Chinese Physics B (¥¥¥IIIÔÔÔnnn B)
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Phys. B Vol. 26, No. 2 (2017) 020304
Probabilistic direct counterfactual quantum communication∗
Sheng Zhang(张盛)† Department of Electronic Technology, China Maritime Police Academy, Ningbo 315801, China
(Received 31 May 2016; revised manuscript received 3 November 2016; published online 20 December 2016)
It is striking that the quantum Zeno effect can be used to launch a direct counterfactual communication between two spatially separated parties, Alice and Bob. So far, existing protocols of this type only provide a deterministic counterfactual communication service. However, this counterfactuality should be payed at a price. Firstly, the transmission time is much longer than a classical transmission costs. Secondly, the chained-cycle structure makes them more sensitive to channel noises. Here, we extend the idea of counterfactual communication, and present a probabilistic-counterfactual quantum communication protocol, which is proved to have advantages over the deterministic ones. Moreover, the presented protocol could evolve to a deterministic one solely by adjusting the parameters of the beam splitters.
Keywords: quantum communication, quantum cryptography, optical implementation of quantum information processing PACS: 03.67.Dd, 03.67.Hk, 42.50.Ex DOI: 10.1088/1674-1056/26/2/020304
1. Introduction launching a counterintuitive trojan horse attack.[14] Since the Quantum communication is now widely accepted to be rate of information photons in the Noh09 protocol, only up to one of the most promising candidates in future quantum tech- 12.5% in an ideal setting, is not satisfactory, Sun and Wen [6] nology. Using quantum mechanics, several amazing tasks, improved it to reach 50% using an iterative module. Ex- such as dense coding,[1,2] teleportation[3,4] and counterfactual perimental verifications of the Noh09 protocol have also been [15,16] quantum key distribution,[5,6] are naturally achieved. Since the reported. invention of quantum key distribution (QKD) protocol, i.e., the Most interestingly, the topic of counterfactual quantum BB84 protocol,[7] quantum communication has enjoyed great communication (CQC), has been repainted by Salih et al., success with both theoretical and commercial aspects. One of who claimed a new protocol (SLAZ2013 protocol) with a [17,18] the most significant contributions, which is impossible to be better rate, using the quantum Zeno effect. They also achieved by classical means, is counterfactual quantum com- announced a tripartite counterfactual quantum key distribu- [19] munication. It enables two remote parties, Alice and Bob, to tion protocol, to improve the counterfactuality and secu- [20] exchange messages without transmitting any information car- rity of a previous scheme by Akshata Shenoy et al. Other riers. interesting applications, such as semi-counterfactual quan- [21] The idea of counterfactual quantum communication was tum cryptography, counterfactual quantum-information [22] [19,20] initialized by interaction-free measurement,[8–10] with the im- transfer, are also found in recent papers. pressive phenomenon that an object can be detected with- Although conventional CQC protocols based on the quan- out being intuitively measured. The first example, presented tum Zeno effect, such as the SLAZ2013 protocol, are sup- by Noh,[5] was realized in a QKD protocol. Later, we an- posed to be more efficient than early versions, there are un- nounced a variant adapted to the deterministic key distribution expected side-effects directly induced by the chained-cycle scenario.[11] In sharp contrast to conventional QKD schemes, structure. Firstly, the transmission time could be multiplied these protocols are counterintuitive that the quantum states, by the number of the cycles, since a photon pulse should travel served as the information carriers, never travel through the through all the cycles before it is detected by the legitimate de- channel. A translated no-cloning theorem prevents the eaves- tectors. In other words, the time taken by transferring a single droppers from getting any information of the private key. A bit might be much longer than a classical transmission may strict security proof of Noh’s protocol (Noh09 protocol) was cost, even though Alice and Bob stand close to each other. presented by Yin et al.[12] We further proved that, although Secondly, these schemes seem to be more sensitive to channel this protocol is secure under a general intercept-resend at- noises (concerning only those blocking the channel), since the tack in an ideal mode, the practical security could be com- transmission time is systematically multipled. In Ref. [17], it promised due to the dark count rate and low efficiency of was estimated that an acceptable noise rate only reaches 0.2%. the detectors.[13] Surprisingly, we also found that Eve could Motivated by removing the above side effects, we ex- get full information of the key from a real implementation by tend the idea of ‘counterfactual’, and consider a new paradigm, ∗Project supported by the National Natural Science Foundation of China (Grant No. 61300203). †Corresponding author. E-mail: [email protected] © 2017 Chinese Physical Society and IOP Publishing Ltd http://iopscience.iop.org/cpb http://cpb.iphy.ac.cn 020304-1 Chin. Phys. B Vol. 26, No. 2 (2017) 020304 namely probabilistic counterfactual quantum communication Prob{k = 0} denotes the probability of the case k = 0. (PCQC). Here, we use the word ’probabilistic’ to define the purity of the counterfactuality. Specifically, a deterministic Alice Bob quantum channnel counterfactual communication scheme is one in which none of the information-carriers travels through the channel. How- Fig. 1. A primitive prototype of communication systems. ever, in a probabilistic one, there is a non-zero probability for We should note that the information carriers in counter- a carrier passing the channel. The idea mostly contributes factual and probabilistic counterfactual communications are to bridging the gaps between the classical and deterministic supposed to be quantum photons, which are well known for counterfactual communication schemes. In classical commu- their wave-particle duality.[23] We argue that the counterfac- nications, all information carriers must pass the channel. In tuality should only be referred to the particle-property of contrast, they are never allowed to do so in a deterministic the quantum photons. Otherwise, it is difficult to determine counterfactual communication scheme. However, in a PCQC whether a protocol is counterfactual or not. There have been protocol, they might travel through the channel with uncer- controversies around the topic of ’counterfactual’ in recent tainty. It naturally follows that existing counterfactual quan- papers.[24–27] For example, the SLAZ2013 protocol seems to tum communication schemes fall into the paradigm of deter- be not counterfactual for some results, i.e., logic 0, accord- ministic ones. For instance, Noh’s protocol[5] is a determinis- ing to the trace definition proposed by Vaidman.