Cyclic joint remote state preparation in noisy environment

We propose a scheme of cyclic joint remote state preparation for three sides, which takes advantage of three GHZ states to compose product state as quantum channel. Suppose there are six legitimate participants, says Alice, Bob, Charlie, David, Emma and Fred in the scheme. It can be shown that Alice and David can remotely prepare a single-qubit state on Bob’s side; meanwhile, Bob and Emma can remotely prepare a desired quantum state on Charlie’s side, and Charlie and Fred can also remotely prepare a single-qubit state on Alice’s side at the same time. Further, it can be achieved in the opposite direction of the cycle by changing the quantum channel. Based on it, we generalize this protocol to \(N (N\ge 3)\) sides utilizing three multi-qubit GHZ-type states as quantum channel. Therefore, the scheme can achieve cyclic joint remote state preparation, which remotely prepares N states in quantum network with N-party, simultaneously. In addition, we consider that the effect of amplitude-damping noise of the initial states is prepared in four different laboratory. Clearly, we use fidelity to describe how much information has been lost in the cyclic process. Our investigation about the effect of noise shows that the preparing of the initial state in different laboratories will affect the loss of information.     

Bidirectional controlled teleportation by using nine-qubit entangled state in noisy environments

A theoretical scheme is proposed to implement bidirectional quantum controlled teleportation (BQCT) by using a nine-qubit entangled state as a quantum channel, where Alice may transmit an arbitrary two-qubit state called qubits \(A_1\) and \(A_2\) to Bob; and at the same time, Bob may also transmit an arbitrary two-qubit state called qubits \(B_1\) and \(B_2\) to Alice via the control of the supervisor Charlie. Based on our channel, we explicitly show how the bidirectional quantum controlled teleportation protocol works. And we show this bidirectional quantum controlled teleportation scheme may be determinate and secure. Taking the amplitude-damping noise and the phase-damping noise as typical noisy channels, we analytically derive the fidelities of the BQCT process and show that the fidelities in these two cases only depend on the amplitude parameter of the initial state and the decoherence noisy rate.     

A highly efficient scheme for joint remote preparation of multi-qubit W state with minimum quantum resource

We present a highly efficient scheme for perfect joint remote preparation of an arbitrary \( 2^{n} \)-qubit W state with minimum quantum resource. Both the senders Alice and Bob intend to jointly prepare one \( 2^{n} \)-qubit W state for the remote receiver Charlie. In the beginning, they help the remote receiver Charlie to construct one n-qubit intermediate state which is closely related to the target \( 2^{n} \)-qubit W state. Afterward, Charlie introduces auxiliary qubits and applies appropriate operations to obtain the target \( 2^{n} \)-qubit W state. Compared with previous schemes, our scheme requires minimum quantum resource and least amount of classical communication. Moreover, our scheme has a significant potential for being adapted to remote state preparation of other special states.     

Generalized teleportation by quantum walks

We develop a generalized teleportation scheme based on quantum walks with two coins. For an unknown qubit state, we use two-step quantum walks on the line and quantum walks on the cycle with four vertices for teleportation. For any d-dimensional states, quantum walks on complete graphs and quantum walks on d-regular graphs can be used for implementing teleportation. Compared with existing d-dimensional states teleportation, prior entangled state is not required and the necessary maximal entanglement resource is generated by the first step of quantum walk. Moreover, two projective measurements with d elements are needed by quantum walks on the complete graph, rather than one joint measurement with \(d^2\) basis states. Quantum walks have many applications in quantum computation and quantum simulations. This is the first scheme of realizing communicating protocol with quantum walks, thus opening wider applications.     

Preparing large-scale maximally entangled <Emphasis Type="Italic">W</Emphasis> states in optical system

We propose an optical scheme to prepare large-scale maximally entangled W states by fusing arbitrary-size polarization entangled W states via polarization-dependent beam splitter. Because most of the currently existing fusion schemes are suffering from the qubit loss problem, that is the number of the output entangled qubits is smaller than the sum of numbers of the input entangled qubits, which will inevitably decrease the fusion efficiency and increase the number of fusion steps as well as the requirement of quantum memories, in our scheme, we design a effect fusion mechanism to generate \(W_{m+n}\) state from a n-qubit W state and a m-qubit W state without any qubit loss. As the nature of this fusion mechanism clearly increases the final size of the obtained W state, it is more efficient and feasible. In addition, our scheme can also generate \(W_{m+n+t-1}\) state by fusing a \(W_m\), a \(W_n\) and a \(W_t\) states. This is a great progress compared with the current scheme which has to lose at least two particles in the fusion of three W states. Moreover, it also can be generalized to the case of fusing k different W states, and all the fusion schemes proposed here can start from Bell state as well.     

