one whch the ender may take? We cl that the anwer no; the ender may alo perform eraure or erae path nformaton of the part of Q t nteract wth. After defnng th acton n the next ecton, we look at the effect on the correlaton tattc for the recever, gven that the ender allowed to perform eraure. In a later ecton, expermental utfcaton for eraure gven. berhard and Ro do not conder eraure. Hence ther proof of no gnalng ncomplete and thu nvald. Th the reaon why ther concluon contradct the concluon of th artcle. Contructon of eraure. Conder a tate equaton repreentng two entangled partcle a and b wth bae { a, a } and { b, b } repectvely. Further, uppoe the partcle are repreented by the tate equaton We wh to erae partcle b;.e. reduce (9) to [ a b a b ]. (9) [ a a ]. () The proecton operator whch accomplhe th tak the followng: ϕ ϕ [ b b b b b b b b ]. () That, ung (), (9) become [ b b b b b b b b ][ a b a b ] [ a b a b a b a b ] ( a a )( b b ). () In comparng (9) to () we ee the two partcle whch were formerly entangled are no longer o. Thu the olated partcle a gven by () wll gve the e tattc a a gven by () (upon normalzaton); hence the partcle b made rrelevant or rather ha 7

8 been eraed. hycally, a partcle egenvalue or path nformaton eraed f we allow the partcle to be detected wthout meaurng t egenvalue nformaton. For exple, f a ngle partcle allowed to pa through a double-lt wthout the oberver attemptng to dcover whch lt the partcle pae through, then the path nformaton of the partcle ha been eraed. We mply refer to uch acton a erang the partcle. Now the general eraure proecton operator we defne a ϕ ( t ) ϕ( t ) k m k N N l m n α kl * ( t ) α ( t ) Nk where ( t ) α k ( ) V( A) l kl t A kl tattc ( a m ) at t a doe ( t ) V( A) V( B) V( C) mn A kl A mn (3) ϕ normalzed and gve the e egenvalue, the tate equaton of the quantum ytem Q under tudy. Snce the egenvalue meaurement converely do not affect the egenvalue tattc of the ender, we ee that (3) well-defned. Now θkl α kl rkle where r kl real and nonnegatve and the phae factor θ kl real. But we wh to keep the path a partcle may take, ndtnguhable. Therefore we et all phae factor equvalent to a global phae factor φ n (3); thu the α kl can be condered to be real and nonnegatve. raure not equvalent to takng no acton/egenvalue meaurement. Suppoe then that the ender perform eraure at tme t. By extenon of the ffth potulate we have ung (3): t ε, (4) ( ) N U ( t ) ( t ) ( ) where N a real normalzaton contant, defned below, and. (5) ( ) U ( t ) ( t ) U ( t ) t A mlar extenon of the ffth potulate preented n the Cohen-Tannoud text [3] n ecton III e. By (4) and (5) the condtonal probablty of the recever obtanng egenvalue b and c, gven that the ender ha performed eraure, ( c & b ) N ( ) ( t ) ( t ) ( t ) ( t ) ( t ) ( ) b c b [cf. (3)] But nce the ender only perform eraure, we have. (6) ( c & b ) N ( ) ( t ) ( t ) ( t ) ( t ) ( t ) ( ) b c b. (7) Ung axom (I), and the dempotent property of (3) we have from (7), 8

9 ( c & b ) N ( ) b ( t ) c ( t ) b ( t ) ( t ) ( ) ( c & b ) ( c & b ) (8) n general. The excepton to the nequalty where the eraure proecton operator equvalent to the dentty operator (n th cae, N ), but th not true n general. Ung (6), we ee that N / t. (9) ( ) ( ) ( ) In the next ecton, we apply the equaton derved n thee lat two ecton toward calculaton of equaton () and (3);.e. the tattc for the two confguraton of the apparatu hown n fgure. Calculaton of equaton () and (3). We begn the calculaton of (), the tattc for the recever gven ender egenvalue (path) meaurement, wth equaton (), and n conderaton of the apparatu hown n fgure. Relatve to t polarzer, uppoe photon 3 ha polarzaton angle ϕ. Ung the rotaton tranformaton equaton 3 coϕ 3 nϕ 3 3 nϕ 3 coϕ 3 (3) equaton () become, n the ba of polarzer 3, ψ nϕ 3 coϕ 3 coϕ 3 nϕ 3 (3) Next, defne the angle of the polarzer of photon and a α and β repectvely. Then from (3) and tranformaton equaton analogou to (3), we get, after droppng prme, 9

