GHZ-type States Research Articles

Assisted cloning of an unknown shared quantum state.

We first propose a novel protocol to realize quantum cloning of an arbitrary unknown shared state with assistance offered by a state preparer. The initial phase of this protocol involves the utilization of quantum teleportation (QT), enabling the transfer of quantum information from an arbitrary number of senders to another arbitrary number of receivers through a maximally entangled GHZ-type state serving as a network channel, without centralizing the information at any specific location. In the second stage of this protocol, the state preparer performs a special single-qubit projective measurement and multiple Z-basis measurements and then communicates a number of classical bits corresponding to measurement results, the perfect copy or orthogonal-complementing copy of an unknown shared state can be produced at senders hands. Then, using a non-maximally entangled GHZ-type state instead of the aforementioned quantum channel, we extend the proposed protocol from three perspectives: projective measurement, positive operator-value measurement (POVM), and a single generalized Bell-state measurement. Our schemes can relay quantum information over a network without requiring fully trusted central or intermediate nodes, and none of participants can fully access the information.

Quantum teleportation of shared high-dimensional quantum secret

We present an innovative approach for quantum teleportation (QT) in a three-dimensional (3D) quantum system, enabling the transmission of 3D quantum information from multiple senders to multiple receivers using a 3D maximally entangled GHZ-type state as a network channel.By substituting the quantum channel with a partially entangled GHZ-type state in a three-dimensional (3D) setting, we obtain an extension of the above scheme in which, when an auxiliary qubit is introduced, the receivers implement a two-particle unitary transformation and some proper 3D Weyl operators to jointly reconstruct the transmitted state with a certain probability and unit fidelity. Subsequently, inspired by the proposed schemes, a protocol for transferring a shared d-dimensional (dD) quantum state to multiple distant parties by using a dD maximally entangled GHZ-type state as quantum channel is presented, and it is generalized to the case of a dD partially entangled GHZ-type network channel by introducing an auxiliary qubit and executing a two-particle unitary transformation. Our schemes can relay quantum information over a network without requiring fully trusted central or intermediate nodes, and none of the participants can fully accesses the information.

Circular semi-quantum secret sharing based on hybrid single particle and GHZ-type states

Semi-quantum secret sharing (SQSS) is a branch of quantum cryptography, with the advantage of fewer quantum resources. In this paper, we present a SQSS protocol based on hybrid single particle and GHZ-type states. Our protocol adopts circular transport structure to share secret information between classical and quantum parties, employing the entanglement correlation and uncertainty of GHZ-type states to guarantee the security of the transmission. Security analysis indicates that the proposed SQSS protocol enables resilience against various potential attacks such as measure-resend, entangle-measure, internal, and Trojan attacks. Furthermore, our protocol is easy to generalize to multi-party scenarios without increasing the complexity of state preparation. Compared with some typical SQSS protocols, our protocol has higher qubit efficiency without the need for entanglement swapping operations. The proposed SQSS protocol has the potential for broader applications in practical scenarios.

Optimal entanglement generation in GHZ-type states

The entanglement production is key for many applications in the realm of quantum information, but so is the identification of processes that allow to create entanglement in a fast and sustained way. Most of the advances in this direction have been circumscribed to bipartite systems only, and the rate of entanglement in multipartite system has been much less explored. Here we contribute to the identification of processes that favor the fastest and sustained generation of tripartite entanglement in a class of 3-qubit GHZ-type states. By considering a three-party interaction Hamiltonian, we analyze the dynamics of the 3-tangle and the entanglement rate to identify the optimal local operations that supplement the Hamiltonian evolution in order to speed-up the generation of three-way entanglement, and to prevent its decay below a predetermined threshold value. The appropriate local operation that maximizes the speed at which a highly-entangled state is reached has the advantage of requiring access to only one of the qubits, yet depends on the actual state of the system. Other universal (state-independent) local operations are found that conform schemes to maintain a sufficiently high amount of 3-tangle. Our results expand our understanding of entanglement rates to multipartite systems, and offer guidance regarding the strategies that improve the efficiency in various quantum information processing tasks.

