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Review

Quantum Information December 2012 Vol. 57 No. 36: 4694–4700 doi: 10.1007/s11434-012-5600-6

Recent development in communication

SONG SiYu1,2 & WANG Chuan3*

1State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China; 2Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing 100084, China; 3School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received September 26, 2012; accepted November 1, 2012

In this review article, we will review the recent process of quantum communications. In the past decades, there are many developments in quantum communication, for instance, , quantum , quantum secure direct communication, de- terministic secure quantum communication, quantum secret sharing and so on. And we focus our attention on the recent developments in quantum communication protocols.

, quantum key distribution, quantum teleportation, quantum secure direct communication (QSDC), quantum secret sharing

Citation: Song S Y, Wang C. Recent development in quantum communication. Chin Sci Bull, 2012, 57: 4694–4700, doi: 10.1007/s11434-012-5600-6

The principles in quantum provide novel ways for users which solves the problem for secure distributing of keys quantum information transmission and processing, such as in the classical one-time-pad protocol [7]. However, quan- quantum computation and quantum communication. In the tum communication offers more power than QKD. Quantum past decades, quantum information processing has emerged secret sharing (QSS) distributes secret keys to two or more as a promising technology with strategic importance. Be- shared users [8], which can be viewed as the quantum key cause of the peculiar properties of quantum systems, quantum distribution between multi-users. Quantum teleportation is a computers possess enormous power that is superior to classi- basic ingredient in quantum information architectures [9,10]. cal computer. Using quantum computer, factorization of an The principle of quantum teleportation is to transfer an un- integer can be accomplished in polynomial time with the Shor known state to the legal user at a distant distance. [1]. And we can find a marked item with high prob- secure direct communication (QSDC) offers direct communi- ability from an unsorted database with a square-root speedup cation of secret messages between distant users, which saves with the Grover algorithm [2]. In the past decades, the field completely the need for another classical communication as of quantum information processing and quantum computa- in the QKD case. In recent years, there have been consider- tion have attracted much attention [3–6]. With these quantum able developments from researchers in the design of quantum algorithms and a quantum computer, many classical cryptog- communication protocols. In this article, we will focus on raphy protocols can be attacked. Thus it is vital to find new these developments in quantum communications. cryptographic systems for defending against these attacks. In the following years, there are many branches of quan- tum communications that are generated which provides us 1 A brief history and key techniques of quan- secure ways of communications, such as quantum key distri- tum communication bution (QKD), quantum teleportation, quantum secure direct communication, quantum secret sharing and so on. QKD pro- QKD provides an unconditional secure way of information vides a secure way to distribute secret keys between distant exchange between two distant users. The first QKD proto- col is proposed by Bennett and Brassard [7], called the BB84 *Corresponding author (email: [email protected]) protocol. In 1992, Bennett proposed a simplified version of