10 ψ ( nαn βnϕ coαco βcoϕ) 3 n co n co n co 3 ( α β ϕ α β ϕ) ( α β ϕ α β ϕ) ( α β ϕ α β ϕ) ( α β ϕ α β ϕ) ( nαco βcoϕ coαn β ϕ ) ( α β ϕ α β ϕ) ( α β ϕ α β ϕ) co n n n co co 3 co co n n n co 3 n n co co co n 3 n 3 co n co n co n 3 co co co n n n 3. (3) Next, we calculate (, ) ung equaton (8). Snce the ytem gven by () tme ndependent, all evoluton operator vanh. Recall that photon 3 ent to the ender and the photon and are ent to the recever. The probablty n th cae, of the recever obtanng reult,, ung (), (8), and (3): (, ) (,, ) α βϕ (33) [( coα co β coϕ nα n β nϕ ) ( coα co β nϕ nα n β coϕ ) ( coα n β coϕ nα co β nϕ ) ( nα co β coϕ coα n β nϕ ) ( coα n β nϕ nα co β coϕ ) ( nα co β nϕ coα n β coϕ ) ( nα n β coϕ coα co β nϕ ) ( nα n β nϕ coα co β coϕ ) 3 ] 3

11 ( coαco βcoϕ nαn βnϕ) 3 co co n n n co 3 co n co n co n 3 ( α β ϕ α β ϕ) ( α β ϕ α β ϕ) ( α β ϕ α β ϕ) co n n n co co 3 ( coαco β coϕ nαn βnϕ) 3 ( coαco βnϕ nαn β coϕ) 3 ( coα co β coϕ nαn βnϕ) ( coαco βnϕ nαn β coϕ) co ( α) co ( β). 4 (33) The reaon for the tlde () above n (33) wll become apparent n a moment. For now, fx the angle θ of polarzer relatve to polarzer (agan, ung the normal N to the plane a reference). Th fxed angle equvalent to the dfference between angle α and β nce the two photon have the e, albet ndetermnate polarzaton angle. Thu we have θ α β. Thu (33) become ( β ) co ( ) co ( ) 4 θ β β co θ co( θ 4 β) (34) quaton (34) now a functon of a ngle varable, β; the polarzaton angle of photon whch pcked up by the recever. But the # photon a a populaton have all poble angle β from to π, each angle wth equal probablty. Th the reaon for the tlde that wa put n earler; (34) not qute the probablty we are lookng for. To fnd that probablty, the average probablty, we treat β a a unform random varable and ntegrate (34) a follow: π ( β ) dβ π θ 4 8 co. (35) quaton (35) the e probablty a that hown n (). The remanng three probablte n () are mlarly calculated. Next, we repeat the calculaton of the ont probablty of obtanng, by the recever, aumng that the ender perform eraure;.e. n (3). Ung (3), the eraure operator

12 [ ] 3. (36) Thu the probablty of the recever obtanng, f the ender perform eraure, ung (8): (, ) N (37) coαcoβ 3 nαco β 3 coαn β 3 nαn β 3 nαn β 3 nαco β 3 coαn β 3 coαco β 3 coαcoβ nαco β coαn β nαn β nαn β nαco β coαn β ( ) coαco β 3 3 coαcoβ coαn β nαn β ( ) nαco β 3 3