[27] Also, one tic one on that no information-carrier goes through the chan- may argue that Noh’s protocol[5] is not counterfactual based nel, though it produces a probabilistic (or random) key. In on the following fact. As demonstrated by a quantum delayed this paper, we present a PCQC protocol, in which the chained choice experiment,[28] it is Bob’s operation choice (blocking structure is removed, thus the transmission time is greatly re- or passing) that determines the path where the photon finally duced and the sensitivity to channel noises is simultaneously travels. Before he made his choice, the photon, if observed degraded. as a wave, would exist in all paths of the interferometer, other- The rest of the paper is organized as follows. In Section 2, wise, quantum interference would never take place. Therefore, the definition of probabilistic counterfactual communications things become more complex than we ever expected, if coun- is given. Then, we present a probabilistic counterfactual quan- terfactuality and wave function are both concerned. Here, in tum communication protocol in Section 3. Next, the coun- Table1, I only take into account their classical description, terfactuality rate and the robustness against channel noises are i.e., the particle-property. analyzed to show the advantages over the SLAZ2013 protocol. In Section 5, we have a brief discussion on how to combine Table 1. Definitions of Communication prototypes. the presented protocol with quantum key distribution. Finally, Prototype l Prob{k = 0} a conclusion is drawn. Classical communications 1 0 Deterministic counterfactual communications 1 1 2. Definition Probabilistic counterfactual communications 1 p(0 < p < 1)
Before the protocol is introduced, it is necessary to define In previous schemes,[5,6,17] it is known that projective the probabilistic counterfactual communications. Figure1 is measurement is important to perform deterministic counter- a primitive prototype of a communication system, where the factual computations and communications, since the infor- quantum channel is presumed to be noiseless for simplicity. mation that whether the photon passes the channel can be Define three binary registers x, y, and z for Alice, Bob, and obtained from the detection results. Figure 2(a) is an ana- the channel, respectively. A successful communication pro- log of the detections in quantum deterministic counterfactual cedure is described as follows: the sender, Alice, prepares a schemes. Obviously, one can confirm that the photon is absent signal bit (0 or 1) and stores it in register x; Bob resets his from the channel with certainty, if it reaches the bottom tele- register y for depositing the received signal; Alice and Bob scope. Therefore, an intuitive way to achieve quantum prob- carry out a communication protocol p, which sets y = z = x; abilistic counterfactual communications is to replace the pro- the procedure ends with the result l. Consequently, the pro- jective measurement device by a photon counter. For exam- cedure can be written as the function l = F(x,y,z, p), where ple, in Fig. 2(b), where a photon screen is located at point l = 1 for x = y = z, and l = 0 for otherwise. A successful A, it is obvious that one can never confirm the path infor- communication procedure is featured with l = 1. We need an- mation from the detection result, which can be expressed by √ √ other binary function k = N(z), where k = 0(1) implies the |ϕi = R|0i + 1 − R|1i. Here, |0(1)i represents that the information carrier (not) passing the channel. Naturally, clas- photon is reflected (transmitted) by the BS, and R is the reflec- sical, deterministic counterfactual and probabilistic counter- tivity of the BS. In this case, the probability of a photon being factual communications can be defined by Table1, in which absent from the channel is R from a classical view. However, 020304-2 Chin. Phys. B Vol. 26, No. 2 (2017) 020304 it may be argued that the photon exists in both arms with re- with respect to interference. Specifically, the following condi- spect to the wave-property. In this paper, ’probabilistic coun- tion should be satisfied, terfactual’ is only discussed in the classical settings, since it L − L = L , (1) may lead to controversies if it is considered with a quantum ODi+1 ODi 0 description. for i = 1,2,...,N − 1. Here, LODi and L0 denote the opti- BS BS cal lengths of ODi, and the interval between two neighbor- MR MR ing ODs, respectively. Also, LOD1 is initialized by the optical length of the real channel in terms of matching. A D2 A MR S Alice MR screen
D1 C (a) D1 (b) Fig. 2. Two detection modes. Here, BS stands for beam splitter and v PBS MR is a mirror. The transmission mode of the BS is supposed to be 0 D2 the quantum channel. (a) Detectors D1 and D2, e.g., two telescopes, are placed here to observe incoming photons from the top and the side of SM Bob the apparatus, respectively. (b) A photon screen is placed at point A to MR MR MR N receive photons from both arms. SPR D4 OD OD 2 OD N
3. Protocol v BS 1 BS 2 BS N PBS1 SW
First, we give a brief introduction of the SLAZ2013 pro- MR B OD 0 tocol. To achieve the goal of counterfactuality, a chained quan- D() D3(2) D(N) tum Zeno effect, acting as the core principle, is introduced by MR employing a series of beam splitters and mirrors. Correspond- ingly, the optical circuit is divided into two types of cycles, Fig. 3. Experimental setup. In contrast with the SLAZ2013 protocol, an i.e., the outer cycle and inner cycle shown in Ref. [17]. At the iterative module in the dashed box is introduced to replace the original inner very beginning, a photon, which has nothing to do with the cycle. Here, BSi stands for a beam splitter, and D3(i) denotes a photon de- tector for i = 1,2,...,N. Bob uses a switch (SW) to carry out the blocking information bit, is injected by the source, and enters the input operation. SPR and SM stand for switchable polarization rotator and switch- port of the outer cycle. The other thing Alice has to do is to ob- able mirror, respectively. Other notations: C is a circulator; D stands for the serve which of her detectors, D and D , clicks. At Bob’s end, single-photon detector; S is the single-photon source; PBS stands for the po- 1 2 larizing beam splitter which only reflects vertically polarized photons; OD he just chooses to block (pass) the photon, if logic “1” (“0”) and MR stand for the optical delay and Mirror, respectively. In real imple- is selected to be transmitted. Let us see how Alice knows the mentations, the MR could be replaced by the Faraday mirror (FM) to offset the side effects induced by the noises and birefringence. The settings of transmitted bit. When “0” is selected, two events, denoted by PBS0, PBS1, SPR, and SM are the same as those in Ref. [17]. For instance, we have the rotating angle of SPR as β = θ/2 = π/4M. E1 and E2 can be observed by Alice: M (i) (E1) The photon has been caught in detector D1. In Alice’s station, a horizontally polarized (H) photon is (ii) (E2) The photon has been caught in detector D3. emitted by the source, and it certainly arrives at SM, which Note that E2 implies that the photon must have gone is switched off initially to allow the photon to be transmitted through the channel. Therefore, E2 should be discarded. Sim- but it then remains on for M cycles, and is turned off again ilarly, when “1” is selected, events E3 and E4 can be observed: after M cycles are completed. Due to the polarization rota- (iii) (E3) The photon has been caught in detector D2. tion by SPR, the photon will either be reflected or transmitted (iv) (E4) The photon has been caught in detector D4. by PBS1. If the photon is not blocked by the SW at Bob’s Again, E4, which