Quantum Private Comparison via Cavity QED

Transcription

1 Commun. Theor. Phys. 67 (2017) Vol. 67, No. 2, February 1, 2017 Quantum Prvate Comparson va Cavty QED Tan-Yu Ye ( 叶天语 ) College of Informaton and Electronc Engneerng, Zhejang Gongshang Unversty, Hangzhou , Chna (Receved August 18, 2016; revsed manuscrpt receved October 9, 2016) Abstract The frst quantum prvate comparson (QPC) protocol va cavty quantum electrodynamcs (QED) s proposed n ths paper by makng full use of the evoluton law of atom va cavty QED, where the thrd party (TP) s allowed to msbehave on hs own but cannot conspre wth ether of the two users. The proposed protocol adopts two-atom product states rather than entangled states as the ntal quantum resource, and only needs sngle-atom measurements for two users. Both the untary operatons and the quantum entanglement swappng operaton are not necessary for the proposed protocol. The proposed protocol can compare the equalty of one bt from each user n each round comparson wth one two-atom product state. The proposed protocol can resst both the outsde attack and the partcpant attack. Partcularly, t can prevent TP from knowng two users secrets. Furthermore, the qubt effcency of the proposed protocol s as hgh as 50%. PACS numbers: Dd, Hk, Pp DOI: / /67/2/147 Key words: quantum prvate comparson (QPC), thrd party (TP), cavty quantum electrodynamcs (QED), product state, partcpant attack 1 Introducton In the past two decades, quantum nformaton processng had greatly aroused the nterest of researchers throughout the world and ganed consderable developments. Quantum cryptography, whch was frst proposed by Bennett and Brassard [1] n 1984, s the development outcome of quantum nformaton processng n the realm of cryptography. It can attan uncondtonal securty on the bass of quantum mechancs prncples such as the Hesenberg uncertanty prncple, the quantum no-clonng theorem and so on, and has greatly attracted the attentons of many researchers. Up to now, t has establshed many branches, such as quantum key dstrbuton (QKD), [1 10] quantum secret sharng (QSS), [11 15] quantum secure drect communcaton (QSDC), [16 24] quantum dalogue (QD), [25 31] quantum teleportaton (QT) [32 37] etc. Quantum prvate comparson (QPC), whch was frst suggested by Yang et al. [38] n 2009, s another nterestng branch of quantum cryptography. It ams to compare the equalty of secrets from dfferent users wthout leakng them out on the bass of quantum mechancs prncples. As ponted out by Lo [39] that t s mpossble to securely evaluate the equalty functon n a two-party scenaro, QPC always requres some addtonal assumptons such as a thrd party (TP), etc. In recent years, QPC has been greatly developed so that dfferent quantum states and dfferent quantum technologes have been utlzed to construct dfferent knds of QPC protocols. There are QPC protocols wth sngle partcles, [40 43] Bell states, [38,42,44 52] GHZ states, [53 56] W states, [52,57 58] cluster states, [59 60] χ-type entangled states. [61 63] There are QPC protocols requrng the untary operatons [38,40,43,45,53 54,57,59 60,62] and QPC protocols requrng the quantum entanglement swappng operaton. [44,50 52,55,61] At present, the physcal systems for realzng quantum nformaton processng manly nclude cavty quantum electrodynamcs (QED), on trap, nuclear magnetc resonance, quantum dot, superconductng system wth Josephson effect, etc. [64] Many works, such as entanglement detecton, [65] Bell-state analyss, [66 67] entanglement concentraton, [68 71] entanglement purfcaton, [72] entanglement generaton [71,73 74] and quantum repeater, [75] have been realzed va these physcal systems. Cavty QED can guarantee a hgh level of coherence so that t s an deal canddate for the experment of quantum nformaton processng. [64] Cavty QED has become one of the most promsng physcal systems due to ts unque contrbuton. Based on the above analyss, followng some deas n the protocol of Ref. [46], we put forward the frst QPC protocol va cavty QED by makng full use of the evoluton law of atom va cavty QED. Dfferent from the standard sem-honest TP frst proposed by Chen et al., [53] n our protocol, TP s assumed to be a more practcal thrd party. That s, TP s allowed to msbehave on hs own but cannot conspre wth ether of the two users. Smlar to the protocol of Ref. [41], our protocol adopts product states rather than entangled states as the ntal quantum resource. Unlke the protocols of Refs. [38,40,43,45,53 54,57,59-60,62], our protocol does not need the untary operatons. Unlke the protocols of Refs. [44,50 52,55,61], our protocol does not need the quantum entanglement swappng operaton. Supported by the Natonal Natural Scence Foundaton of Chna under Grant No E-mal: happyyty@alyun.com c 2017 Chnese Physcal Socety and IOP Publshng Ltd