c The Author(s) 2012. This article is published with open access at Springerlink.com csb.scichina.com www.springer.com/scp Song S Y, et al. Chin Sci Bull December (2012) Vol. 57 No. 36 4695 the BB84, called the B92 protocol [11]. Since then there have are discarded. Therefore, ILBED is eliminated by dropping been many important theoretical improvements and experi- the transmitted data in QKD. In QSS, similar to QKD, the mental demonstrations of BB84 and other QKD protocols. transmitted data is also dropped if the eavesdropper has been Quantum teleportation is pertinent to quantum communi- discovered. Avoiding ILBED is also important in QSDC. cation only, and there is no classical counterpart [12]. Quan- This is achieved in QSDC by the essential technique of block tum teleportation transmits an unknown state to a remote transmission. Quantum information carriers are transported place without actually transporting the actual particle. It has in batches. The information carriers consist of a sequence become a basic ingredient in quantum information architec- of single , or particles formed by taking one parti- tures [9, 10]. Teleportation includes two legal users and two cle from each Einstein-Podolsky-Rosen (EPR) pairs. The se- communication channels, which are the sender and the re- curity of these information carriers is checked by sampling ceiver, and the and the classical channel. measurement. In QKD, secret message is then transmitted by The first quantum teleportation protocol is proposed by Ben- classical transmission of the ciphertext encoded with the keys nett, Brassard, Cr´epeau, Jozsa, Peres, and Wootters [12]. Up generated by QKD. If eavesdropper is found in the quantum to now, there have been many researches on quantum tele- channel, then we withhold the key and ILBED is avoided. portation, some of the recent developments can be found in [13–16]. Also quantum teleportation has been experimen- 1.2 Methods of quantum communication tally implemented with photonic [17–23]. A quantum secret sharing (QSS) protocol is to distribute In this section, we will briefly review several key methods for secret keys among two or more legal users. The shared se- constructing quantum communication protocols. cret can only be recovered by the legal users when they co- (i) Multi-step transmission. If we have an entangled operate together. In 1999, Hillery et al. proposed the first quantum system, we can transmit the system from one user QSS protocol [8] for sharing a secret with three-particle and to another in multiple steps. Because it is entangled, mea- four-particle entangled Greenberger-Horne-Zeilinger (GHZ) surement on part of an entangled quantum system does not states. Up to now, QSS has been extensively studied in both provide the whole information of the quantum system, this theory and experiments, for instance, in [24–27] for theory, provides us with a novel way for constructing quantum com- and in [28–30] for experiments. In parallel, the sharing of a munication protocols. Multi-step transmission was first pro- , which is called quantum state sharing (QSTS), posed in [37]. It has been extensively used in various protocol has also been developed [29]. QSTS protocols of an arbitrary designs of quantum communications. single-particle state [31, 32], two-particle state [33, 34] and (ii) Block transmission. Block transmission is essential multi-particle state [35, 36] have been studied. for QSDC. In block transmission, the information carriers are Quantum secure direct communication (QSDC) as a new transmitted in a block. For instance in [37], the two ordered way to implement information transmission has attracted particle sequences are transmitted in a block of N particles. much attention. In 2000, the first QSDC scheme was pro- Security is guaranteed by checking on the block of N par- posed [37]. In QSDC, secret information is transmitted ticles which are chosen randomly and measured to give an directly from the sender to the receiver which is different estimated error rate. from the QKD schemes with an advanced encryption process. (iii) Order Rearrangement. Similar to conjugate-basis QSDC has a good application prospect because it is complete method where an eavesdropper does not know which of the quantum but the communication process should be more se- conjugate-basis the legal users are used, one can reorder the cure than the security for QKD. QSDC protocols have been orders of the particles within a block. The order number of proposed with different implementation ways [38–48]. a particle is completely unknown to the eavesdropper. The Here we will discuss some key problems of quantum com- eavesdropper can only guess the order number of the particle. munication. The order rearrangement method was first proposed in [50], called the CORE protocol. The method has been used exten- 1.1 Information leakage before eavesdropper detection sively.