Bidirectional controlled quantum teleportation and secure direct communication using five-qubit entangled state

A scheme is presented to implement bidirectional controlled quantum teleportation (QT) by using a five-qubit entangled state as a quantum channel, where Alice may transmit an arbitrary single qubit state called qubit A to Bob and at the same time, Bob may also transmit an arbitrary single qubit state called qubit B to Alice via the control of the supervisor Charlie. Based on our channel, we explicitly show how the bidirectional controlled QT protocol works. By using this bidirectional controlled teleportation, espcially, a bidirectional controlled quantum secure direct communication (QSDC) protocol, i.e., the so-called controlled quantum dialogue, is further investigated. Under the situation of insuring the security of the quantum channel, Alice (Bob) encodes a secret message directly on a sequence of qubit states and transmits them to Bob (Alice) supervised by Charlie. Especially, the qubits carrying the secret message do not need to be transmitted in quantum channel. At last, we show this QSDC scheme may be determinate and secure.     

Controlled teleportation against uncooperation of part of supervisors

We study the teleportation of an unknown quantum state from a sender (Alice) to a receiver (Bob) via the control of many supervisors (Charlie 1, Charlie 2, . . .) in a network. It has been shown that such a task can be achieved by distributing a GHZ-type entangled state among the participants in advance. In the protocols with GHZ-type entanglement channel, the achievement of teleportation between Alice and Bob is conditioned on the cooperation of all the supervisors. In other words, if anyone of the supervisors does not cooperate, the teleportation will fails. In this paper, we introduce another kind of controlled teleportaton protocol with other types of entangled states acting as the quantum channel, in which the teleportation between Alice and Bob can be realized with high degree of endurance against uncooperation of part of supervisors.      

Deterministic controlled bidirectional remote state preparation via a six-qubit entangled state

In this paper, we presented a controlled bidirectional remote state preparation scheme which used the six-qubit entangled state as quantum channel. In our scheme, Alice and Bob can prepare simultaneously an arbitrary single-qubit state in each other’s place with the control of the supervisor Charlie. The success probability for our scheme reaches unit. Furthermore, we analyze the expression of quantum channel for controlled bidirectional remote state preparation. Finally, we discuss the security of our scheme, the detailed security analysis shows that the supervisor Charlie’s control can greatly improve the security of our scheme.

     

Quantum secure two-party computation for set intersection with rational players

Recently, Shi et al. (Phys Rev A 92:022309, 2015) proposed quantum oblivious set member decision protocol where two legitimate parties, namely Alice and Bob, play a game. Alice has a secret k, and Bob has a set \(\{k_1,k_2,\ldots k_n\}\). The game is designed towards testing if the secret k is a member of the set possessed by Bob without revealing the identity of k. The output of the game will be either “Yes” (bit 1) or “No” (bit 0) and is generated at Bob’s place. Bob does not know the identity of k, and Alice does not know any element of the set. In a subsequent work (Shi et al in Quant Inf Process 15:363–371, 2016), the authors proposed a quantum scheme for private set intersection (PSI) where the client (Alice) gets the intersected elements with the help of a server (Bob) and the server knows nothing. In the present draft, we extended the game to compute the intersection of two computationally indistinguishable sets X and Y possessed by Alice and Bob, respectively. We consider Alice and Bob as rational players, i.e. they are neither “good” nor “bad”. They participate in the game towards maximizing their utilities. We prove that in this rational setting, the strategy profile ((cooperate, abort), (cooperate, abort)) is a strict Nash equilibrium. If ((cooperate, abort), (cooperate, abort)) is strict Nash, then fairness and correctness of the protocol are guaranteed.     

任意二粒子纠缠态的受控量子通信

为了解决任意二量子通信问题,首先给出了五粒子和七粒子纠缠态的构造方法,并提供了它们的量子线路图。其次,以该五粒子纠缠态为量子信道,提出一个任意二粒子未知量子态的受控隐形传态协议。该协议在监察者Charlie的控制下,Alice进行四粒子投影测量和经典通信,Bob采用简单酉变换就能以100%的概率成功重构一个任意二粒子纠缠态。最后,利用七粒子纠缠态为量子信道,提出了任意二粒子纠缠态的联合受控远程制备方案。在此方案中,发送者Alice用自己掌握被制备态的部分信息构造测量基,发送者Bob采用前馈测量策略,接收者Diana在监控者Charlie的帮助下,通过简单幺正变换就能确定性地恢复原始态。     

New quantum codes from dual-containing cyclic codes over finite rings

Let \(R=\mathbb {F}_{2^{m}}+u\mathbb {F}_{2^{m}}+\cdots +u^{k}\mathbb {F}_{2^{m}}\), where \(\mathbb {F}_{2^{m}}\) is the finite field with \(2^{m}\) elements, m is a positive integer, and u is an indeterminate with \(u^{k+1}=0.\) In this paper, we propose the constructions of two new families of quantum codes obtained from dual-containing cyclic codes of odd length over R. A new Gray map over R is defined, and a sufficient and necessary condition for the existence of dual-containing cyclic codes over R is given. A new family of \(2^{m}\)-ary quantum codes is obtained via the Gray map and the Calderbank–Shor–Steane construction from dual-containing cyclic codes over R. In particular, a new family of binary quantum codes is obtained via the Gray map, the trace map and the Calderbank–Shor–Steane construction from dual-containing cyclic codes over R.     