2 148 Communcatons n Theoretcal Physcs Vol. 67 The rest of ths paper s organzed as follows. Secton 2 ntroduces the model of cavty QED. Secton 3 llustrates the QPC protocol va cavty QED. Secton 4 analyzes ts correctness, securty and qubt effcency. Secton 5 dscusses ts comparson wth some prevous QPC protocols. Secton 6 gves the concluson. 2 Model of Cavty QED Drven by a classcal feld, two dentcal two-level atoms can smultaneously nteract wth a sngle-mode cavty. The nteracton Hamltonan between the sngle-mode cavty and the atoms under the rotatng-wave approxmaton can be depcted as [73 74,76 77] 2 H = ω 0 S Z + ω a a a + [g(a S j + as j ) j=1 + Ω(S j e wt + S j e wt )] (1) Here, S Z = (1/2) 2 j=1 ( e j e j g j g j ), S j = g j e j and S j = e j g j, where g j and e j are the ground and excted states of the j-th atom, respectvely. g s the atomcavty couplng strength. a and a are the annhlaton and creaton operators for the cavty mode, respectvely. ω 0, ω a, ω, and Ω are the atomc transton frequency, the cavty frequency, the classcal feld frequency and the Rab frequency, respectvely. t s the nteracton tme. Gven that ω = ω 0, the evoluton operator of the system n the nteracton pcture can be expressed as [73 74,76 77] U(t) = e H0t e Het, (2) where H 0 = Ω 2 j=1 (S j + S j ), and H e s the effectve Hamltonan. Consderng the large detunng case δ g (δ s the detunng between ω 0 and ω a ) and the strong drvng regme Ω δ, g, there s no energy exchange between the atomc system and the cavty. As a result, the effects of cavty decay and thermal feld are erased. Consequently, the effectve nteracton Hamltonan H e n the nteracton pcture can be descrbed as [73 74,76 77] [ 2 H e = (λ/2) ( e j e j + g j g j ) + 2 j=1,j=1, j (S S j + S S j + H.C.) ] where λ = g 2 /2δ. When two atoms are sent nto the above cavty smultaneously, drven by a classcal feld, they nteract wth t. If the nteracton tme and the Rab frequency are made to satsfy λt = π/4 and Ωt = π, two atoms wll have the followng evoluton: 2 gg jk 2 e π/4 ( gg jk ee jk ), (4) 2 ge jk 2 e π/4 ( ge jk eg jk ), (5) 2 eg jk 2 e π/4 ( eg jk ge jk ), (6) 2 ee jk 2 e π/4 ( ee jk gg jk ). (7) (3) 3 QPC Protocol va Cavty QED Two users, Alce and Bob, want to know whether ther secrets are equal or not under the help of TP, who s allowed to msbehave on hs own but cannot conspre wth ether of them. Assume that X and Y are Alce and Bob s secrets, respectvely, where X = L 1 j=0 x j2 j, Y = L 1 j=0 y j2 j, x j, y j {0, 1}. Alce and Bob share two common key sequences K A and K B ndvdual wth length L through the QKD protocols [1 10] beforehand. Here, KA, K B {0, 1}, where KA s the -th bt of K A, KB s the -th bt of K B, and = 1, 2,..., L. The QPC protocol va cavty QED s constructed as follows: Step 1 Alce (Bob) dvdes the bnary representaton of X(Y ) nto L groups G 1 A, G2 A,..., GL A (G1 B, G2 B,..., GL B ), where each group contans one bnary bt. Step 2 TP prepares a quantum state sequence composed of L product states, each of whch s randomly n one of the four states { gg, ge, eg, ee }. Ths quantum state sequence s denoted as S = [SaS 1 b 1, S2 asb 2,..., SL a Sb L ]. Here, the subscrpts a, b represent two atoms n one product state, whle the superscrpts 1, 2,..., L denote the orders of product states n S. Step 3 TP sends SaS b ( = 1, 2,..., L) nto the snglemode cavty descrbed above. Drven by a classcal feld, the two atoms Sa and Sb smultaneously nteract wth the sngle-mode cavty. TP chooses the Rab frequency and the nteracton tme to satsfy Ωt = π and λt = π/4. As a result, SaS b wll undergo the evoluton as shown n formulas (4) (7). Obvously, Sa and