goes against the counterfactuality, is end, it will return to the SM and repeat the travel in a new discarded. Indeed, the quantum Zeno effect has an impor- cycle. Otherwise, the protocol will be restarted. The iterative tant role in both events E1 and E3, however, one should note module and Bob’s station comprise a Michelson-type interfer- that the chained-cycle structure ievitably increases the time of ometer, in which quantum interference can be observed. Here, transmitting a single bit. the combination of PBS1 and the SPR cooperate with each The experimental setup shown in Fig.3, which is adapted other as a beam splitter. Therefore, the presented setup can from the template of the SLAZ2013 protocol, is presented. It be translated to a Mach–Zehnder type interferometer shown in is shown that an iterative module (shown in the dashed rect- Fig.4, if we technically use a fictitious router to approximate angle), ever introduced by Refs. [6] and [14], is employed to the Michelson-type interferometer mentioned above. Bob’s replace the inner cycle. The length of each optical delay (OD) station is simpler: he chooses to block (logic 1) or pass (logic in this module should be carefully chosen to match each other 0) the photon by controlling the SW. 020304-3 Chin. Phys. B Vol. 26, No. 2 (2017) 020304
the paradigm of probabilistic counterfactual communications. |1>BS |0> This property makes the presented scheme distinguished with deterministic counterfactual communication protocols. Inter- FR estingly, the presented scheme could easily evolve to a deter-
ministic counterfactual one when PFRk → 0. When Bob blocks the photon, the interference in the iter- ative module is destroyed. Therefore, it is most probably that a
1 photon exiting PBS1 is detected by Bob’s detector D4 or one of SW the detectors in the iterative module (D3(1),D3(2),...,D3(N)). MR MR 2 SW In my previous work,[14] it is shown that the conditional oc- input n currence rate of this event is obtained by SW output port port N i−1 2 2 Pab = 1 − ∑ ∏ t j (1 −ti) , (2) i=1 j=0 which satisfies FR 1 P ≤ 1 − (1 − p )2. (3) ab N FRk
Here, we define that t0 ≡ 1. Obviously, the Pab approaches 1 asymptotically with N → ∞. Correspondingly, in Fig.4, we can also replace the Michelson-type interferometer by the route FR, if the i-th SW is set to be switched off with proba- D1 D2 N bility PBi , such that ∑i=1 PFRi PBi = Pab. Counterfactual com- Fig. 4. Principle schematics. Here, FR stands for a fictitious probabilistic router, explicitly shown in the right side dashed box. The input node routes munication here is ensured by the quantum Zeno effect, i.e., the photon to the output through one of the n paths. Here, we denote the |10i → cosM−1 θ(cosθ|10i + sinθ|01i) ≈ |10i. (4) probability that the photon goes through path i as PFRi . One of the n paths, say path k, corresponds to the real channel, such as path BSN → SW in Fig.3. Consequently, detector D1 clicks as a result. Note that proba- bilistic counterfactual communication never takes place in this Now, we explain why this router works and show the prin- case, since the photon going through the channel triggers de- ciple of the presented protocol in detail. When Bob passes the tector D4 with certainty (this event should be discarded). photon, representing the fact that Bob chooses logic 0, quan- tum interference immediately takes place in the presented in- 4. Performance terferometer. Explicitly, in each cycle, if the photon leaving Since the equivalent optical distance between Alice and SPR is reflected by PBS1, it enters the iterative module and Bob, Deq, is only M ∗L, where L denotes the practical distance, returns to PBS1 with certainty owing to the interference (the (that is Deq = M ∗N ∗L for SLAZ2013) the transmission time, phase difference is π radians between the two output paths of i.e., t = Deq/c, has been reduced by a factor of N, which is each BS). In other words, the photon will neither be detected a great step forward to implementing direct quantum counter- by Bob nor by the detectors in the iterative module. In this factual communication in real-life channels. Here, c denotes sense, the Michelson-type interferometer is equivalent to the the light speed. Intuitively, the sensitivity to channel noises router FR with all its SWs on. From Fig.3, the conditional is degraded, since the equivalent communication distance is probability that the photon was to manifest itself to the chan- greatly shortened. Analysis of the robustness against channel nel, i.e., P , is estimated to be N t , where t is the trans- FRk ∏i=1 i i noises will be presented in this section. Another advantage is missivity of the i-th BS in Fig.3. In addition, it naturally fol- that the counterfactuality rate of the procotol is improved, in lows from Fig.4 that the initial quantum state |10i, implying contrast with the SLAZ2013 protocol. that the photon enters the first BS from the left hand side arm, ultimately evolves to cosMθ|10i + sinMθ|01i, which equals 4.1. Counterfactuality analysis to |01i. Consequently, it means that the photon will trigger Here, the counterfactuality rate, denoted by C, is defined detector D2. Now, let us see how probabilistic counterfactual by the probability of a successful communication featured communication takes place. In each cycle, we see that PFRk with no transmission of information carriers. In a determin- is non-zero. It means that the information carrier, which trig- istic scheme, it is usually given by a tuple 퐶 = (C0,C1). Here, gers detector D2, may have traveled through the channel or C0 and C1 represent the counterfactuality rates for the signals not. From Table1, it immediately implies that this case is of 0 and 1, respectively. Obviously, Ci (i = 0,1) varies from 0 020304-4 Chin. Phys. B Vol. 26, No. 2 (2017) 020304 to 1, and perfect counterfactual communication is available Fortunately, C0 can be improved by reducing t (or indepen- if and only if Ci = 1 (i = 0,1). For the SLAZ2013 proto- dently increasing N). As is shown in Fig.5, a curve, marked col, C0(1) equals to the detection rate P1(2), which is given by with a smaller t, locates itself over the others with bigger 2 |x(y)M| (see Ref. [17] for more details). Also, this protocol ones. This shows that high counterfactuality (e.g., C0 > 0.9) achieves perfect counterfactuality when N and M approach in- is achievable with acceptable Ms, as long as t is chosen to
finity, leading to 퐶1 → (1,1), i.e., P1 → 1 and P2 → 1. How- be sufficiently small. In order to show the advantages over ever, in the presented protocol, the counterfactual rate C0 could the SLAZ2013 protocol, we list some meaningful results, ob- not be given by the detection rate, due to the absence of pro- tained from numerical estimating, in table 1. It is clear that, for jective measurement. Fortunately, it can be estimated from its the SLAZ2013 protocol, N should be sufficiently large (mean- quantum description, which is a superposition of all possible while things get worse as M increases), in order to achieve paths. acceptable counterfactuality rates (bigger than 0.9). However, Now, we begin to calculate the counterfactuality rates of the same rates can be achieved with less resources in the pre- the presented protocol. When Bob blocks the channel (logic sented protocol, as long as we carefully choose the value of t j ‘1’), deterministic counterfactual communication takes place. ( j = 1,2,...,N).
