Three-qubit GHZ States Research Articles

Optimal quantum control via genetic algorithms for quantum state engineering in driven-resonator mediated networks

We employ a machine learning-enabled approach to quantum state engineering based on evolutionary algorithms. In particular, we focus on superconducting platforms and consider a network of qubits—encoded in the states of artificial atoms with no direct coupling—interacting via a common single-mode driven microwave resonator. The qubit-resonator couplings are assumed to be in the resonant regime and tunable in time. A genetic algorithm is used in order to find the functional time-dependence of the couplings that optimise the fidelity between the evolved state and a variety of targets, including three-qubit GHZ and Dicke states and four-qubit graph states. We observe high quantum fidelities (above 0.96 in the worst case setting of a system of effective dimension 96), fast preparation times, and resilience to noise, despite the algorithm being trained in the ideal noise-free setting. These results show that the genetic algorithms represent an effective approach to control quantum systems of large dimensions.

A relation among tangle, 3-tangle, and von Neumann entropy of entanglement for three qubits

In this paper, we derive a general formula of the tangle for pure states of three qubits and present three explicit local unitary (LU) polynomial invariants. Our result goes beyond the classical work of tangle, 3-tangle, and von Neumann entropy of entanglement for Acín et al.’ Schmidt decomposition (ASD) of three qubits by connecting the tangle, 3-tangle, and von Neumann entropy for ASD with Acín et al.’s LU invariants. In particular, our result reveals a general relation among tangle, 3-tangle, and von Neumann entropy, together with a relation among their averages. The relations can help us find the entangled states satisfying distinct requirements for tangle, 3-tangle, and von Neumann entropy. Moreover, we obtain all the states of three qubits of which tangles, concurrence, 3-tangle, and von Neumann entropy do not vanish and these states are endurable when one of three qubits is traced out. We indicate that for the three-qubit W state, its average von Neumann entropy is maximal only within the W SLOCC class, and that under ASD the three-qubit GHZ state is the unique state of which the reduced density operator obtained by tracing any two qubits has the maximal von Neumann entropy.

Robust self-testing of multipartite Greenberger-Horne-Zeilinger-state measurements in quantum networks

Self-testing is an examination for characterizing unknown quantum devices based on correlations of observed statistics in a black-box scenario. With development of large-scale quantum networks, the requirement for self-testing multipartite entangled measurements has become very demanding. We develop here a general procedure for self-testing arbitrary generalized Greenberger-Horne-Zeilinger-state (GHZ-state) measurements which applies to any number of parties. Moreover, it turns out that the existing result for the three-qubit GHZ-state measurement is recovered as a special case. Our results will motivate operational certification of quantum devices related to device-independent quantum information tasks for various scenarios in complicated quantum networks.

Asymmetric Bidirectional Controlled Quantum Teleportation of Three- and Four-Qubit States

In this paper, we theoretically realize bidirectional controlled quantum teleportation by using ten-qubit entangled state method. This paper uses a case to introduce the specific process of realizing quantum teleportation: Alice sends an unknown four-qubit GHZ state to Bob, and Bob sends an arbitrary three-qubit GHZ state to Alice. In addition, Charlie controls the transfer to ensure the integrity of the protocol. A ten-qubit quantum channel is constructed and used in this paper. Then, the unitary matrix transformation is used to complete the communication protocol. The research results show that the communication protocol constructed in this paper is more efficient than most communication protocols.

Construct maximally five- and seven-qubit entangled states via three- qubit GHZ state

Different mathematics forms of entangled state can judge prepared many particles is if entangled. Entangled state is a key role of quantum information technology. The more entangled states are generated, the better performances are presented. In order to make it more convenient to generate entangled state or judge the state prepared is entangled, we investigate three-qubit GHZ state and expand recurrence relation based on an expand recurrence relation of multi-qubit state. Furthermore, new forms of maximally five and seven-qubit entangled states are reconstructed via three-qubit GHZ state. These new forms stand for universal law of n-qubit and [Formula: see text]-qubit can have direct application in quantum entangle state generation and quantum communications.