Comment on “quantum oblivious transfer: a secure practical implementation”

We study the entanglement-based attack on a recently proposed quantum oblivious transfer (OT) protocol (Nagy and Nagy in Quantum Inf Process 15:5037, 2016). While in secure OT, Bob’s probability of obtaining Alice’s secret bit unambiguously should be limited to \(50\%\), we show that if Bob has the technology to handle 5-body entangled states in the current protocol, then he can increase this probability to \(64.6\%\). More importantly, in contrast to what the authors claimed, increasing the number of qubits used in the protocol cannot increase the hardness of Bob’s attack.     

Quantum broadcast scheme and multi-output quantum teleportation via four-qubit cluster state

In this paper, two theoretical schemes of the arbitrary single-qubit states via four-qubit cluster state are proposed. One is three-party quantum broadcast scheme, which realizes the broadcast among three participants. The other is multi-output quantum teleportation. Both allow two distant receivers to simultaneously and deterministically obtain the arbitrary single-qubit states, respectively. Compared with former schemes of an arbitrary single-qubit state, the proposed schemes realize quantum multi-cast communication efficiently, which enables Bob and Charlie to obtain the states simultaneously in the case of just knowing Alice’s measurement results. The proposed schemes play an important role in quantum information, specially in secret sharing and quantum teleportation.     

Teleportation of a qubit using entangled non-orthogonal states: a comparative study

The effect of non-orthogonality of an entangled non-orthogonal state-based quantum channel is investigated in detail in the context of the teleportation of a qubit. Specifically, average fidelity, minimum fidelity and minimum assured fidelity (MASFI) are obtained for teleportation of a single-qubit state using all the Bell-type entangled non-orthogonal states known as quasi-Bell states. Using Horodecki criterion, it is shown that the teleportation scheme obtained by replacing the quantum channel (Bell state) of the usual teleportation scheme by a quasi-Bell state is optimal. Further, the performance of various quasi-Bell states as teleportation channel is compared in an ideal situation (i.e., in the absence of noise) and under different noise models (e.g., amplitude and phase damping channels). It is observed that the best choice of the quasi-Bell state depends on the amount non-orthogonality, both in noisy and noiseless case. A specific quasi-Bell state, which was found to be maximally entangled in the ideal conditions, is shown to be less efficient as a teleportation channel compared to other quasi-Bell states in particular cases when subjected to noisy channels. It has also been observed that usually the value of average fidelity falls with an increase in the number of qubits exposed to noisy channels (viz., Alice’s, Bob’s and to be teleported qubits), but the converse may be observed in some particular cases.     

Controlled quantum secure direct communication by entanglement distillation or generalized measurement

We propose two controlled quantum secure communication schemes by entanglement distillation or generalized measurement. The sender Alice, the receiver Bob and the controllers David and Cliff take part in the whole schemes. The supervisors David and Cliff can control the information transmitted from Alice to Bob by adjusting the local measurement angles \(\theta _4\) and \(\theta _3\). Bob can verify his secret information by classical one-way function after communication. The average amount of information is analyzed and compared for these two methods by MATLAB. The generalized measurement is a better scheme. Our schemes are secure against some well-known attacks because classical encryption and decoy states are used to ensure the security of the classical channel and the quantum channel.     

Generation of singlet states with Rydberg blockade mechanism and driven by adiabatic passage

A single state is a special state that entangles multi-state quantum systems and plays a significant role in the field of quantum computation. In this paper, we propose a scheme to realize the generation of single states for Rydberg atoms, where one Rydberg atom is trapped in an optical potential and the others are trapped in an adjacent optical potential. Moreover, combining Rydberg blockade and adiabatic-passage technologies, an N-atom singlet state can be generated with the interaction of an N-dimensional Rydberg atom and an (\(N-1\))-atom singlet state. Compared to previous schemes, the advantage of our proposal is that an N-particle N-level singlet state with \(N\ge 3\) may be realized more simply.     