Therefore, C1 is directly given by the detection rate of detector . D2, i.e., .
2M . C1 = cos θ. (5) . Obviously, perfect counterfactuality is achievable for signal 0 . “1”, when M approaches infinity. C . In the case of Bob passing the photon (logic ‘0’), it is t/. . impossible to determine C0 from the detection rate of detec- t/. . t/. tor D1, since there are probabilistic counterfactual events here. t/. Therefore, C0 should be estimated from the superposition state of each cycle. In Fig.4, the superposition in the m-th cycle M can be expressed by |ϕmi = cosmθ|10i + sinmθ|01i, if the Fig. 5. C0 as a function of M. Here, t = PFRk . router is not taken into account (see Ref. [17]). Now, if the photon is in the right-hand side arm of the BS (the probability Table 2. Numerical estimating results. 2 is sin mθ), the photon enters the router, and the conditional M = 25 M = 50 M = 75 M = 100 M = 150 probability of it passing the channel is given by P . In total, FRk PFRk = 0.001 0.987 0.975 0.963 0.951 0.927 C0 is P = 0.0005 0.994 0.987 0.981 0.975 0.963 (I)1 FRk P = 0.0001 0.999 0.997 0.996 0.995 0.992 M FRk 2 PFRk = 0.00005 0.999 0.999 0.998 0.997 0.996 C0 = ∏ (1 − sin mθ · PFRk ). (6) m=1 N = 320 0.912 0.831 0.758 0.693 0.582 N = 500 0.943 0.887 0.836 0.788 0.702 Obviously, equations (5) and (6) imply that perfect direct 2 (II) N = 1250 0.977 0.953 0.930 0.908 0.865 counterfactual communication can also be achieved when M N = 2500 0.988 0.976 0.964 0.953 0.930 approaches infinity, i.e., C0,C1 → 1. One could also obtain (I)1: The first half of the table, corresponding to the presented protocol. C → 1 by setting P → 0, keeping M unchanged. In this 0 FRk The content units are filled with values of C0, referring to different pFRk case, the presented protocol evolves to a deterministic one. and M. (II)2: The second half of the table, corresponding to the SLAZ2013 proto- More interestingly, the presented protocol could also turn out col. The content units are filled with values of p2, referring to different M and N. to be totally classical when PFRk = 1. In this case, the router in Fig.4 contains only one path, i.e., the channel. Therefore, At last, we concluded the detector rates, Prob{D1 clicks} this result is consistent with the one referring to Fig. 2(a) in and Prob{D2 clicks}, which are given by Ref. [17], whose counterfactuality rate C0 is also equal to 0. 2M Prob{D1 clicks} = cos θ, (7) We have loosely plotted the counterfactuality rate C0, il- lustrating how it varies as a function of M. In Fig.5, it is and showed that all curves descend as M increases. In other words, Prob{D clicks} = 1. (8) the performance becomes worse with a bigger M, since the 2 probability that a photon exposes itself in the channel evi- The difference between Eq. (6) and (8) shows the probabilis- dently increases when the number of the cycles grows up. tic-counterfactual property of the protocol. 020304-5 Chin. Phys. B Vol. 26, No. 2 (2017) 020304
4.2. Robustness against channel noises unnormalized quantum state |ψi = c|01i, arrives at the (i+1)- Here, the robustness of the presented protocol is only in- th BS in Fig.4, the final state after the following M − i BSs is vestigated in a most representative scenario that the channel written by noise acts as an obstacle which definitely registers an event |ψi = c ∗ (cos(M − i)θ|01i − sin(M − i)θ|10i), (12) of “Block”. Errors only occur in the case of Bob choosing final to pass the photon, where interference is destroyed by noises. owing to quantum interference. Obviously, it is seen from Remarkably, for the presented protocol, the presence of noises Eq. (12) that this independent pulse definitely contributes to definitely induces errors as well as an increase of the probabil- the rate of detector D2. Therefore, Prob{D2 clicks}, which ity that detector D3( j), ( j = 1,2,...,N) clicks, which indepen- 2 is given by Prob{D2 clicks} = (1 − (1 − c)yi cos(M − i)θ) , dently discounts the performance of the protocol. directly increases as c increases. Equation (10) shows the bal- When Bob passes the photon, it will produce a click of de- ance of c and N, and that c = 0 when N → ∞ for the worst tector D with certainty owing to quantum interference, if the 2 case. Now, we use the same technique, that random numbers channel is noiseless. Let us see what happens when a “block” between 0 and 1 are employed to play the role of noise, to plot in one cycle is triggered by the noise other than Bob. With- the successful rate of the right detector. The curves in Fig. 6(a) out loss of generality, we assume that the channel of the i-th are statistically averaged on a 2000-times repetition to achieve cycle is blocked due to the noise. Given that the state of the better smoothness. Obviously, the protocol outperforms the i-th cycle is |ϕii = xi|10i + yi|01i, the quantum state after the SLAZ2013 protocol on the tolerance of noise given the same (i + 1)-th BS is written as M. Moreover, a smaller M implies a bigger tolerance of B for