Sb become entangled together after the evoluton. After they fly out the snglemode cavty, TP pcks up Sa and Sb to form sequences S a and S b, respectvely. That s, S a = [Sa, 1 Sa, 2..., Sa L ] and S b = [Sb 1, S2 b,..., SL b ]. For securty check, TP prepares two sets of sample sngle atoms D a and D b randomly n one of the four states { g, e, +, }. Here, ± = (1/ 2)( g ± e ). Note that { g, e } s denoted as Z bass whle { +, } s denoted as X bass. Then, TP randomly nserts D a (D b ) nto S a (S b ) to form a new sequence S a(s b ). Fnally, TP sends S a(s b ) to Alce (Bob). After confrmng that Alce (Bob) has receved S a(s b ), TP tells Alce (Bob) the postons and the preparaton bass of sample sngle atoms from D a (D b ). Then, Alce (Bob) measures the sample sngle atoms n S a(s b ) wth the bass TP told and tells TP her (hs) measurement results. By comparng the ntal states of sample sngle atoms n S a(s b ) wth Alce s (Bob s) measurement results, TP can judge whether the quantum channel s secure or not durng the transmsson of S a(s b ). If the error rate s unreasonably hgh, the communcaton s stopped; otherwse, Alce (Bob) drops out the sample sngle atoms n

3 No. 2 Communcatons n Theoretcal Physcs 149 S a(s b ) to recover S a(s b ), and goes to the next step. Fg. 1 The flow chart of the proposed QPC protocol,takng SaS b for example. (a) TP prepares quantum product state SaS b as the quantum carrer. Here, the sold ellpse denotes a partcpant, whle the sold rectangle denotes the quantum state preparaton operaton; (b) TP sends atom Sa(S b) nto cavty QED for evoluton, and transmts t to Alce (Bob) after t fles out cavty QED. Here, the sold crcle denotes cavty QED, whle the sold lne wth an arrow denotes the quantum state transmsson operaton; (c) Alce (Bob) measures atom Sa(S b) wth Z bass, computes RA(R B) and sends RA(R B) to TP. Here, the dotted rectangle, the dotted crcle and the dotted lne wth an arrow denote the quantum measurement operaton wth Z bass, the classcal computaton operaton and the classcal nformaton transmsson operaton, respectvely; (d) TP computes R, and sends R to Alce and Bob; (e) Alce and Bob compute R. Step 4 For the -th ( from 1 to L) round comparson, Alce (Bob) measures atom Sa(S b ) wth Z bass. The measurement result of Sa(S b ) s coded wth one classcal bt whch s represented by MA (M B ). Concretely speakng, f the measurement result of Sa(S b ) s g, M A (M B ) wll be 0; otherwse, f the measurement result of Sa(S b ) s e, MA (M B ) wll be 1. Then, Alce (Bob) computes RA = G A M A K A (R B = G B M B K B ). Here, s the module 2 operaton. Fnally, Alce (Bob) tells TP RA (R B ) publcly. Step 5 TP transforms SaS b prepared n Step 2 nto one classcal bt MT accordng to ts ntal state. Concretely speakng, f the ntal state of SaS b s gg or ee, M T wll be 0; otherwse, f the ntal state of SaS b s ge or eg, MT wll be 1. That s, M T represents the party of Sa and Sb prepared by TP. Then, TP computes R = RA R B M T, and tells R to Alce and Bob publcly. Step 6 After recevng R, both Alce and Bob compute R = R KA K B. They termnate the protocol and conclude that X Y as long as they fnd out that R 0; otherwse, they set = + 1 and repeat the protocol from step 4. If they fnd out that R = 0 for all n the end, they wll conclude that X = Y. Now t concludes the descrpton of our protocol. For clarty, we further gve out the flow chart of our protocol n Fg. 1, takng SaS b for example. It should be emphaszed that n ths knd of dsspatve system, the effects of cavty decay and thermal feld are of great concerns. In order to erase the effects of cavty decay and thermal feld, we need to use the large detunng case and the strong drvng regme. That s, δ should be chosen to satsfy δ g and Ω should be chosen to satsfy Ω δ, g. In ths way, there s no energy exchange between the atomc system and the cavty. In addton, n order to make our protocol work well, formulas (4) (7) should be establshed frst. Therefore, both of λt = π/4 and Ωt = π should be also satsfed. 4 Analyss In ths secton, we analyze our protocol on three aspects ncludng the correctness of ts output, the securty and the qubt effcency. 