The security of classical cryptography relies on mathematical 1.3 Information carriers and measurement complexities. However, the security relies on the principles of . Information In the early stage, quantum communication protocols with leakage before eavesdropper detection (ILBED) is essential discrete variables are based on single photons [7, 11] and en- for the security of quantum communication, which has been tangled states [51] as the information carriers. Now extensively used in practice, but is recently pointed explicitly multi-photons entangled states are proposed for quantum in [49]. In quantum communication, eavesdroppers are de- communication realization, such as the GHZ state, cluster tected by sampling measurement, usually in alternative con- states [44], highly entangled six- genuine state [16], χ- jugate basis. For example in QKD, if some eavesdroppers are state [13], and so on. Recently, entangled photons with multi- detected, the transmission is halted and the transmitted data photon have been implemented in experiment, for example 4696 Song S Y, et al. Chin Sci Bull December (2012) Vol. 57 No. 36 the two photons entanglement [52], the four photons entan- 3 Quantum teleportation glement [53], the six photons entanglement [54]. The real- ization of entangled photon sources is becoming a crucial el- The original idea of quantum teleportation was first proposed ement for quantum communication. by Bennett et al. [12] and was experimentally realized by To implement quantum communication, the measurement Bouwmeester et al. [65]. The task of quantum teleportation of single photons or entangled photons is another important is to transmit and reconstruct over arbitrary distances of the ingredient. Many related works have been done for investi- state of a quantum system. Many related works have been gating the measurements of single photon and entangled pho- proposed in the past decades. Recently, the protocol to tele- tons. The avalanche photodiodes are used as the detector for port an unknown two-qubit state is given in [66]. Different single photons detection. The single photon detectors should from the original protocol [12], teleporting one-qubit state fulfill the following requirements: firstly, the detector should with two qubits quantum channel, four qubits state is used be response to a wide range wavelength light with high de- as the quantum channel in [66]. An arbitrary unknown two tection efficiency; secondly, the noise of the detector should qubits state can be presented as be lower; thirdly, the time between detection of a photon and generation of an electrical signal should be constant; fourthly, |ψ = a|00 + b|01 + c|10 + d|11, (1) the dead time should be short enough to allow the detectors where a, b, c,andd are complex numbers and {|ij} is an or- work at high frequency situation. For these four points, the thonormal basis set. The channel state |φ can be written by response ability and working requirements of the single pho- c Schmidt decomposition as ton detectors are investigated [55] to improve the detection efficiency. 1 1 |ψ = |ψ , ⊗|ϕ , c 2 i j A i j B i, j=0 2 Quantum key distribution = ⊗ T | ⊗| , (1A VU ) EPR A1B1 EPR A2B2 (2)  √ QKD, as an important branch of quantum information, pro- | = | , / where the state EPR i i i 2. Alice performs a joint vides a secure way for creating secret keys between commu- measurement on the four qubits A1, A2, U1,andU2.After nication parties, Alice and Bob. In this section, we will re- Alice got the measurement results, Bob’s two qubits become view the recent QKD protocols. Since Bennett and Brassard to be a state similar with the state that Alice transmits. Then presented the BB84 QKD protocol [7], quantum key distribu- when receiving the classical information of Alice’s result, he tion has progressed quickly [11, 51, 56–61]. makes a special unitary operation on his particles, to get the “Plug and play” system is proposed in [62], which uses the transmitting unknown state information. Faraday mirrors to make a compensation for the polarization While in the protocol of quantum teleportation of [66] or of the photons automatically. A plug and play QKD in 50 even in latter improved paper [67], the four-qubit entangled km optic fibers is implemented by Zeng et al. [63]. In the channel can be reduced to a tensor product of two Bell states. experiment, B92 protocol is implemented. In the experiment, To avoid this problem and to ensure the success of faithfully Alice prepares and sends the photons with one of two non- teleporting any arbitrary two-qubit state, Ye et al. proposed a orthogonal phases randomly to Bob. Bob makes measure- protocol to implement teleporting process using a four-qubit ment randomly selected in two non-orthogonal bases. Secret entangled channel. At first, Alice and Bob share a priori two keys are created between Alice and Bob when Bob’s base pairs of particles, A3, A4,andB1, B2 in the state matched Alice’s state, while those mismatched results are 3 discarded. In order to reduce the noises in fiber, a variable 1 |χ00 = |J ⊗|J . (3) attenuator which controls the photon number is connected A3A4 B1B2 A3A4 B1B2 2 = with the on Alice’s site. The experimental results show J 0 that quantum key distribution system can be hopefully used in The |Js constitute a set of orthonormal bases practical secret communication, and to work at a high speed | = θ | + θ | , with a lower error rate. 0 cos 1 00 sin 1 11 | = φ | + φ | , Recently, a new QKD protocol is proposed by Gao et al. 1 cos 1 01 sin 1 10 (4) [64], and the quantum public-key cryptography (QPKC) is in- |2 = − sin φ1|01 + cos φ1|10, vestigated. In the proposed protocol, is divided into |3 = − sin θ1|00 + cos θ1|11, two parts, one is used for the public key, and the other one is used to generate the private key. Symmetric keys are reason- then using the new channels for teleportation, it can be per- able to be used. The security of the scheme is discussed, and fect completed. it reveals a good character. The unconditional security must Perfect teleportation of an arbitrary three-qubit state are be assured for QKD, and then QPKC can replace it to com- discussed in many works [16, 68, 69]. In [16], quantum tele- plete the task. This scheme is an important work for QPKC. portation using highly entangled six-qubit state as the quan- Song S Y, et al. Chin Sci Bull December (2012) Vol. 57 No. 36 4697 tum channel was investigated. In the beginning, the two in- The subscripts A and B represent the two photons in an EPR volved parties share the state in the form pair, and |0 and |1 are the two eigenvectors of the measur- ing basis (MB) Z (for instance, the polarizations of a photon |G a1a2a3b1b2b3 along the z-direction). 