|ϕii+1 = (xi cosθ − c ∗ yi sinθ)|10i the presented protocol, which is consistent with the fact that an increase of the number of cycles immediately increases the +(xi sinθ + c ∗ yi cosθ)|01i, (9) risk of suffering from channel noises. where c denotes the rate that the single-photon pulse in the M/, c/ (a) channel of the ith cycle is not absorbed. For instance, in the 0.95 M/, c/ SLAZ2013 protocol, c = 0(1), corresponding to Bob’s choice “Block(pass)”, means that the pulse is fully(never) absorbed 0.85 by Bob’s detector D4. Interestingly, c varies from 0 to 1 for the presented protocol, since the iterative module also contributes 0.75 to the benefit that the photon in the right-hand side arm is not absorbed. 0.65 Next, it is necessary to fix the rate “c” with given parame- Successful clicking rate clicking Successful ters of the module. Suppose that a photon is reflected by PBS1 0.55 in the i-th cycle, it is easy to conclude the probability that it is 0 0.004 0.008 0.012 0.016 0.020 reflected back to PBS1 by one of the mirrors in the module as Noise B 1.0 N i−1 M/, N/ (b) 2 2 Pref = ∑ ∏ t j (1 −ti) , (10) 0.9 M/,N/ i=1 j=0 0.8 due to the absence of quantum interference. Also, the proba- bility that it is absorbed is 0.7
N i−1 N 2 2 0.6 Pabs = 1 − ∑ ∏ t j (1 −ti) − ∏ti. (11) i=1 j=0 i=o
Successful clicking rate clicking Successful 0.5 Obviously, we have c = Pref. Moreover, it is seen that a photon 0.4 will be detected by D3( j), ( j = 1,2,...,N) with unit proba- 0 0.004 0.008 0.012 0.016 0.020 bility, when N approaches infinity.[14] Nevertheless, it is still Noise B interesting to investigate the robustness of the presented proto- Fig. 6. (color online) Numerical estimating results. (a) Successful click- ing rate of the presented protocol as a function of the noise rate B. Here, col in finite settings, where c is indeed a non-zero real number c = 0, corresponding to the worst case, is chosen as a better sample less than 1. In order to find how c discounts the rate of detector to make a comparison with the SLAZ protocol. The solid (dash–dot) curve is plotted for M = 25 (50). (b) Successful clicking rate of the D2, we try to correlate Prob{D2 clicks} with c formally. As- SLAZ2013 protocol as a function of the noise rate B. The solid (dash– sume independently that a single-photon pulse, denoted by an dot) curve is plotted for M = 25 (50), N = 320 (1250). 020304-6 Chin. Phys. B Vol. 26, No. 2 (2017) 020304 5. Discussions References Although the side-effect of the chained quantum Zeno ef- [1] Bennett C H and Wiesner S J 1992 Phys. Rev. Lett. 69 2881 [2] Mattle K and Weinfurter H and Kwiat P G and Zeilinger A 1996 Phys. fect is greatly reduced by the iterative module, another arises Rev. Lett. 76 4656 from this component. When Bob chooses to block the photon, [3] Bennett C H, Brassard G, Crepeau´ C, Jozsa R, Peres A and Wootters it is likely in a single cycle that he cannot capture it, even if WK 1993 Phys. Rev. Lett. 70 1895 [4] Boschi D, Branca S, De Martini F, Hardy L and Popescu S 1998 Phys. it enters the module, since the photon could be reflected by Rev. Lett. 80 1121 one of the mirrors in the module, i.e., MR1, MR2,...,MRN, [5] Noh T G 2009 Phys. Rev. Lett. 103 230501 and returns back to PBS1 (the conditional probability told by [6] Sun Y and Wen Q Y 2010 Phys. Rev. A 82 052318 Eq. (2) is N i−1 t2(1 −t )2 ). Fortunately, this effect con- [7] Bennett C H, Brassard G, et al. 1984 Proceedings of IEEE Interna- ∑i=1 ∏ j=0 j i tional Conference on Computers, Systems and Signal Processing, De- tributes, though unobviously, to the counterfactualitiy C1. cember 9–12, 1984, Bangalore, India, p. 175 It is impossible to directly apply this protocol or [8] Elitzur A C and Vaidman L 1993 Found. Phys. 23 987 SLAZ2013-like ones to secure communications, such as quan- [9] Kwiat P G et al. 1999 Phys. Rev. Lett. 83 4725 [10] Noh T G and Hong C K 1999 Quantum Semiclass. Opt. 10 637 tum key distribution. The central problem is that a no-cloning [11] Zhang S and Wang J and Tang C J 2013 Commun. Theor. Phys. 10 637 theorem is not included in principle. In these protocols, only [12] Yin Z Q, Li H W, Chen W, Han Z F and Guo G C 2010 Phys. Rev. A 82 042335 orthogonal states, say, |φ0i and |φ1i, are employed. Fortu- nately, it is not difficult to make them secure. All one should [13] Zhang S, Wang J and Tang C J 2012 Chin. Phys. B 21 060303 [14] Zhang S, Wang J and Tang C J 2012 Europhys. Lett. 98 30012 do is to change the pure states into nonorthogonal mixed states, [15] Liu Y, Ju L, Liang X L, Tang S B, Tu G L, Zhou S, Peng L, Chen C Z, i.e., Tr[ρ0ρ1] 6= 0. For example, the Noh09 protocol is of this Chen K, Chen T Y, et al. 2012 Phys. Rev. Lett. 109 030501 kind. Here, we also highlight an open question that whether it [16] Brida G, Cavanna A, Degiovanni I P, Genovese M and Traina P 2012 Laser Phys. Lett. 9 247 is possible to explore unconditional security directly from the [17] Salih H, Li Z H, Al-Amri M and Zubairy M S 2013 Phys. Rev. Lett. quantum Zeno effect, thus leading to a new paradigm outper- 110 170502 forming existing quantum key distribution schemes. [18] Vaidman L 2007 Phys. Rev. Lett. 98 160403 [19] Salih H 