Approximate conditional teleportation of a $$\varLambda $$-type three-level atomic state based on cavity QED method beyond Bell-state measurement

Inspiring from the scheme proposed in (Zheng in Phys Rev A 69:064,302 2004), our aim is to teleport an unknown qubit atomic state using the cavity QED method without using the explicit Bell-state measurement, and so the additional atom is not required. Two identical \(\varLambda \)-type three-level atoms are interacted separately and subsequently with a two-mode quantized cavity field where each mode is expressed with a single-photon field state. The interaction between atoms and field is well described via the Jaynes–Cummings model. It is then shown that how if the atomic detection results a particular state of atom 1, an unknown state can be appropriately teleported from atom 1 to atom 2. This teleportation procedure successfully leads to the high fidelity F (success probability \(P_g\)) in between \(69\%\lesssim F\lesssim 100\%\) (\(0.14\lesssim P_g\lesssim 0.56\)). At last, we illustrated that our scheme considerably improves similar previous proposals.     

Quantum private comparison protocol based on the entanglement swapping between $$\chi ^+$$ state and W-Class state

Quantum private comparison (QPC) protocol, including Alice, Bob and the third party Charlie, aims at comparing Alice and Bob’s secret inputs correctly without leaking them. Firstly, \(\chi ^+\) state and W-Class state are used to conduct the entanglement swapping in this protocol. Either the basis \(\{|\phi ^\pm \rangle ,|\psi ^\pm \rangle \}\) or the basis \(\{|\chi ^\pm \rangle ,|\omega ^\pm \rangle \}\) is chosen by Alice and Bob based on the predetermined value to measure the particle pairs. And three bits of secret inputs can be compared in this protocol in every comparison time, while most of previous QPC protocols can only compare one or two bits. The qubit efficiency of this protocol is 60% more than others, which are 50% at most. Secondly, if the eavesdropper intends to obtain the secret inputs, it is important and primary to get the measurement results of particle pairs. In this protocol, even if the eavesdropper gets the accurate particle pairs, he cannot get the right measurement results without the right basis. Finally, this protocol is analyzed to be able to defend the secret inputs against various kinds of attack.     

Quantum sealed-bid auction using a modified scheme for multiparty circular quantum key agreement

A feasible, secure and collusion attack-free quantum sealed-bid auction protocol is proposed using a modified scheme for multiparty circular quantum key agreement. In the proposed protocol, the set of all (n) bidders is grouped into l subsets (sub-circles) in such a way that only the initiator (who prepares the quantum state to be distributed for a particular round of communication and acts as the receiver in that round) is a member of all the subsets (sub-circles) prepared for a particular round, while any other bidder is part of only a single subset. All n bidders and auctioneer initiate one round of communication, and each of them prepares l copies of a \(\left( r-1\right) \)-partite entangled state (one for each sub-circle), where \(r=\frac{n}{l}+1\). The efficiency and security of the proposed protocol are critically analyzed. It is shown that the proposed protocol is free from the collusion attacks that are possible on the existing schemes of quantum sealed-bid auction. Further, it is observed that the security against collusion attack increases with the increase in l, but that reduces the complexity (number of entangled qubits in each entangled state) of the entangled states to be used and that makes the scheme scalable and implementable with the available technologies. The additional security and scalability are shown to arise due to the use of a circular structure in place of a complete-graph or tree-type structure used earlier.     

Invariance of bipartite separability and PPT-probabilities over Casimir invariants of reduced states

Milz and Strunz (J Phys A 48:035306, 2015) recently studied the probabilities that two-qubit and qubit–qutrit states, randomly generated with respect to Hilbert–Schmidt (Euclidean/flat) measure, are separable. They concluded that in both cases, the separability probabilities (apparently exactly \(\frac{8}{33}\) in the two-qubit scenario) hold constant over the Bloch radii (r) of the single-qubit subsystems, jumping to 1 at the pure state boundaries (\(r=1\)). Here, firstly, we present evidence that in the qubit–qutrit case, the separability probability is uniformly distributed, as well, over the generalized Bloch radius (R) of the qutrit subsystem. While the qubit (standard) Bloch vector is positioned in three-dimensional space, the qutrit generalized Bloch vector lives in eight-dimensional space. The radii variables r and R themselves are the lengths/norms (being square roots of quadratic Casimir invariants) of these (“coherence”) vectors. Additionally, we find that not only are the qubit–qutrit separability probabilities invariant over the quadratic Casimir invariant of the qutrit subsystem, but apparently also over the cubic one—and similarly the case, more generally, with the use of random induced measure. We also investigate two-qutrit (\(3 \times 3\)) and qubit–qudit (\(2 \times 4\)) systems—with seemingly analogous positive partial transpose-probability invariances holding over what has been termed by Altafini the partial Casimir invariants of these systems.