Efficient schemes for the quantum teleportation of a sub-class of tripartite entangled states

In this paper we propose two schemes for teleportation of a sub-class of tripartite states, the first one with the four-qubit cluster state and the second one with two Bell pairs as entanglement channels. A four-qubit joint measurement in the first case and two Bell measurements in the second are performed by the sender. Appropriate unitary operations on the qubits at the receiver’s end along with an ancilla qubit result in the perfect teleportation of the tripartite state. Analysis of the quantum circuits employed in these schemes reveal that in our technique the desired quantum tasks are achieved with lesser quantum cost, gate count and classical communication bits compared with other similar schemes.     

Residual entanglement with negativity for pure four-qubit quantum states

In this work we study the entanglement of pure four-qubit quantum states. The analysis is realized, firstly, through the comparison between two different entanglement measures: the Groverian entanglement measure and the residual entanglement calculated with negativities. After, we use the last to measure the entanglement of several four-qubit states and the variation of the entanglement when the four-qubit state is processed by a two-qubit gate.     

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.     

基于多参数测量的双向受控隐形传态

融合了双向隐形传态、受控隐形传态、概率隐形传态及多参数测量思想,提出了一个新的双向受控概率隐形传态协议。在该协议中,以五粒子非最大纠缠团簇态为信道,发送者采用多参数通用测量,接收者引入辅助粒子,并在控制者的允许下,利用测量信息施行适当酉变换,就能以一定概率同时交换他们的量子态。分析了成功概率（经典耗费）与量子纠缠参数及测量参数间的依赖关系,说明了该协议可以根据量子信道的参数来调整多参数测量的参数,达到调节成功概率或经典耗费,满足真实世界中多种不同需求的目的。此外,该协议是经典双向受控隐形传态的推广。     

Quantum information splitting of an arbitrary three-qubit state by using two four-qubit cluster states

A new application of the four-qubit cluster state is investigated for quantum information splitting (QIS) of an arbitrary three-qubit state. Muralidharan and Panigrahi (Phys Rev A 78:062333, 2008) argued that a four-qubit cluster state is impossible for QIS of an arbitrary two-qubit state. In this paper, we demonstrate that two four-qubit cluster states can be used to realize the deterministic QIS of an arbitrary three-qubit state by performing only the Bell-state measurements. Our scheme considered here is secure against certain eavesdropping attacks.     

Teleportation of a general two-photon state employing a polarization-entangled $$\chi $$ state with nondemolition parity analyses

Employing a polarization-entangled \(\chi \) state, which is a four-photon genuine entangled state, we propose a protocol teleporting a general two-photon polarization state. Firstly, the sender needs to perform one Controlled-NOT gate, one Hadamard gate, and one Controlled-NOT gate on the state to be teleported in succession. Secondly, the sender performs local nondemolition parity analyses based on cross-Kerr nonlinearities and publicizes the achieved outcomes. Finally, conditioned on the sender’s analysis outcomes, the receiver executes the single-photon unitary transformation operations on his own photons to obtain the state originally sit in the sender’s location. Due to the employment of nondemolition parity analyses rather than four-qubit joint measurement, it can be realized more feasible with currently available technologies. Moreover, the resources of Bell states can be achieved because the nondestructive measurement is exploited, which facilitates other potential tasks of quantum information processing.     

量子隐形传态的通用线路

EPR态作为最基本的量子纠缠态,在量子隐形传态中起着重要作用.研究适应任意类型EPR通道的单量子比特隐形传送通用线路,并推广到任意N比特量子隐形传送通用线路.首先设计出4种EPR态,分别作为量子通道的单比特量子隐形传态,通过分析EPR量子通道与量子操作门之间的关系,设计一种单比特通用线路;然后,设计两比特的标准量子隐形传态线路,并用Mathematica进行仿真验证线路的正确性,再把它推广到N比特量子隐形传送线路;最后,将单量子比特通用线路与N比特量子隐形传送线路进行融合,最终设计出任意N比特量子隐形传送通用线路.N粒子量子比特通用线路通过信息接受者进行带参数的幺正变换,其中,参数由制备出的EPR对类型确定,解决了因EPR制备中心出错导致的信息传送失败问题.     

Bidirectional teleportation of a pure EPR state by using GHZ states

In the present paper, a novel bidirectional quantum teleportation protocol is proposed. By using entanglement swapping technique, two GHZ states are shared as a quantum channel between Alice and Bob as legitimate users. In this scheme, based on controlled-not operation, single-qubit measurement, and appropriate unitary operations, two users can simultaneously transmit a pure EPR state to each other, While, in the previous protocols, the users can just teleport a single-qubit state to each other via more than four-qubit state. Therefore, the proposed scheme is economical compared with previous protocols.     

Schemes for teleportation of quantum gates

Quantum teleportation is a computational primitive that allows non-local quantum communication and quantum computation. In this work, we present two schemes for quantum gate teleportation. The first scheme shows under what conditions an n-qudit gate can be teleported using a generalization of Gottesman-Chuang procedure [Nature 402, 390 (1999)]. The second scheme shows that quantum gate teleportation can be transformed in the teleportation of a single-qudit.     

Classical communication cost and probabilistic remote two-qubit state preparation via POVM and W-type states

I present a new scheme for probabilistic remote preparation of a general two-qubit state by using two W-type states as the shared quantum channel and a proper POVM instead of the usual positive measurement. Also I explore the scheme??s applications to five special ensembles of two-qubit states. The success probability and the classical communication cost in different cases are calculated minutely, respectively, which show that the remote two-qubit preparation can be realized with higher probability after consuming some more classical bits provided that the two-qubit state to be prepared is chosen from the special ensembles.     