2014 Phys. Rev. A 90 012333 [20] Shenoy A, Srikanth R and Srinivas T 2014 Phys. Rev. A 89 052307 6. Conclusion [21] Shenoy H A, Srikanth R and Srinivas T 2013 Europhysics Lett. 103 60008 In summary, we have opened the door of probabilistic [22] Guo Q, Cheng L Y, Chen L, Wang H F and Zhang S 2014 arXiv: counterfactual quantum communication. Generally, a high 1404.6401 [quant-ph] counterfactuality rate can be achieved with less resources, in [23] Greiner W 2001 Quantum Mechanics: An introduction (Berlin: Springer) contrast with previous schemes based on the chained quantum [24] Hosten O, Rakher M T, Barreiro J T, Peters N A and Kwiat P G 2006 Zeno effect. Also, we should point out that this protocol is Nature 439 949 not symmetrical, since probabilistic counterfactual communi- [25] Mitchison G Jozsa R 2007 arXiv: quant-ph/0606092v3 cation only occurs when the quantum interference remains. It [26] Vaidman L 2016 arXiv: 1511.006615v2 [quant-ph] [27] Vaidman L 2016 arXiv: 1605.02181v1 [quant-ph] is a challenge whether this symmetry could help to further re- [28] Marlow A R 1978 Mathematical Foundations of Quantum Theory. duce the transmission time. (New York: Academic Press) pp. 36
020304-7 Chinese Physics B
Volume 26 Number 2 February 2017
REVIEW
027501 The magnetic properties and magnetocaloric effects in binary 푅–푇 (푅 = Pr, Gd, Tb, Dy, Ho, Er, Tm; 푇 = Ga, Ni, Co, Cu) intermetallic compounds Xin-Qi Zheng and Bao-Gen Shen
GENERAL
020201 Ranking important nodes in complex networks by simulated annealing Yu Sun, Pei-Yang Yao, Lu-Jun Wan, Jian Shen and Yun Zhong 020301 Enhanced electron–positron pair production by frequency chirping in one- and two-color laser pulse fields Nuriman Abdukerim, Zi-Liang Li and Bai-Song Xie 020302 Optimal multi-photon entanglement concentration with the photonic Faraday rotation Lan Zhou, Dan-Dan Wang, Xing-Fu Wang, Shi-Pu Gu and Yu-Bo Sheng 020303 Round-robin differential quadrature phase-shift quantum key distribution Chun Zhou, Ying-Ying Zhang, Wan-Su Bao, Hong-Wei Li, Yang Wang and Mu-Sheng Jiang 020304 Probabilistic direct counterfactual quantum communication Sheng Zhang 020305 Creating nitrogen–vacancy ensembles in diamond for coupling with flux qubit Ya-Rui Zheng, Jian Xing, Yan-Chun Chang, Zhi-Guang Yan, Hui Deng, Yu-Lin Wu, Li Lu,¨ Xin-Yu Pan, Xiao- Bo Zhu and Dong-Ning Zheng 020501 Pattern dynamics of network-organized system with cross-diffusion Qianqian Zheng, Zhijie Wang and Jianwei Shen 020502 Magnetic phase diagrams of Fe–Mn–Al alloy on the Bethe lattice Erhan Albayrak 020503 Spurious symmetry-broken phase in a bidirectional two-lane ASEP with narrow entrances Bo Tian, Rui Jiang, Mao-Bin Hu and Bin Jia 020504 An image encryption scheme based on three-dimensional Brownian motion and chaotic system Xiu-Li Chai, Zhi-Hua Gan, Ke Yuan, Yang Lu and Yi-Ran Chen
020701 Room temperature NO2-sensing properties of hexagonal tungsten oxide nanorods Yaqiao Wu, Ming Hu and Yuming Tian
ATOMIC AND MOLECULAR PHYSICS
023101 Effect of P impurity on NiAlΣ5 grain boundary from first-principles study Xue-Lan Hu, Ruo-Xi Zhao, Yang Luo and Qing-Gong Song
(Continued on the Bookbinding Inside Back Cover) 023102 Dirac 푅-matrix calculations of photoionization cross sections of Ni XII and atomic structure data of Ni XIII R T Nazir, M A Bari, M Bilal, S Sardar, M H Nasim and M Salahuddin 023103 The inelastic electron tunneling spectroscopy of edge-modified graphene nanoribbon-based molecular devices Zong-Ling Ding, Zhao-Qi Sun, Jin Sun, Guang Li, Fan-Ming Meng, Ming-Zai Wu, Yong-Qing Ma, Long-Jiu Cheng and Xiao-Shuang Chen 3,1 o 2 1 023104 Uncertainty evaluation of the isotope shift factors for 2s2p P1–2s S0 transitions in B II Jianpeng Liu, Jiguang Li and Hongxin Zou 023105 MRCI+Q study of the low-lying electronic states of CdF including spin–orbit coupling Shu-Tao Zhao, Bing Yan, Rui Li, Shan Wu and Qiu-Ling Wang 023201 Parameter analysis for a nuclear magnetic resonance gyroscope based on 133Cs–129Xe/131Xe Da-Wei Zhang, Zheng-Yi Xu, Min Zhou and Xin-Ye Xu 103202 Equivalent electron correlations in nonsequential double ionization of noble atoms Shansi Dong, Qiujing Han and Jingtao Zhang 103203 Ionization in an intense field considering Coulomb correction Jian Li, Yi-Ning Huo, Zeng-Hua Tang and Feng-Cai Ma 103204 Theoretical study on non-sequential double ionization of carbon disulfide with different bond lengths in linearly polarized laser fields Kai-Li Song, Wei-Wei Yu, Shuai Ben, Tong-Tong Xu, Hong-Dan Zhang, Pei-Ying Guo and Jing Guo 103301 Controllable optical activity of non-spherical Ag and Co SERS substrate with different magnetic field Chun-Zhen Fan, Shuang-Mei Zhu and Hao-Yi Xin 103401 Optical potential approach for positron scattering by metastable 23푆 state of helium Xi-Gang Wu, Yong-Jun Cheng, Fang Liu and Ya-Jun Zhou