Mermin's inequalities in Quantum Field Theory

A relativistic Quantum Field Theory framework is devised for Mermin's inequalities. By employing smeared Dirac spinor fields, we are able to introduce unitary operators which create, out of the Minkowski vacuum |0〉, GHZ-type states. In this way, we are able to obtain a relation between the expectation value of Mermin's operators in the vacuum and in the GHZ-type states. We show that Mermin's inequalities turn out to be maximally violated when evaluated on these states.

Quantum metrology with an N -qubit W superposition state under noninteracting and interacting operations

We study the performance of an $N$-qubit $W$ superposition state composed of a $W$ state and its obverse in quantum metrology. Taking advantage of the general Ising-type Hamiltonian (including noninteracting and interacting operation), we analytically present the quantum Fisher information (QFI) of an $N$-qubit $W$ superposition state under different situations and then investigate its phase sensitivity. The results show that the phase sensitivity under noninteracting operation displays a crossover from the $W$ state to Greenberger-Horne-Zeilinger (GHZ) state, where it is same as $W$ state in the few-qubit case $(N\ensuremath{\le}6)$ but asymptotically equal to the GHZ state for large-qubit cases $(N\ensuremath{\gg}1)$. Interestingly, the 4-qubit $W$ superposition state is found to have the same sensitivity as the 4-qubit GHZ state. And the optimal measurement protocols are provided for ideal metrology. Under the phase-amplitude damping channel, the phase sensitivity of the $W$ superposition state (except for $N=3$) is ultimately decreased to the standard quantum limit, while it turns worse in a depolarizing channel. Finally, the tunable phase sensitivity under interacting operation is studied, and the general Heisenberg limit is surpassed with the increasing interaction strength $\ensuremath{\gamma}$. Meanwhile, a plateau of QFI and phase sensitivity is found for all large-qubit $W$ superposition states, which is similar to the study of the GHZ state and again verifies the common feature of GHZ-type states in quantum metrology.

Entangled state distillation from single copy mixed states beyond LOCC

No pure entangled state can be distilled from a 2⊗2 or 2⊗3 mixed state by separable operations. In 3⊗3, pure entanglement can be distilled by separable operation but not by LOCC. In this letter, we proved the conjecture (Chitambar and Duan (2009) [21]) that it is possible to distill pure entanglement for 2⊗4 system by LOCC and further improve these in higher dimensions to distill a pure entangled state of Schmidt rank d from a m⊗n mixed state by separable operation when m+n⩾3d. We found results for tripartite systems with target state d-level GHZ-type state. These results provide a class of systems where separable operation is strictly stronger than LOCC.

Generation of a GHZ-type optical entangled coherent state without measurements

Typically, multipartite entangled coherent states are difficult to be extended and produced without measurement. We here propose a way to deterministically generate a GHZ (Greenberger–Horne–Zeilinger)-type entangled coherent state of cavities, utilizing a system consisting of a single superconducting qutrit (i.e., a three-level quantum system) and multiple microwave cavities. Due to the use of only a coupler qutrit, the architecture of the circuit system is quite simple. More importantly, our proposal does not require measurement on the state of qutrit compared with the previous proposals. Since the qutrit's third energy level is not populated during the operation, decoherence from the higher energy level is greatly minimized. Furthermore, the entire operation time is independent of the number of microwave cavities. As an example, our numerical simulations show that high-fidelity generation of a three-cavity GHZ-type entangled coherent state is feasible with present circuit quantum electrodynamics technology. This proposal is universal and can be applied to other physical systems, such as microwave or optical cavities, which are coupled to a single natural or artificial three-level atom.