1 = √ [|000000 + |111111 + |000011 In the communication process, Alice first prepares an or- + √1 32 dered N EPR pairs in the same state |φ AB = (|0A|0B + + | + | + | + | 2 111100 000101 111010 000110 |1A|1B), then she takes one particle from each EPR pair to + |111001 + |001001 + |110110 + |001111 form an ordered particle sequence. This sequence is made up of all the photons A in the ordered N EPR pairs. Af- + |110000 + |010001 + |101110 + |010010 ter that, Alice sends the checking sequence to Bob and they + | + | + | + | 101101 011000 100111 011101 check the security of this transmission. If they confirm that + |100010−|001010−|110101−|001100 the transmission of the checking sequence is secure, Alice −|110011−|010100−|101011−|010111 encodes her secret message on the message-coding sequence = , , , −|101000−|011011−|100100−|011110 with four unitary operations Ui (i 0 1 2 3) and then sends the sequence to Bob. The coding operations can be described −| , 100001 ] (5) as follows: where particles a , a ,anda belong to Alice and particles 1 2 3 U = I = |00| + |11| , (11) b , b ,andb belong to Bob. Alice wants to transmit the 0 1 2 3 = σ = |  |−|  | , information state U1 z 0 0 1 1 (12) = σ = |  | + |  | , 1 1 1 U2 x 1 0 0 1 (13) | = ξ | . = σ = |  |−|  | . u x1 x2 x3 ijk ijk x1 x2 x3 (6) U3 i y 0 1 1 0 (14) i=0 j=0 k=0 Alice and Bob agree that the four Bell states |φ+, |φ−, |ψ+ Then Alice chooses a proper measurement base to measure − and |ψ are encoded as 00, 01, 10 and 11, respectively. Bob her six particles a , a , a , x , x ,andx . Bob only needs 1 2 3 1 2 3 can read out the secret message directly with Bell-state mea- to perform an appropriate unitary operation on his three par- surements. The security checking process are also discussed ticles to recover the initial state. The teleportation of three in the proposed protocol. Later, there are many researches in qubits state can be completed through this way. the world studying the subject of QSDC [39–42, 46–48]. Similarly, quantum teleportation of arbitrary n-qubit state Recently, fault tolerant QSDC protocol against collective with 2n-qubit pure state [70] and probabilistic teleportation noises is investigated [43]. In the proposed paper, two QSDC [71] are investigated. schemes are proposed, one is proposed for defending against the collective-dephasing noises and the other one is for de- 4 Quantum secure direct communication fending against the collective-rotation noises. The DF states are used in these two protocols, which can resist collective Quantum secure direct communication (QSDC) is to transmit dephasing noises and collective-rotation noises, they contain the secret information directly. For securely and effectively two logical qubits. Then the sender-Alice can prepare her in- complete the QSDC, three requirements are needed: firstly, formation carriers on these DF states. The transmitting pro- the secret informaiton can be transmit and readout directly, cess is similar with the implementation process in [38], for the additional classical information is not needed. Secondly, defending the Eves, decoy state photons are inserted into the Eve cannot gain any useful information about the secret mes- information photons sequence. At last, the receiver simply sage. Thirdly, the secret information should not be revealed performs two Bell state measurements to obtain the secret before the encoding process. message. In these two protocols, twice times qubit efficiency Two-step QSDC scheme is the first secure communica- are obtained, they are robust against general attacks. More- tion model for quantum direct communication proposed in over, they can defend against Trojan horse attacks. [37, 38]. The proposed QSDC exploits an EPR pair which is In [72], robust QSDC with a quantum one-time pad over in one of the four Bell states, a collective-noise channel is proposed. The original one time pad QSDC scheme is proposed by Long et al. [39], it real- |ψ− 1 = √ (|0A|1B −|1A|0B), (7) izes the information direct communication using single pho- 2 tons. In [72], two robust QSDC schemes are presented, one is + 1 |ψ = √ (|0A|1B + |1A|0B), (8) implemented with a quantum one-time pad over a collective- 2 dephasing noise channel, the other one is to build a quan- − 1 tum one-time pad over a collective-rotation. The informa- |φ = √ (|0A|0B −|1A|1B), (9) 2 tion is encoded using two unitary operations on each logical + 1 qubit, each logical qubit is implemented with two photons- |φ = √ (|0A|0B + |1A|1B). (10) 2 two physical , entangled photon pairs can be used for one 4698 Song S Y, et al. Chin Sci Bull December (2012) Vol. 57 No. 36  logical qubit. The information is transmitted from Alice to where the coefficient N = 1/ 1 + |n|2. Bob, the transmitting process is similar with [39]. After Bob Now Alice wants to build the communication channel, she received the photons, he makes single-photon measurements keeps the particles a1, a2 at her hand and distributes the gen- for each photons and construct the information from each log- eralized GHZ state |GHZ+ n1 particles to Bob and Charlie re- ical qubit-two single photons. spectively. Not lose generality, the initial state prepared by Recently, Cao et al. proposed a QSDC with cluster states Alice is chosen as |τxy = α|00 + β|01 + γ|10 + δ|11.The [44], which uses two steps to implement the transmitting of state of composite system can be described as information. 2 |Λs = N (α|00000000 + αn|00111000 5 Quantum secret sharing and quantum state + β|01000000 + βn|01111000 sharing + γ|10000000 + γn|10111000 + δ|11000000 + δn|11111000 Quantum secret sharing (QSS) is an important branch of + αn|00000111 + αn2|00111111 quantum communication, which has attracted much attention. + β | + β 2| The purpose of QSS is to distribute secret message between n 01000111 n 01111111 2 the boss and two or more agents. The boss expects to generate + γn|10000111 + γn |10111111 secret keys with the two agents separately and the two agents + δn|11000111 + δn2|11111111). (17) cannot reveal the boss’s information until they combine their results together. QSS is a special utilization of quantum me- Firstly Alice performs joint generalized Bell state mea- chanics in classical secret sharing. QSS was first proposed surements on her four particles x, a1 and y, a2,andthen by Hillery et al. [8] (here we called HBB QSS protocol). The she announces her results publicly. The particles marked , , , ⊗ idea of QSS have attracted a vast amount of effort ever since with x y a1 a2 are in the product state: Rxa1 Rya2 ,here ∈{|φ± , |ψ± } the work [8] in the following years. There have been many Rx(y)a1(a2) m m . Assuming that her measurement |φ+ |φ+ theoretical development in this subject [73–76]. results are m x,a1 m y,a2 , the composite system of particles Another generalization of secret sharing is the quantum b1b2c1c2 becomes to state sharing (QSTS) which replace a quantum state by the N2 nβ secret information. Cleve et al. [24] introduced a way for a |Λ = α| + | sub 2 ( 0000 0101 (k, n) threshold QSTS scheme to split a secret quantum state. M m γ 2δ Later, Li et al. [31] proposed a scheme for sharing an un- n n + |1010 + |1111)b b c c . (18) known single qubit with EPR pairs and multi-particle joint m m2 1 2 1 2 measurement. In 2010, Wang et al. generalized a QSTS pro- Secondly, Bob applies a joint X basis measurement Xˆ ⊗ tocol of an arbitrary two-particle state using non-maximally b1 Xˆ on his two particles b and b whichistheVonNeumann GHZ states and generalized Bell state measurement in [77]. b2 1 2 measurement on the basis: |±X = √1 (|0±|1). And it is the In QSTS protocol, Alice wants to transmit an arbitrary 2 same for Charlie’s two particles. Then Alice’s results are cor- two-particle state to Bob or Charlie. Alice holds the initial related with Bob’s outcomes and Charlie’s states. For exam- known state of the particles marked with x and y which is de- ple, in the case of Alice’s generalized Bell state measurement scribed as |τ = α|00 + β|01 + γ|10 + δ|11 .The xy xy xy xy xy results |φ+ |φ+ , the correspondence between Bob’s results composite quantum system which consists of the eight parti- m1 m2 and Charlie’s state is listed in Table 1. cles are Lastly, Charlie makes some unitary operations on his two |Λ = |τ | | , particles: s xy GHZm a1,b1,c1 GHZm a2,b2,c2 (15)