4.1 Correctness In our protocol, under the help of TP, Alce and Bob compare the equalty of G A and G B n the -th round comparson by usng the evoluton law of SaS b va cavty QED. Here, G A s the -th bt of Alce s secret X, G B s the -th bt of Bob s secret Y, and SaS b s the -th product state n S prepared by TP. For convenence, we use IS to denote the ntal state of SaS b prepared by TP. Accordngly, MT s the one-bt classcal code of IS. Accordng to the descrpton of our protocol, t s apparent that MA s the one-bt classcal code of the Z bass measurement result of Sa after evoluton n cavty QED, and MB s the one-bt classcal code of the Z bass measurement result of Sb, after evoluton n cavty QED. Moreover, t follows that RA = G A M A K A, R B = G B M B K B, R = RA R B M T and R = R KA K B, where K A s the -th bt of K A, and KB s the -th bt of K B. The relatonshps of these essental varables n our protocol are further shown n Table 1. Accordng to formulas (4) (7) or Table 1, t s easy to get that MA M B M T = 0. Consequently, we obtan R = R K A K B = (R A R B M T ) K A K B

4 150 Communcatons n Theoretcal Physcs Vol. 67 = ((G A M A K A) (G B M B K B) M T ) K A K B = (G A G B) (M A M B M T ) = G A G B. (8) Accordng to formula (8), f R = 0, we wll get that G A = G B ; otherwse, we wll get that G A G B. It can be concluded now that the correctness of the output of our protocol s valdated. Table 1 The relatonshps of essental varables n the proposed QPC protocol (G A s the -th bt of Alce s secret X, and G B s the -th bt of Bob s secret Y ; IS denotes the ntal state of SaS b prepared by TP, and MT s the one-bt classcal code of IS ; SaS b after evoluton s the state of IS after evoluton n cavty QED; MA s the one-bt classcal code of the Z bass measurement result of Sa after evoluton n cavty QED, and MB s the one-bt classcal code of the Z bass measurement result of Sb after evoluton n cavty QED; KA s the -th bt of K A, and KB s the -th bt of K B; RA = G A MA K A, RB = G B MB KB, R = RA RB MT and R = R KA KB.) G A G B IS M T S as b (after evoluton) M A M B K A, K B R A R B R R 0 0 gg 0 gg 0 0 0, , , , ee 1 1 0, , , , ge 1 ge 0 1 0, , , , eg 1 0 0, , , , eg 1 ge 0 1 0, , , , eg 1 0 0, , , , ee 0 gg 0 0 0, , , , ee 1 1 0, , , , gg 0 gg 0 0 0, , , , ee 1 1 0, , , , ge 1 ge 0 1 0, ,

5 No. 2 Communcatons n Theoretcal Physcs 151 Table 1 (contnued) 1, , eg 1 0 0, , , , eg 1 ge 0 1 0, , , , eg 1 0 0, , , , ee 0 gg 0 0 0, , , , ee 1 1 0, , , , gg 0 gg 0 0 0, , , , ee 1 1 0, , , , ge 1 ge 0 1 0, , , , eg 1 0 0, , , , eg 1 ge 0 1 0, , , , eg 1 0 0, , , , ee 0 gg 0 0 0, , , , ee 1 1 0, , , , gg 0 gg 0 0 0, ,

6 152 Communcatons n Theoretcal Physcs Vol. 67 Table 1 (contnued) 1, , ee 1 1 0, , , , ge 1 ge 0 1 0, , , , eg 1 0 0, , , , eg 1 ge 0 1 0, , , , eg 1 0 0, , , , ee 0 gg 0 0 0, , , , ee 1 1 0, , , , Note that smlar to the QPC protocol of Ref. [46], our protocol utlzes the party of two atoms to accomplsh the equalty comparson of prvate secrets. Concretely speakng, n the -th round comparson, G A s encrypted wth MA and K A to derve R A, and G B s encrypted wth M B and KB to derve R B. Here, M A, K A, M B and K B play the role of one-tme-pad key. After dong the calculatons of R = RA R B M T and R = R KA K B, we get the XOR value of G A and G B, as shown n formula (8). As a result, the equalty comparson result of G A and G B can be easly obtaned. It s obvous that formula (8) reles deeply on the XOR relaton of MA, M B and M T,.e., MA M B M T = 0. Actually, M A M B essentally mples the party of two atoms Sa and Sb after evoluton va cavty QED, whle MT represents the party of S a and Sb before evoluton va cavty QED. Accordng to formulas (4) (7), the party of Sa and Sb keeps unchanged durng the evoluton va cavty QED so that MA M B M T = 0 s easly establshed, whch guarantees the correctness of the equalty comparson result of G A and G B. It can be concluded now that the party of two atoms Sa and Sb s utlzed to accomplsh the equalty comparson of G A and G B. Apparently, n the whole equalty comparson process of G A and G B, our protocol employs nether the untary operatons nor the quantum entanglement swappng operaton. 