13 nα n β [ co θ [ coα co β coα n β nα n β nα n β nα co β coα n β coα co β nα n β ]( 3 3 ) coα co β 3 nα co β ][ coα ]( 3 3 ) co β (37) whch matche the probablty gven n (3). Agan, the remanng probablte n (3) maybe mlarly calculated. Unlke n the prevou cae, where equaton (33) wa neceary to ntegrate, t not neceary to ntegrate (37) nce t come out to be a contant wth repect to β anyway. Note that the Bell correlaton functon f ( ) ( θ ) 3co 3 ( θ) co( 6θ) equaton (3) (ee Ruhla text [4] for calculatng th) twce f( )( ) functon calculated from equaton ();.e. f( )( θ ) f 3 ( )( θ ). Th mean that f ( ) ( θ ) doe not volate Bell nequalty (.e. f ( )( θ ) ) a ( 3 ) ( ) expected nce equaton () ( f( )( θ ) eparable equaton calculated from θ, the correlaton f θ doe, whch to be ) are obtanable from a : tattcal mxture of and repreentng par of unentangled partcle. Note alo that f R are correct n ther analy, then the tattc () are the only one obtaned from the trply-entangled ytem (). It doe not matter whether a concdence crcut preent or not; no experment done on the ytem () wll how the tattc (3). Snce there no expermental evdence whch argue for one way or another regardng (), we reort to a -partcle ytem n the next ecton, for whch there expermental evdence. Obecton to the eraure proecton operator (3). Some reader may obect to the ue of the proecton operator (3) ued to defne eraure. We argue n favor of t ue here, wth expermental data. 3

14 We wll argue by contradcton: uppoe that the eraure operator (3) nvald. Suppoe further, a R cl, the ender performng a meaurement or takng no acton are the only two poble acton the ender may take. We wll alo aume that the tattc are the e for both operaton, a R have found. Now Apect and co-worker [5] have found ung a Mach-Zehnder (MZ) nterferometer and ytem of entangled photon par repreented by equaton (9), that nterference pattern are obtaned from the photon whch pae through MZ, when the polarzaton of the econd photon of every par not meaured. Behnd MZ are two detector, whch revealed expermental data, howng a perodc ntenty gnal, one oppotely modulated from the other. See fgure for the apparatu, and fgure 3 for the expermental data. Fgure. The expermental apparatu of Apect and co-worker [5]. A par of photon emtted by S. hoton goe through the Mach Zehnder nterferometer contng of mrror M, M, and halflvered mrror H, H. hoton detected by D or D. hoton reflected by mrror M3, M4, and detected by D3. olarzaton of photon not meaured. It erve a a gatekeeper, only allowng data from D or D to be admtted to the data collecton devce ( Data ) f D3 regter a multaneou photon. Fgure 3. xpermental reult (photon count v. L) of Apect et al [5] ung the ntrument of fgure urophyc Letter (reprnt permon pendng). 4

15 Now f R are correct, then the data of fgure 3 can be calculated, aumng that the expermenter take no acton on photon, the photon whch doe not pa through MZ. We frt the re-label (9): ( ) (38) where, repreent the numberng of the photon and /- repreent polarzaton. A wa done wth equaton (3) n the prevou ecton, we tranform (38) nto the ba of the plane of MZ: [( coϕ nϕ )( coϕ nϕ ) ( nϕ coϕ )( nϕ coϕ )] ( ) (39) where φ the angle between MZ, and polarzaton angle of ether photon. Note that (39) ha the e form a (38), although techncally ther bae are dfferent. Ung the e tranformaton equaton (3), we tranform photon nto the ba of the polarzer (recall n the lat tep t wa tranformed nto the ba of MZ): Here, θ ( L) { [ coθ ( L) nθ ( L) ] [ nθ ( L) coθ ( L) ]} [ coθ ( L) nθ ( L) nθ ( L) coθ ( L) ] θ the phae dfference at the half-lvered mrror H n the nterferometer between photon takng one of the two path through the nterferometer. Th phae dfference depend lnearly on the dfference between the two path length, L, whch very mall compared to ether path total length. The probablty of obtanng an egenvalue α at tme t r gven by ( α ) ( ) ( t ) ( ) (4) r, (4) α gven that no acton taken on the repectve partcle. Th equaton () n the R paper []. We are now ready to calculate the polarzer tattc of photon, gven that no acton taken on photon. We frt calculate the probablty ( ), the probablty the MZ detector D regter photon. We get 5