Multi-party semi-quantum private comparison based on the maximally entangled GHZ-type states

The goal of semi-quantum privacy comparison (SQPC) is to use a small amount of quantum capabilities to compare private information for equality. In recent years, research on semi-quantum privacy comparison protocol has made some achievements. However, most of SQPC protocols can merely compare the private information of two parties, and the research of multi-party SQPC protocols are still scarce. If the number of participants is more than two, the protocol needs to be executed multiple times. Therefore, we proposed a multi-party semi-quantum private comparison protocol based on the maximally entangled GHZ-type state, which has the capability to compare the equality of n parties by executing the protocol once. What is more, the transmission of participant’s encrypted information is not through the classical channel, which improves the security of the protocol. Finally, the security analysis shows that outsider attacks, dishonest participants attacks and semi-honest TP attacks are all invalid for this protocol.

Coordinately assisted distillation of quantum coherence in multipartite system

We investigate the issue of assisted coherence distillation in the asymptotic limit, by coordinately performing the identical local operations on the auxiliary systems of each copy. When we further restrict the coordinate operations to projective measurements, the distillation process branches into many sub-processes. Finally, a computable measure of the assisted distillable coherence is derived as the maximal average coherence of the residual states with the maximization taken over all the projective measurements on the auxiliary. The measure can be conveniently used to evaluate the assisted distillable coherence in experiments, especially suitable for the case that the system and its auxiliary are in mixed states. By using the measure, we for the first time study the assisted coherence distillation in multipartite systems. Monogamy-like inequalities are derived to constrain the distribution of the assisted distillable coherence in the subsystems. Taking a three-qubit system for example, we experimentally prepare two types of tripartite correlated states, i.e., the W-type and GHZ-type states in a linear optical setup, and experimentally test the assisted distillable coherence. Theoretical and experimental results agree well to verify the distribution inequalities given by us. Three measures of multipartite quantum correlation are also considered. The close relationship between the assisted coherence distillation and the multipartite correlation is revealed.

Controlled Dense Coding Using Generalized GHZ-type State in a Noisy Network

Controlled Dense Coding Using Generalized GHZ-type State in a Noisy Network

Multi-party quantum secret sharing based on logical GHZ-type states against collective noise

In this paper, we discussed the local preparation methods of two types of multi-qubit logical GHZ-type states using controlled quantum gates, and drew the corresponding quantum circuits. Subsequently, we investigated the measurement-related properties of logical GHZ-type state and thus proposed two multi-party quantum secret sharing schemes against collective-dephasing and collective-rotation noise, respectively. Further, we demonstrated that the schemes can effectively resist some familiar attack strategies. Finally, we analyzed the quantum efficiency of our schemes and made a comprehensive comparison with previous similar schemes.

Effects of classical random external field on the dynamics of entanglement in a four-qubit system

We investigate the dynamics of entanglement through negativity and witness operators in a system of four non-interacting qubits driven by a classical phase noisy laser characterized by a classical random external field (CREF). The qubits are initially prepared in the GHZ-type and W-type states and interact with the CREF in two different qubit-field configurations, namely, common environment and independent environments in which the cases of equal and different field phase probabilities are distinguished. We find that entanglement exhibits different decaying behavior, depending on the input states of the qubits, the qubit-field coupling configuration, and field phase probabilities. On the one hand, we demonstrate that the coupling of the qubits in a common environment is an alternative and more efficient strategy to completely shield the system from the detrimental impacts of the decoherence process induced by a CREF, independent of the input state and the field phase probabilities considered. Also, we show that GHZ-type states have strong dynamics under CREF as compared to W-type states. On the other hand, we demonstrate that in the model investigated the system robustness’s can be greatly improved by increasing the number of qubits constituting the system.