4.2 Securty The securty towards both the outsde attack and the partcpant attack s dscussed n ths secton. () Outsde Attack We analyze the outsde attack accordng to each step of our protocol. As for steps 1, 2, and 6, an outsde eavesdropper has no chance to launch an attack, snce there s not any quantum transmsson or classcal transmsson n these steps. As for step 3, there are quantum transmssons as TP sends S a(s b ) to Alce (Bob). An outsde eavesdropper may try to obtan the two users secrets by performng the ntercept-resend attack, the measure-resend attack, the entangle-measure attack, etc. Fortunately, the sample sngle atoms randomly n one of the four states { g, e, +, } are used to detect the outsde attack. Ths securty check method s equvalent to the decoy pho-

7 No. 2 Communcatons n Theoretcal Physcs 153 ton technology, [78 79] whch has been valdated n detal n Refs. [28 29]. Note that the decoy photon technology can be regarded as a varant of the BB84 securty check method, [1] whch has also been valdated n Ref. [80]. Therefore, the attacks from an outsde eavesdropper are nvald n ths step. As for step 4, Alce (Bob) tells TP RA (R B ), publcly. Apparently, G A (G B ) s encrypted wth K A (K B ) n ths step. However, an outsde eavesdropper has no knowledge about KA (K B ). In ths case, she stll has no access to G A (G B ), even though she hears R A (R B ) from Alce (Bob). As for step 5, TP tells R to Alce and Bob publcly. It can be derved that R = R A R B M T = (G A M A K A) (G B M B K B) M T = (G A K A) (G B K B). (9) Even though she hears R from TP, an outsde eavesdropper stll cannot extract anythng useful about G A or G B n ths step, as she has no access to K A and K B. It can be concluded now that our protocol has a hgh level of securty towards the outsde attack. () Partcpant Attack Partcpant attack s a knd of attack from a dshonest partcpant. As suggested by Gao et al., [81] partcpant attack s generally more powerful than outsde attack so that t should be pad more attenton to. Two cases of partcpant attack ncludng the attack from a dshonest user and the attack from TP are analyzed here. Case 1 The attack from a dshonest user In our protocol, Alce role s smlar to Bob s. Wthout loss of generalty, Alce s assumed to be the dshonest user who wants to obtan the secret of the other user. In step 3, Alce may want to ntercept S b TP sends to Bob. However, as she has no knowledge about the postons and the preparaton bass of sample sngle atoms from D b, she wll nevtably leave her trace and be caught as an outsde attacker f she launches ths attack. In step 4, Alce may hear RB from Bob. S a and Sb become entangled together after the evoluton va cavty QED n step 3. Snce Alce does not know the ntal product state of SaS b prepared by TP n step 2, she has no knowledge about the entangled state composed by Sa and Sb after the evoluton. Accordng to formulas (4) (7), she cannot correctly deduce MB from M A. The only thng she can do s to randomly guess the true value of MB. Because G B s encrypted wth M B, she cannot know G B at all. In step 5, Alce hears R from TP. Accordng to formula (8), she can obtan G B by computng G R A. However, our protocol has to be termnated as long as Alce and Bob fnd out that R 0 for certan. Therefore, Alce can know all the G B where R = 0 has been derved and only obtan at most 1 bt of the G B where 0 R has been derved. Case 2 The attack from TP In our protocol, TP s allowed to try hs best to obtan the secrets from two users wthout consprng wth ether of Alce and Bob. In step 4, Alce (Bob) tells TP RA (R B ) publcly. Snce TP has no access to KA (K B ) he stll cannot extract G A (G B ) from R A (R B ). In step 6, both Alce and Bob do not tell TP R. However, once the protocol s termnated by Alce and Bob n the mddle, TP naturally knows that X Y. Ths case happens wth the probablty of 1 (1/2) L 1. Or f the protocol s not termnated by Alce and Bob untl G L A and G L B are compared, TP has to randomly guess the comparson result between X and Y. Ths case happens wth the probablty of (1/2) L 1. It can be concluded that TP knows the exact comparson result between X and Y (.e. X Y ) wth the probablty of 1 (1/2) L Qubt Effcency The qubt effcency η e here s defned as η e = n c /n q, where n c and n q are the number of compared classcal bts and the number of consumed qubts n each round comparson, respectvely. [14 15] In our protocol, one twoatom product state can be used to compare one classcal bt from each user. Therefore, the qubt effcency of our protocol s 50%. 