16 ( ), coθ( L) nθ( L) ( L) θ( L) nθ co (4). Smlarly, for D we get ( ). (43) Thu accordng to (4) and (43), there hould be no ntenty varaton between D and D, a L changed. Th clearly n contradcton to the data of fgure 3. Therefore the orgnal aumpton nvald; contrary to R cl, takng no acton or makng egenvalue meaurement are not the only acton whch may be taken. (We tll agree wth ther aerton however that the two operaton condered gve the e tattc.) On the other hand, we calculate what the tattc hould be, gven that eraure a vald operaton. The relevant eraure operaton here ( ). (44) The aocated probablty : ( α ) N ( ) ( t ) α ( tr ) ( ) (45) where eraure done at tme t. Applyng (44) and (45) th to (4), we get the probablty D regter a photon (cf. (4)) ( ) N, [ coθ nθ ( L) nθ ( L) ( L) coθ ( L) ] (46) nθ ( )[ coθ ( L) ( L) ] [ n θ ( L) ] 6

17 Smlarly, for D we have ( ) [ n θ ( L) ] (47) The equaton (46) and (47) are plotted n fgure 4. Thee plot match the expermental data of fgure 3. Thu we cl here that the eraure operaton vald. quaton (46) and (47) were orgnally derved n [6], ung a mpler, but more ad hoc argument. Fgure 4. quaton (46) and (47) plotted on the left and rght, repectvely. Thee are the theoretcal probablty plot for detector D and D photon detecton repectvely. Thee plot ft the expermental data of fgure 3, upon normalzaton. Some bac on mplementng FTLC ung the devce of fgure. In applcaton to FTLC, the devce of fgure wll have no concdence crcut between recever and ender, n whch to ndcate when data are ent, and what data are noe. (Note the concdence crcut n fgure, where data from photon are collected n concdence wth photon.) We argue for FTLC ung photon, however mlar argument may be etablhed for ytem of other partcle. Overcomng lack of a concdence crcut. The frt problem, lack of a concdence crcut, can be overcome by etablhng rule for ender and recever, and tandardzng tme at whch bt of nformaton are to be ent. Tme can be tandardzed by ntallng a beacon near the ource, whch emt pule of ordnary lght to ether end, at gven tme nterval. Now for the rule: a. The apparatu of fgure placed n the top confguraton by the ender f a to be ent, and that of the bottom f a to be ent. b. Upon recevng a pule of lght from the beacon, the tranmon of one bt fnhed, and the tranmon of the next bt begun. Hence the apparatu can only be wtched by the ender at the tme at whch a pule of lght from the beacon receved. Between pule, the ender detector fxed ether at one confguraton or the other. c. Upon recevng a pule of lght from the beacon on the recevng end, data collecton for one bt fnhed, and data collecton for the next bt begun. 7