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS 024101 Electromagnetic coupling reduction in dual-band microstrip antenna array using ultra-compact single- negative electric metamaterials for MIMO application Xiao-Long Fu, Guo-Cheng Wu, Wei-Xiong Bai, Guang-Ming Wang and Jian-Gang Liang 024102 Metamaterial beam scanning leaky-wave antenna based on quarter mode substrate integrated waveg- uide structure Guo-Cheng Wu, Guang-Ming Wang, Xiao-Long Fu, Jian-Gang Liang and Wei-Xiong Bai 024201 Propagation factor of electromagnetic concentric rings Schell-model beams in non-Kolmogorov turbu- lence Zhen-Zhen Song, Zheng-Jun Liu, Ke-Ya Zhou, Qiong-Ge Sun and Shu-Tian Liu 024202 Theoretical investigation of hierarchical sub-wavelength photonic structures fabricated using high-order waveguide-mode interference lithograph Ru Wang, Xiangxian Wang, Hua Yang and Yunping Qi
(Continued on the Bookbinding Inside Back Cover) 024203 Sub-Rayleigh imaging via undersampling scanning based on sparsity constraints Chang-Bin Xue, Xu-Ri Yao, Long-Zhen Li, Xue-Feng Liu, Wen-Kai Yu, Xiao-Yong Guo, Guang-Jie Zhai and Qing Zhao 024204 Probe gain via four-wave mixing based on spontaneously generated coherence Hong Yang, Ting-gui Zhang and Yan Zhang
024205 Tunable Nd, La:SrF2 laser and passively Q-switched operation based on gold nanobipyramids saturable absorber Feng Zhang, Hua-Nian Zhang, Dan-Hua Liu, Jie Liu, Feng-Kai Ma, Da-Peng Jiang, Si-Yuan Pang, Liang-Bi Su and Jun Xu
024206 Efficient Nd:YVO4 laser in-band pumped by wavelength-locked 913.9-nm laser diode and Q-switch op- eration Bin Li, Peng Lei, Bing Sun and Yang-Bo Bai 024207 The influence of stimulated temperature-dependent emission cross section on intracavity optical para- metric oscillator S Samimi and A Keshavarz 024208 Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals Si-Qi Zhang, Jing-Bin Lu, Yu Liang, Ji Ma, Hong Li, Xue Li, Xiao-Jing Liu, Xiang-Yao Wu and Xiang-Dong Meng 024209 Tunable optical filter using second-order micro-ring resonator Lin Deng, Dezhao Li, Zilong Liu, Yinghao Meng, Xiaonan Guo and Yonghui Tian 024210 Degree of polarization based on the three-component pBRDF model for metallic materials Kai Wang, Jing-Ping Zhu and Hong Liu 024211 Simplified modeling of frequency behavior in photonic crystal vertical cavity surface emitting laser with tunnel injection quantum dot in active region Mehdi Riahinasab, Vahid Ahmadi and Elham Darabi 024212 Tunable wavelength filters using polymer long-period waveguide gratings based on metal-cladding di- rectly defined technique Ji-Hou Wang, Chang-Ming Chen, Yang Zheng, Xi-Bin Wang, Yun-Ji Yi, Xiao-Qiang Sun, Fei Wang and Da- Ming Zhang 024213 Hot-embossing fabrication of chalcogenide glasses rib waveguide for mid-infrared molecular sensing Ting-Yang Yan, Xiang Shen, Rong-Ping Wang, Guo-Xiang Wang, Shi-Xun Dai, Tie-Feng Xu and Qiu-Hua Nie 024301 Study on shock wave-induced cavitation bubbles dissolution process Huan Xu, Peng-Fei Fan, Yong Ma, Xia-Sheng Guo, Ping Yang, Juan Tu and Dong Zhang 024302 Ultra-broadband asymmetric acoustic transmission with single transmitted beam Ding Jia, Hong-xiang Sun, Shou-qi Yuan and Yong Ge 024701 Numerical investigation of the interaction of the turbulent dual-jet and acoustic propagation Yi-Ming Li, Bao-Kuan Li, Feng-Sheng Qi and Xi-Chun Wang
(Continued on the Bookbinding Inside Back Cover) PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES
025101 Effect of electrical discharge in water on concentration of nitrate solution F Sohbatzadeh, H Bagheri and R Safari 025201 Pulse chirping effect on controlling the transverse cavity oscillations in nonlinear bubble regime H Vosoughian, Z Riazi, H Afarideh and G Sarri 025202 Production of a large area diffuse arc plasma with multiple cathode Cheng Wang, Hai-Chao Cui, Wan-Wan Li, Meng-Ran Liao, Wei-Luo Xia and Wei-Dong Xia 025203 Lower order three-dimensional Burgers equation having non-Maxwellian ions in dusty plasmas Apul N Dev 025204 Detailed calibration of the PI-LCX:1300 high performance single photon counting hard x-ray CCD cam- era Wei Hong, Xian-Lun Wen, Lai Wei, Bin Zhu, Yu-Chi Wu, Ke-Gong Dong, Chun-Ye Jiao, Bo Wu, Ying-Ling He, Fa-Qiang Zhang, Wei-Min Zhou and Yu-Qiu Gu 025205 High sampling-rate measurement of turbulence velocity fluctuations in Mach 1.8 Laval jet using inter- ferometric Rayleigh scattering Li Chen, Fu-Rong Yang, Tie Su, Wei-Yi Bao, Bo Yan, Shuang Chen and Ren-Bing Li 025206 New progress on beam availability and reliability of PKU high intensity CW proton ECR ion source Shi-Xiang Peng, Ai-Lin Zhang, Hai-Tao Ren, Yuan Xu, Tao Zhang, Jing-Feng Zhang, Jia-Mei Wen, Zhi-Yu Guo and Jia-Er Chen 025207 Microwave absorption properties of Ag naowires/carbon black composites Hai-Long Huang, Hui Xia, Zhi-Bo Guo, Yu Chen and Hong-Jian Li
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES
3+ 2+ 026101 Local microstructural analysis for Y2O3/Eu /Mg nanorods by Raman and photoluminescence spec- tra under high pressure Jin-Hua Wang, Ze-Peng Li, Bo Liu and Bing-Bing Liu 026102 Irradiation-induced void evolution in iron: A phase-field approach with atomistic derived parameters Yuan-Yuan Wang, Jian-Hua Ding, Wen-Bo Liu, Shao-Song Huang, Xiao-Qin Ke, Yun-Zhi Wang, Chi Zhang and Ji-Jun Zhao 026501 Anomalous low-temperature heat capacity in antiperovskite compounds Xin-Ge Guo, Jian-Chao Lin, Peng Tong, Shuai Lin, Cheng Yang, Wen-Jian Lu, Wen-Hai Song and Yu-Ping Sun 026502 Orbital electronic heat capacity of hydrogenated monolayer and bilayer graphene Mohsen Yarmohammadi