5 Dscusson We dscuss the comparson between our protocol and some prevous QPC protocols [38,41,46,52 53,58,60] n ths secton. The comparson result s summarzed n Table 2. Here, the symbol n s the comparson tmes on the condton that Alce and Bob s secrets are dentcal. From Table 2, we can conclude that the advantage of our protocol les n havng the followng features smultaneously: () It employs two-partcle product states as the ntal quantum resource, whch are much easer to prepare than entangled states; () It only needs to perform sngle-atom measurements, whch are easer to accomplsh than Bell state measurements; () It does not requre the untary operatons or the quantum entanglement swappng operaton; (v) It can be automatcally halted once Alce and Bob dscover the nequalty of ther secrets n the mddle, whch means that not all the secrets are necessary to be compared when ther secrets are not dentcal; (v) It has a hgh qubt effcency equal to 50%. It should be emphaszed that our protocol needs the use of QKD method to guarantee the securty, just as

8 154 Communcatons n Theoretcal Physcs Vol. 67 analyzed n Subsec Lkewse, the QPC protocol of Ref. [38] uses the hash functon to guarantee the securty. In fact, the QPC protocol n Ref. [53] s not secure, snce Alce and Bob can perform the ntercept-resend attack to obtan each other s secret wthout beng dscovered, just as ponted out by Ref. [54]. The QPC protocol n Ref. [46] s also not secure when TP s a more practcal thrd party who tres hs best to extract useful nformaton about two users secrets wth actve attacks, just as ponted out by Refs. [47 49]. When TP s a more practcal thrd party than the one assumed, the QPC protocols n Refs. [53,60] have the smlar securty loophole nduced by TP to that n Ref. [46] ndcated above. Actually, n ths case, the QKD method can be utlzed to guarantee the securty of the QPC protocols n Refs. [46,53,60]. In addton, dfferent from the QPC protocols n Refs. [38,41,46,52 53,58,60], our protocol s realzed va cavty QED, thus t can make full use of the evoluton law of atom va cavty QED. Actually, our protocol s the frst QPC protocol va cavty QED. Table 2 Comparson between our protocol and some prevous QPC protocols. Ref. [38] Ref. [41] Ref. [46] Ref. [52] Ref. [53] Ref. [58] Ref. [60] Our protocol Intal Bell Two-partcle Bell entangled Four-partcle GHZ Three-partcle Four-partcle Two-atom quantum entangled product states W entangled entangled W entangled cluster product resource states state states and states states entangled state Bell entangled states states Quantum Bell state Sngle- Sngle- Bell state Sngle- Sngle- Sngle- Snglepartcle partcle partcle partcle partcle atom measure- measure- measure- measure- measure- measure- measure- measure- measurement ments ments ments ments ments ements ments ments (except that for securty check) Use of QKD No (Use of Yes No Yes No Yes No Yes method Hash functon nstead) Use of Yes No No No Yes No Yes No untary operatons Use of No No No Yes No No No No entanglement swappng TP s No Yes Yes Yes Yes Yes (wth the Yes Yes (wth the knowledge probablty of probablty of about the 1 (1/2) L 1 ) 1 (1/2) L 1 ) comparson result Bt number L 1 1 L 1 1 L 1 compared each round Comparson 1 L L 1 L L 1 L tmes n Qubt eff- 25% 50% 50% 33% 33% 33% 25% 50% cency η e 6 Concluson In ths paper, by makng full use of the evoluton law of atom va cavty QED, we propose the frst QPC protocol va cavty QED. Here, TP s allowed to msbehave on hs own but cannot conspre wth ether of the two users. Our protocol adopts two-atom product states rather than entangled states as the ntal quantum resource, and only needs sngle-atom measurements for two users. It needs nether the untary operatons nor the quantum entanglement swappng operaton. It can compare the equalty of one bt from each user n each round comparson wth one two-atom product state. It can resst both the outsde attack and the partcpant attack. Partcularly, t can pre-

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