18 d. The data are collected nto bn;.e. one bn for each bt. If the data from one bn plotted and hown to ft equaton (), then the bt that wa ent nterpreted a a. If the data ft equaton (3), then th mean that a wa ent. Thu, f entangled photon,,, N are receved by the ender detector() between tme demarcated by two conecutve lght pule from the beacon, and hence the apparatu confguraton held fxed between thoe two tme, then deally thoe N photon blng par wll be receved on the recever end, and the data collected from thoe photon wll be put nto a ngle bn. Further, the recever wll know that all the entangled photon receved between the two conecutve tme tp ether gve data fttng equaton () or equaton (3), f the rule are adhered to. Thu the problem of overcomng lack of concdence crcutry urmountable, ung a et of rule whch both ender and recever have agreed upon beforehand. Note that th technque of communcaton not ntantaneou; becaue a bt of nformaton requre N >> partcle to contruct, unle of coure everal apparat are ued n parallel. However, f a ngle apparatu ued, and f the tme requred to contruct a bt of nformaton t, and f M bt of nformaton are to be tranmtted, then o long a the dtance between ender and recever greater than cm t (c peed of lght), nformaton tranmon ung th method fater than ung a conventonal lght pule to end the nformaton. Ade, John Crer of the Unverty of Wahngton expermentng wth a devce ung entangled photon par and eraure, n order to demontrate retrocaual, or backward-n-tme nformaton tranmon. If FTLC poble, there no reaon to beleve that retrocaual nformaton tranfer not poble. That, changng the locaton of the ource o that t cloer to the recever than the ender, doe not change any of the above calculaton; thu t hould be poble for the recever to receve the nformaton before the ender ha ent t! Of coure th lead to a paradox, unle of coure the recever ha no ablty to change the future after the future ha been preented to hm. Reducng noe. The econd problem, how to flter out noe, a techncal ue, lke the frt. There no theory whch ndcate that the level of random photon emtted from entangledphoton ource n general o great that effect due to entangled photon cannot be detected wthout the ad of a concdence crcut. In fact, f there were uch a theory, then any fater-than-lght communcaton cheme ung entangled photon would fal due to exce noe, and hence the no-gnalng theorem of R [] would be uperfluou. On the other hand t ha been demontrated ung paretrc down converon that concdence count a hgh a 86% [7] are obtanable, a a percentage of total photon count. In the applcaton here, the concdence count wll not be o hgh. However, there one advantage to FTLC when more than one partcle ent to the recever. The recever can weed out noe by collectng data only from photon t receve multaneouly. Th elmnate noe from ngle and n fact, by far the mot noe n the recever data wll come from recever-only double, whch only one of three knd of double whch may be emtted by the ource. It antcpated that the rato of trple to recever-only double greater for the 3-partcle ytem than the double-to- 8

19 ngle rato for the -partcle ytem. Thu the gnal-to-noe rato of the former hould be greater than that of the latter. A queton ha been raed by a revewer a to whether or not a GHZ tate expermentally realzable. The anwer to th ye [8]. It mportant to note however that every entangled photon propagatng toward the ender mut be detected, otherwe noe wll ncreae. Th becaue by not detectng a gven photon, the ender n fact, takng no acton. The argument preented n th ecton are modfcaton of an earler argument [9]. Concluon. It ha been hown above that f one conder the act of eraure by the ender, then t theoretcally poble to end fater-than-lght gnal between ender and recever ung the devce n fgure and a three-way Greenberger-Horne-Zelnger entangled tate decrbed by equaton (). The ender of nformaton alternate between egenvalue meaurement and eraure. The concdence data collected by the recever dffer between meaurement and eraure by the ender, a ndcated by equaton () and (3) repectvely. Th dfference allow the recever to receve nformaton fater-than-lght from the ender, by aocatng each wth one of two dfferent knd of bt of nformaton. The procedure for th outlned above. xpermental reult ndcate that eraure, a defned by equaton (3), a real operaton. Reference. [] A. Apect,. Granger, G. Roger, hy. Rev. Lett. 49 (98) 9. []. berhard, R. Ro, Found. hy. Lett. (989) 7. [3] C. Cohen-Tannoud, B. Du and F. Laloë, Quantum Mechanc Volume I (Wley, NY, 977) p. 3ff. [4] C. Ruhla, The hyc of Chance (Oxford, Oxford, 995) 8-. [5] Granger,., Roger, G. and Apect, A., urophyc Letter (986) 73. [6] R. Jenen, STAIF-6 roceedng, M. l-genk, ed. (AI, Melvlle NY, 6) 49. [7] T. J. Herzog, J. G. Rarty, H. Wenfurter, A. Zelnger, hy. Rev. Lett. 7 (994) 69. [8] J.-W. an, D. Bouwmeeter, M. Danell, H. Wenfurter, A. Zelnger, Nature, 43 () 55. [9] R. Jenen, I fater-than-lght communcaton poble ung entangled photon and a double lt? (6, camrnttute.net/ coherence/jenen.pdf). Raymond Jenen 55 Hurley Bldg Notre De IN renen@allmal.net 9