Deterministic Multi-hop Teleportation of Arbitrary Single Qubit State via Partially Entangled GHZ-type State

Deterministic Multi-hop Teleportation of Arbitrary Single Qubit State via Partially Entangled GHZ-type State

Authenticated Semi-Quantum Secret Sharing Based on GHZ-Type States

As is known to all that entities authentication can provides secure communication for QSS protocol. In this paper, the authors propose a novel semi-quantum secret sharing (SQSS) scheme where identity authentication is adopted to verify the identification of partners in communication based on GHZ-type states. Any related quantum operations can be performed by the quantum Alice, however, classical partners can only perform classical operations on the transmitted qubits as well as unitary transformation. In addition, the paper also shows that the protocol is secure resist some eavesdropping attacks.

Tripartite Entanglement for Three-Qubit System in the Generalized Coleman-Hepp Model

Based on the solvable dynamical model for quantum measurement process, we consider three uncoupled particles interacting with their local one-dimensional (1D) spin arrays. Here the 1D spin arrays can be regarded as the local phase decoherence environments for the particles. To demonstrate the dynamics of quantum entanglement among three particles in measuring process, the tripartite negativity is introduced. Our study indicates that the tripartite negativity is determined jointly by the initial states and the dephasing factors for four kinds of initial states, including GHZ-type states, W-type states, Weiner-GHZ states, and Weiner-W states. We find the particle-spin array interaction can destroy the tripartite negativity, and the tripartite negativity is the same for the family of entangled GHZ states or the family of entangled W states. Furthermore, there exists the sudden death of tripartite negativity when the initial states are Weiner-GHZ states or Weiner-W states.

Two-Way Remote Preparations of Inequivalent Quantum States Under a Common Control

In this paper we design a deterministic controllable quantum communication protocol for remotely preparing three-qubit GHZ-type and four-qubit W-type entangled states at two different locations at the same time. Two parties (the preparers) along with a third party (the controller) are connected through a proper multipartite entangled resource. The states to be prepared are not physically available, only the classical information of each state is known by a party who intends to remotely prepare it at the end of the other party under the same control of a third party. Concretely, it is a multi-tasking protocol in which remote preparations of the two inequivalent states are accomplished not only simultaneously but also controllably through execution of a single protocol by utilizing an eleven-qubit entangled state as shared quantum resource. We also propose a generation process of the multipartite quantum resource used.

A comparative study of system size dependence of the effect of non-unitary channels on different classes of quantum states

We investigate the effect of different types of non-unitary quantum channels on multiqubit quantum systems. For an n-qubit system and a particular channel, in order to draw unbiased conclusions about the system as a whole as opposed to specific states, we evolve a large number of randomly generated states under the given channel. We increase the number of qubits and study the effect of system size on the decoherence processes. The entire scheme is repeated for various types of environments which include dephasing channel, depolarizing channel, collective dephasing channel and zero temperature bath. Non-unitary channels representing the environments are modeled via their Kraus operator decomposition or master equation approach. Further, for a given n we restrict ourselves to the study of particular subclasses of entangled states, namely the GHZ-type and W-type states. We generate random states within these classes and study the class behaviors under different quantum channels for various values of n.

Control power of high-dimensional controlled teleportation

To quantitatively analyze the control power of arbitrary $d$-dimensional controlled teleportation (CT), this paper investigates channels of entangled high-dimensional three-qudit standard Greenberger-Horne-Zeilinger (GHZ) and GHZ-type states. The upper bound on the controller's power is established in the $d$-dimensional CT scheme. We identify a trade-off between the control power and the capacity of the quantum channels. The control power can be enhanced by reducing the dimension of the teleported information in a suitably high-dimensional quantum channel, or by increasing the dimension of the qudit held by the controller. Under controlled teleporting of a single qubit in a perfect CT scheme, the control power is maximized in the three-dimensional GHZ-type state channel. This maximum control power exceeds the highest predicted value in previous works and the upper bounds of control power in a two-dimensional quantum channel. Our studies provide a feasible method for achieving higher control power, and it may provide approaches to define high-dimensional entanglement of multibody systems.

A GHZ-type state preparation method and related properties

A GHZ-type state preparation method and related properties