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Acta Physica Polonica A

Remarks on Entanglement, its Sources and Applications

Marek Żukowski

Published Jan 1, 2002• 2 citations
Publisher

Abstract

R em ar k s on En tan gle m en t , its Sou r ces an d A p p lic ation s M .`uk ow sk i I n st yt ut F izy ki T eorety cznej i Astro Ùzyki , Uni wersytet G da¥ski W i ta Stw osza 57, 80-952 G da ¥sk, Po l and and Insti tut f ur Ex peri m enta l physi k, Uni versi t at Inns bruck, 6020 Innsbruck, Austri a W e shall discuss the cent ral r ole pla yed in the quantu m information theory by entan glement .A generali zed version of Bell ' s theorem w ill be presented , as well as metho ds in multiphoton interf erometry to obtain correlations violatin g the Bell inequali tie s.Finally , w e shall present some quantum inf ormationa l applicati on s of entanglement.PAC S numb ers: 03.65.U d, 03.67.{a, 42.50.A r 1.I n t r o d u ct io n Current adv ances i n the op erati ona l contro l of qua ntum pheno m ena enabl e us to use the para do xi cal aspects of the qua ntum wo rl d as sources of pra cti cal appl i cati ons.The mai n areas i n whi ch qua ntum pheno m ena can b e harnessed to p erform ta sks im p ossibl e for classical theo ry of i nf orm ati on are qua ntum crypto gra phy (a l ready a rel i abl e techno l ogy), qua ntum com muni cati on (a t the sta ge of bi rth, e.g. the tel eporta ti on exp eri ments) and qua ntum com puta ti on (stunni ng theo reti cal resul ts, brea ki ng the l i m its of the T uri ng -t yp e machines, but sti l l far away fro m op erati onal real i zati ons).The basic no ti on i n the qua ntum i nform a ti on theo ry i s tha t of the qua ntum bi t or the qubi t.Cl a ssical bi ts can ta ke one of the two p ossibl e values 0 or 1 ( \ on " or \ o˜" , etc.).The qubi ts (the simpl est quantum system s wi th pure sta tes descri bed by a two -dim ensional Hi l b ert space, e.g.spins 1/ 2), since they are qua ntum enti ti es, they can b e in an arbi tra ry sup erp ositi on of two ba sis states j 0 i and j 1 i : j q u bi t i = ˜j 0 i + Ù j 1 i :(1 ) (2 1)

DOI
10.12693/aphyspola.101.21

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R em ar k s on En tan gle m en t , its Sou r ces an d A p p lic ation s M .`uk ow sk i I n st yt ut F izy ki T eorety cznej i Astro Ùzyki , Uni wersytet G da¥ski W i ta Stw osza 57, 80-952 G da ¥sk, Po l and and Insti tut f ur Ex peri m enta l physi k, Uni versi t at Inns bruck, 6020 Innsbruck, Austri a W e shall discuss the cent ral r ole pla yed in the quantu m information theory by entan glement .A generali zed version of Bell ' s theorem w ill be presented , as well as metho ds in multiphoton interf erometry to obtain correlations violatin g the Bell inequali tie s.Finally , w e shall present some quantum inf ormationa l applicati on s of entanglement.PAC S numb ers: 03.65.U d, 03.67.{a, 42.50.A r 1.I n t r o d u ct io n Current adv ances i n the op erati ona l contro l of qua ntum pheno m ena enabl e us to use the para do xi cal aspects of the qua ntum wo rl d as sources of pra cti cal appl i cati ons.The mai n areas i n whi ch qua ntum pheno m ena can b e harnessed to p erform ta sks im p ossibl e for classical theo ry of i nf orm ati on are qua ntum crypto gra phy (a l ready a rel i abl e techno l ogy), qua ntum com muni cati on (a t the sta ge of bi rth, e.g. the tel eporta ti on exp eri ments) and qua ntum com puta ti on (stunni ng theo reti cal resul ts, brea ki ng the l i m its of the T uri ng -t yp e machines, but sti l l far away fro m op erati onal real i zati ons).The basic no ti on i n the qua ntum i nform a ti on theo ry i s tha t of the qua ntum bi t or the qubi t.Cl a ssical bi ts can ta ke one of the two p ossibl e values 0 or 1 ( \ on " or \ o˜" , etc.).The qubi ts (the simpl est quantum system s wi th pure sta tes descri bed by a two -dim ensional Hi l b ert space, e.g.spins 1/ 2), since they are qua ntum enti ti es, they can b e in an arbi tra ry sup erp ositi on of two ba sis states j 0 i and j 1 i : j q u bi t i = ˜j 0 i + Ù j 1 i :(1 ) (2 1)
W e descri be a new scheme for perf ormin g quan tum key distributi on .W e present tw o physica l implementations for the quantum key distribu tio n system.T he Ùrst implementation uses a typ e-I I optical-parametri c ampliÙer to generate the optical pulses w hich contain the key inf ormation.T he second implementation uses correlated semicondu ctor emitters to generate the optical pulses.PAC S numb ers: 03.67.Dd , 03. 67.H k, 42.50.D v, 42.50.Lc 1 .I n t r o d u ct i on : qu an t u m st at es p r o vi d e secu r i t y Let us consider the fol l owing scenari o: one p erson (Al i ce) wa nts to send a secret m essage to a second p erson ( Bo b).At the sam e ti me, an eavesdropp er (Eve) i s attem pti ng to obta i n the secret m essage.Al i ce and Bo b can use a One-Ti me Pa d crypto gra phi c pro to col in order to securely tra nsm i t thei r secret m essage.Thi s pro to col consists of Al i ce and Bo b ha vi ng a shared secret key pri or to the sending of the secret m essage.The key wi ll consi st of a stri ng of ra ndo m bi nary da ta .The key i s used to encode the secret m essage by a sim pl e bi nary addi ti on of the secret m essage wi th the key .The encoded secret message can then b e tra nsm i tted over a publ i c channel (i .e. a channel whi ch can b e seen by any one i ncl udi ng Eve).As l ong as the key data i s shared by onl y Al i ce and Bo b and the key i s onl y used once, i t i s pro vabl y i m p ossibl e for Eve to decode the encoded m essage.Thi s wo ul d app ear to b e a very p owerful techni que for sending secret messages.The catch i s tha t i t i s ha rd to create and di stri bute a key tha t i s shared by Al i ce and Bo b but al so rem ai ns secret after the di stri buti on pro cedure.Presum -Ê corr esp on din g au t h o r; e-m ail : ray me r@ore gon .uor ego n. edu (4 37)
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at iona l Co n f er ence \ Qu an tu m O p t i cs V " , Ko ƒci el isko, Po la nd , 200 1 O n M i x ed St ate s Entan gle m ent an d Q u antu m C om m u n ication : As p ects of Qu antu m C h an n els Th eor y P .H oro d eck i Fa cul t y of A ppl i ed Phy sics and Ma the mati cs, T echnical Uni versity of Gda ¥sk Naruto wi cza 11/ 12, 80 -952 G da¥sk, Po l and Basi c aspects of qua ntu m communication based on quantum channe ls theo ry are re view ed to gether w ith suitable examples .T he key notion of quantum channel capacity is discussed.T he role of mixed states entanglement as a practical to ol in quantum channels theory is explain ed in detail.A pplication of recent results on non-positi ve partial transp ose bound entanglement con j ecture to binding entanglement channels show s that validity of the conj ecture for some states implies n o n a dd i t i v it y of tw o-w ay quantum channel capacity .Some asp ects of robustness of entanglement in context of positive maps theory are also discussed .