Entangled state generation via quantum walks with multiple coins

Generation of entangled state is of paramount importance both from quantum theoretical foundation and technology applications. Entanglement swapping provides an efficient method to generate entanglement in quantum communication protocols. However, perfect Bell measurements for qudits, the key to entanglement swapping, have been proven impossible to achieve by using only linear elements and particle detectors. To avoid this bottleneck, we propose a scheme to generate entangled state including two-qubit entangled state, two-qudit entangled state, three-qubit GHZ state and three-qudit GHZ state between several designate parties via the model of quantum walks with multiple coins. Then we conduct experimental realization of Bell state and three-qubit GHZ state between several designate parties on IBM quantum platform and the result has high fidelity by performing quantum tomography. In the end, we give a practical application of our scheme in multiparty quantum secret sharing.

Comment on “protection of quantum dialogue affected by quantum field”

The novel quantum dialogue (QD) protocol by using the three-qubit GHZ states (Quantum Inf Process (2019) 18: 37) is cryptanalyzed. It is found that there is the information leakage problem in this QD protocol. To be specific, half information of the secret messages exchanged is leaked out unconsciously. Afterwards, a way to improve this protocol is discussed.

Comment on “Quantum Controlled Teleportation of Bell State Using Seven-Qubit Entangled State”

Recently, Chen et al. [Int. J. Theor. Phys. 59, 1402–1412 (2020)] proposed a theoretical scheme for controlled quantum teleportation (CQT) of a Bell state by using seven-qubit entangled state as a quantum channel. In this comment, it is shown that the consumption of both the quantum and classical resources used by Chen et al. is excessively high because the actual task of CQT of a Bell state via seven-qubit entangled state can be reduced to the CQT of an arbitrary single-qubit state via three-qubit GHZ state. Hence, in this work, an improved scheme for CQT has been presented. We have also shown that the CQT of certain class of N-qubit entangled state can also be realized successfully by using a three-qubit GHZ state as the quantum channel. The intrinsic efficiency of the present communication scheme is very large as compared to that proposed by Chen et al.

Nonlocality of tripartite orthogonal product states

Local distinguishability of orthogonal product states is an area of active research in quantum information theory. However, most of the relevant results about local distinguishability are found in bipartite quantum systems and very few are known in multipartite cases. In this paper, we construct a locally indistinguishable subset in $${\mathbb {C}}^{2d}\bigotimes {\mathbb {C}}^{2d}\bigotimes {\mathbb {C}}^{2d}$$ , $$d\ge 2$$ that contains $$18(d-1)$$ orthogonal product states. Further, we generalize our method to arbitrary tripartite quantum systems $${\mathbb {C}}^{k}\bigotimes {\mathbb {C}}^{l}\bigotimes {\mathbb {C}}^{m}$$ . This result helps us to understand the role of nonlocality without entanglement in multipartite quantum systems. Finally, we prove that a three-qubit GHZ state is sufficient as a resource to distinguish each of the above classes of states.

Bidirectional Quantum Teleportation by Using Two GHZ-States as the Quantum Channel

Bidirectional quantum teleportation protocol enables two way quantum communication between two quantum nodes in a quantum communication network. In quantum network, the quantum nodes are linked to each other through a quantum channel. In this letter, by using the quantum channel composed of two three-qubit GHZ states, we propose an improved protocol for asymmetric bidirectional quantum teleportation which is based on local CNOT gate operations, Bell state measurements, GHZ-state measurements and unitary operations. Compared with previous protocols for bidirectional quantum teleportation, the proposed protocol requires less consumption of quantum and classical resources, possesses higher intrinsic efficiency and less operation complexity.