On monogamy of four-qubit entanglement

Our main result is a monogamy inequality satisfied by the entanglement of a focus qubit (one-tangle) in a four-qubit pure state and entanglement of subsystems. Analytical relations between three-tangles of three-qubit marginal states, two-tangles of two-qubit marginal states and unitary invariants of four-qubit pure state are used to obtain the inequality. The contribution of three-tangle to one-tangle is found to be half of that suggested by a simple extension of entanglement monogamy relation for three qubits. On the other hand, an additional contribution due to a two-qubit invariant which is a function of three-way correlations is found. We also show that four-qubit monogamy inequality conjecture of Regula et al. (Phys Rev Lett 113:110501, 2014), in which three-tangles are raised to the power \(\frac{3}{2}\), does not estimate the residual correlations, correctly, for certain subsets of four-qubit states. A lower bound on residual four-qubit correlations is obtained.     

Quantification of entanglement of teleportation in arbitrary dimensions

We study bipartite entangled states in arbitrary dimensions and obtain different bounds for the entanglement measures in terms of teleportation fidelity. We find that there is a simple relation between negativity and teleportation fidelity for pure states, but for mixed states, an upper bound is obtained for negativity in terms of teleportation fidelity using convex-roof extension negativity. However, with this, it is not clear how to distinguish between states useful for teleportation and positive partial transpose (PPT) entangled states. Further, there exists a strong conjecture in the literature that all PPT entangled states, in $3 \otimes 3$ systems, have Schmidt rank two. This motivates us to develop measures capable of identifying states useful for teleportation and dependent on the Schmidt number. We thus establish various relations between teleportation fidelity and entanglement measures depending upon Schmidt rank of the states. These relations and bounds help us to determine the amount of entanglement required for teleportation, which we call the “Entanglement of Teleportation.” These bounds are used to determine the teleportation fidelity as well as the entanglement required for teleportation of states modeled by a two-qutrit mixed system, as well as two-qubit open quantum systems.     

GHZ态的多参数测量控制概率隐形传态

量子隐形传态大多都使用最大化纠缠态作为量子信道,但最大化纠缠资源只存在于理想情况下。研究了非最大化纠缠信道的量子隐形传态,基于非最大化纠缠GHZ态提出了一个新型的概率控制隐形传态方案。通过引入多参数通用测量,可以根据量子信道参数调整测量基参数,进而实现最佳的成功概率。加入了量子控制者,使方案具有更高的灵活性。该方案可以被扩展到接收者没有足够量子能力的半量子通信情况,进一步扩大了概率隐形传态的应用范围。     

Probabilistic resumable bidirectional quantum teleportation

In order to effectively use partially entangled pairs, we consider two kinds of generalized bidirectional quantum teleportation (GBQT) protocols in the different cases: (I) Alice and Bob send messages to each other, and (II) Bob replays Alice after he received Alice’s message, where partially entangled pairs are utilized as the quantum channels. However, the states to be teleported will be destroyed if GBQT fails. To solve this problem, we show an improved project, probabilistic resumable bidirectional quantum teleportation (RBQT), where the states to be teleported can be rebuilt exactly by senders when RBQT has not been successfully achieved. Thus, we are able to carry out RBQT many times until it succeeds, although there are no other copies of the initial states. In RBQT, weak entanglement can also be utilized to bidirectionally teleport unknown states successfully.     

Construction of four-qubit quantum entanglement for SI (S = 3/2, I = 3/2) spin system

In quantum information processing, spin-3/2 electron or nuclear spin states are known as two-qubit states. For SI (S = 3/2, I = 3/2) spin system, there are 16 four-qubit states. In this study, first, four-qubit entangled states are obtained by using the matrix representation of Hadamard and CNOT logic gates. By considering ⁷⁵As@C₆₀ molecule as SI (S = 3/2, I = 3/2) spin system, four-qubit entangled states are also obtained by using the magnetic resonance pulse sequences of Hadamard and CNOT logic gates. Then, it is shown that obtained entangled states can be transformed into each other by the transformation operators.     

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.     

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.     

Analysing nonlocality robustness in multiqubit systems under noisy conditions and weak measurements

We analyse robustness of nonlocal correlation in multiqubit entangled states—three- and four-qubit GHZ class and three-qubit W class—useful for quantum information and computation, under noisy conditions and weak measurements. For this, we use a Bell-type inequality whose violation is considered as a signature for confirming the presence of genuine nonlocal correlations between the qubits. In order to demonstrate the effects of noise and weak measurements, an analytical relation is established between the maximum expectation value of three and four-qubit Svetlichny operators for the systems under study, noise parameter and strengths of weak measurements. Our results show that for a set of three- and four-qubit GHZ class states, maximal nonlocality does not coincide with maximum entanglement for a given noise parameter and a certain range of weak measurement parameter. Our analysis further shows an excellent agreement between the analytical and numerical results.     

基于EPR对的任意四粒子Cluster类态全概率联合远程制备

采用4个EPR(Einstein-Podolsky-Rosen)对作为量子信道,提出一种新的全概率联合远程制备任意四粒子Cluster类态方案。在这个新的方案中,一个制备者执行四粒子投影测量,另一个制备者对手中的粒子执行二粒子投影测量。然后,接收者对手中二粒子进行某种幺正操作,并分别对两个辅助粒子进行受控非门操作,从而最终得到需要制备的Cluster类态。与其他制备任意四粒子Cluster类态的全概率制备方案相比,所提协议效率较高,而且在实验上更经济可行。