U0 = |00| + |11|, U1 = |00|−|11|, where a1, b1, c1 and a2, b2, c2 are the GHZ particles shared by = |  | + |  |, = |  |−|  |. (19) Alice, Bob and Charlie respectively. The generalized GHZ U2 0 1 1 0 U3 0 1 1 0 state in the form: After Alice and Bob announce the results publicly, Charlie | + = | + | , GHZn1 N( 000 n 111 ) | − = ∗| −| , Table 1 The correspondence between Bob’s results and Charlie’s state GHZn1 N(n 000 111 ) with the results of Alice’s result is |φ+ |φ+ | + = | + | , m1 m2 GHZn2 N( 001 n 110 ) − ∗ |GHZ = N(n |001 + |110), Bob’s results (b1,b2) Charlie’s results n2 (16) | + = | + | , | + X| + X α|00 + γn/m|10 + βn/m|01 + δn2/m2|11 GHZn3 N( 010 n 101 ) | − = ∗| −| , | + X| − X α|00 + γn/m|10−βn/m|01−δn2/m2|11 GHZn3 N(n 010 101 ) | + = | + | , |−X| + X α|00−γn/m|10 + βn/m|01−δn2/m2|11 GHZn4 N( 100 n 011 ) | − = ∗| −| , |−X| − X α|00−γn/m|10−βn/m|01 + δn2/m2|11 GHZn4 N(n 100 011 ) Song S Y, et al. Chin Sci Bull December (2012) Vol. 57 No. 36 4699

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