Information leakage in protection of quantum dialogue affected by quantum field

Recently, Huang et al. (Quantum Inf Process 18:37, 2019) proposed a quantum dialogue protocol by using three-qubit GHZ states. We study the security of the proposed protocol and find that it is not secure and has the drawback of information leakage. Finally, we modify only the tenth step in the proposed protocol, so that it can overcome the drawback.

Controlled quantum key agreement based on maximally three-qubit entangled states

In this paper, we propose a two-party and a three-party controlled quantum key agreement (QKA) protocols with three-qubit GHZ states and Bell measurements. Compared with previous protocols, the significant change of our schemes is that a supervisor is introduced for controlling the agreement process to improve the controllability. Moreover, our protocols ensure each communication participant contribute equally to the agreement keys, and all participants can negotiate the shared keys without exchanging classical bits between them. The performance analysis shows that our protocols can be immune to outsider and participant attack.

Arbitrated quantum signature scheme with quantum teleportation by using two three-qubit GHZ states

Arbitrated quantum signature (AQS) scheme based on quantum teleportation has better flexibility and practicability. In this paper, we propose an arbitrated quantum signature scheme with quantum teleportation by using two three-qubit GHZ states. It has been proved that a cluster state has a maximal persistence when compared with an entangled state, and it is also more robust against decoherence. To resist against Alice’s disavowals or Bob’s (outside attacker’s) repudiation, two secret quantum key strings are pre-shared and two random numbers are introduced. The security analysis results show that our AQS scheme can make sure about the impossibility of disavowals by the signer Alice and repudiations by the verifier Bob, and the impossibility of forgeries by any illegal attacker. In addition, the proposed scheme does not require the complex quantum measurement operation, only Bell state measurements, projective measurements and unitary operation are needed to recover the arbitrary two-qubit state, which is the message copy from the signer Alice to the verifier Bob, and that is an appealing advantage in the implementation of a practical quantum communication network.

Quantum Risk Assessment Model Based on Two Three-Qubit GHZ States

With the acceleration of the construction of quantum communication networks, scholars have proposed different quantum communication protocols for different application scenarios. However, few scholars pay attention to the risk assessment process before communication. In this paper, we propose a novel quantum risk assessment model based on quantum teleportation technology with two three-qubit GHZ states. Only by using Bell states measurements (BSMs) and two-qubit projective measurements (PJMs), the communicators can recovery any arbitrary two-qubit state. This protocol can transmit two-dimension risk assessment factors with better security performance. On the one hand, more sufficient evaluation factors allow the two communicating parties to more objectively evaluate the risk level of communication with the other party, and on the other hand, it also improves the qubit efficiency of the protocol. Moreover, we introduce the third party in this scheme can be semi-trusted, which must be full-trusted in our previous work. This change can reduce the dependence of the communication parties on the third-party organization and improve the privacy of communication. The security analysis shows that this scheme can resist internal and external attacks, and the quantum circuit diagrams also prove that our protocol is physically easier to implement.

Joint remote state preparation of mixed states

Joint remote state preparation (JRSP) has gained much attention since its first appearance. However, almost all the proposals have focused on the JRSP of pure states. In this paper, we present a scheme of JRSP for mixed states via the three-qubit GHZ state. The scheme is deterministic for real coefficient mixed states and probabilistic for complex ones. The corresponding quantum circuits are given for the deterministic JRSP schemes. The model of the deterministic JRSP scheme is introduced in the language of density operators. Furthermore, we investigate the efficiency of deterministic JRSP when some qubits in the protocol are subjected to a noisy environment. Four types of noise usually encountered in quantum communication are considered, i.e. the bit-flip, phase-flip (phase-damping), depolarizing and amplitude-damping noise. We find that the fidelity is affected by both coefficients of the target mixed state and noise parameter of the channel. Specifically, the fidelity decreases with the purity parameter in the presence of noise.