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTI- CAL PROPERTIES
027101 Novel high-퐾 with low specific on-resistance high voltage lateral double-diffused MOSFET Li-Juan Wu, Zhong-Jie Zhang, Yue Song, Hang Yang, Li-Min Hu and Na Yuan
(Continued on the Bookbinding Inside Back Cover) 027102 Structural, electronic, optical, and magnetic properties of Co-doped Cu2O I Djabri, T Rezkallah and F Chemam
027103 Structural, electronic, and magnetic properties of vanadium atom-adsorbed MoSe2 monolayer Ping Liu, Zhen-Zhen Qin, Yun-Liang Yue and Xu Zuo 027104 Temperature and hydrogen-like impurity effects on the excited state of the strong coupling bound po- laron in a CsI quantum pseudodot Jing-Lin Xiao 027105 On the reverse leakage current of Schottky contacts on free-standing GaN at high reverse biases Yong Lei, Jing Su, Hong-Yan Wu, Cui-Hong Yang and Wei-Feng Rao
027301 Photon-assisted and spin-dependent shot noise in magnetic-field tunable ZnSe/Zn1−푥Mn푥Se structures Chun-Lei Li, Yong Guo, Xiao-Ming Wang and Yuan Lv 027302 Effect of metal catalyst on the mechanism of hydrogen spillover in three-dimensional covalent-organic frameworks Xiu-Ying Liu, Jing-Xin Yu, Xiao-Dong Li, Gui-Cheng Liu, Xiao-Feng Li and Joong-Kee Lee 027303 Impact of coupling geometry on thermoelectric properties of oligophenyl-base transistor S Ramezani Akbarabadi, H Rahimpour Soleimani, M Bagheri Tagani and Z Golsanamlou 027304 Enhancement of subgap conductance in a graphene superconductor junction by valley polarization Chuan-Xin Li, Sa-Ke Wang and Jun Wang 027305 Ballistic transport and quantum interference in InSb nanowire devices Sen Li, Guang-Yao Huang, Jing-Kun Guo, Ning Kang, Philippe Caroff and Hong-Qi Xu
027401 Thermal stability and electrical transport properties of Ge/Sn-codoped single crystalline 훽-Zn4Sb3 pre- pared by the Sn-flux method Hong-xia Liu, Shu-ping Deng, De-cong Li, Lan-xian Shen and Shu-kang Deng 027502 Electronic structures and magnetic properties of Zn- and Cd-doped AlN nanosheets: A first-principles study Rui-Lin Han, Shi-Min Jiang and Yu Yan
027503 Study of magnetic and optical properties of Zn1−푥푇 푀푥Te (푇 푀 = Mn, Fe, Co, Ni) diluted magnetic semiconductors: First principle approach Q Mahmood, M Hassan and M A Faridi
027701 Crystallization behaviors of ultrathin Al-doped HfO2 amorphous films grown by atomic layer deposition Xue-Li Ma, Hong Yang, Jin-Juan Xiang, Xiao-Lei Wang, Wen-Wu Wang, Jian-Qi Zhang, Hua-Xiang Yin, Hui-Long Zhu and Chao Zhao 027801 Semipolar (112¯2) and polar (0001) InGaN grown on sapphire substrate by using pulsed metal organic chemical vapor deposition Sheng-Rui Xu, Ying Zhao, Ren-Yuan Jiang, Teng Jiang, Ze-Yang Ren, Jin-Cheng Zhang and Yue Hao
INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY 028101 Photoconductive multi-layer graphene photodetectors fabricated on etched silicon-on-insulator sub- strates Yu-Bing Wang, Wei-Hong Yin, Qin Han, Xiao-Hong Yang, Han Ye, Qian-Qian Lv and Dong-Dong Yin
(Continued on the Bookbinding Inside Back Cover) 028102 Electrical and dielectric characterization of Au/ZnO/n–Si device depending frequency and voltage I Orak, A Kocyigit and S¸Alındal 028103 Geometrically induced π-band splitting in graphene superlattices Yanpei Wei, Tiantian Jia and Gang Chen 028501 Investigation on latch-up susceptibility induced by high-power microwave in complementary metal– oxide–semiconductor inverter Yu-Hang Zhang, Chang-Chun Chai, Xin-Hai Yu, Yin-Tang Yang, Yang Liu, Qing-Yang Fan and Chun-Lei Shi 028502 Improvement of the carrier distribution with GaN/InGaN/AlGaN/InGaN/GaN composition-graded bar- rier for InGaN-based blue light-emitting diode Min Guo, Zhi-You Guo, Jing Huang, Yang Liu and Shun-Yu Yao 028503 Spin transfer torque in the semiconductor/ferromagnetic structure in the presence of Rashba effect Javad Vahedi and Sahar Ghasab Satoory 028701 Shifting curves based on the detector integration effect for x-ray phase contrast imaging Jun Yang, Jin-Chuan Guo, Yao-Hu Lei, Ming-Hao Yi and Li Chen 028801 Highly conductive and transparent carbon nanotube-based electrodes for ultrathin and stretchable or- ganic solar cells Qingxia Fan, Qiang Zhang, Wenbin Zhou, Feng Yang, Nan Zhang, Shiqi Xiao, Xiaogang Gu, Zhuojian Xiao, Huiliang Chen, Yanchun Wang, Huaping Liu and Weiya Zhou 028802 Performance improvement of continuous carbon nanotube fibers by acid treatment Qiang Zhang, Kewei Li, Qingxia Fan, Xiaogang Xia, Nan Zhang, Zhuojian Xiao, Wenbin Zhou, Feng Yang, Yanchun Wang, Huaping Liu and Weiya Zhou 028803 Simulation design of P–I–N-type all-perovskite solar cells with high efficiency Hui-Jing Du, Wei-Chao Wang and Yi-Fan Gu 028901 Scaling of weighted spectral distribution in weighted small-world networks Bo Jiao and Xiao-Qun Wu
90 GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS
029201 Effect of air breakdown on microwave pulse energy transmission Pengcheng Zhao, Lixin Guo and Panpan Shu