Quantum teleportation of an arbitrary two-qubit state by using two three-qubit GHZ states and the six-qubit entangled state

In this paper, we show that current two different quantum channels of two three-qubit GHZ states and the six-qubit entangled state can be used for quantum teleportation of an arbitrary two-qubit state deterministically. Moreover, we propose two distinct protocols for quantum teleportation of an arbitrary two-qubit state within a three-qubit, by using a single-qubit measurement under the basis and also using a two-qubit projective measurement under the basis $$\{|+\rangle ,|-\rangle \}$$ , so as to get 16 kinds of possible measured results with equal probability of 1/4. Furthermore, the deterministic quantum teleportation of an arbitrary two-qubit states can be realized in a cavity quantum electrodynamics systems. This is unique, in that a cluster state has a maximal persistence when compared with a entangled state and it is also more robust against decoherence. Furthermore, the schemes are secure against internal and external attacks.

Deterministic Joint Remote State Preparation of an Arbitrary Equatorial Three-Qubit State

We propose a new scheme for joint remote preparation of an arbitrary equatorial three-qubit state by using three three-qubit GHZ states as the quantum channel. In our scheme, eight different projective measurement basis vectors are needed. It is shown that the successful probability of our scheme is 100% by performing the appropriate unitary operations.

Protection of quantum dialogue affected by quantum field

In this paper, we present a secure quantum dialogue protocol (QDP) by using three-qubit GHZ states, which has high capacity and efficiency. However, a real quantum system unavoidably interacts with its environment, which results in the decoherence phenomenon. Decoherence will restrain the effective application of quantum communication protocols. Thus, in this article we also investigate the QDP affected by fluctuating massless scalar field, and how to protect the QDP in noisy environment. The master equation that governs the noisy QDP evolution is firstly derived. Then, we find that the success probability (SP) of QDP decreases exponentially with evolution time, and with a perfectly reflecting boundary SP can be effectively protected and modulated.

Revised Geometric Measure of Entanglement in Infinite Dimensional Multipartite Quantum Systems

In Cao and Wang (J. Phys.: Math. Theor. 40, 3507–3542, 2007), the revised geometric measure of entanglement (RGME) for states in finite dimensional bipartite quantum systems was proposed. Furthermore, in Cao and Wang (Commun. Theor. Phys. 51(4), 613–620, 2009), the authors obtained the revised geometry measure of entanglement for multipartite states including three-qubit GHZ state, W state, and the generalized Smolin state in the presence of noise and the two-mode squeezed thermal state, and defined the Gaussian geometric entanglement measure. In this paper, we generalize the RGME to infinite dimensional multipartite quantum systems, and prove that this measure satisfies some necessary properties as a well-defined entanglement measure, including monotonicity under local operations and classical communications.

An approach for quantitatively analyzing the genuine tripartite nonlocality of general three-qubit states

Nonlocality is an important resource for quantum information processing. Genuine tripartite nonlocality, which is sufficiently confirmed by the violation of Svetlichny inequality, is a kind of more precious resource than the standard one. The genuine tripartite nonlocality is usually quantified by the amount of maximal violation of Svetlichny inequality. The problem of detecting and quantifying the genuine tripartite nonlocality of quantum states is of practical significance but still open for the case of general three-qubit quantum states. In this paper, we quantitatively investigate the genuine nonlocality of three-qubit states, which not only include pure states but also include mixed states. Firstly, we derive a simplified formula for the genuine nonlocality of a general three-qubit state, which is a function of the corresponding three correlation matrices. Secondly, we develop three properties of the genuine nonlocality which can help us to analyze the genuine nonlocality of complex states and understand the nature of quantum nonlocality. Further, we get analytical results of genuine nonlocality for two classes of three-qubit states which have special correlation matrices. In particular, the genuine nonlocality of generalized three-qubit GHZ states, which is derived by Ghose et al. (Phys. Rev. Lett. 102, 250404, 2009), and that of three-qubit GHZ-symmetric states, which is derived by Paul et al. (Phys. Rev. A 94, 032101, 2016), can be easily derived by applying the strategy and properties developed in this paper.