Entangled GHZ State Research Articles

Multiparty sharing of quantum images based on product state of maximally entangled GHZ state

Multiparty sharing of quantum images based on product state of maximally entangled GHZ state

Dynamics of entangled Greenberger — Horne — Zeilinger states in three qubits thermal Tavis — Cummings model

In this paper, we investigated the dynamics of systems of two and three identical qubits interacting resonantly with a selected mode of a thermal field of a lossless resonator. We found solutions of the quantum time-dependent Liouville equation for various three- and two-qubit entangled states of qubits. Based on these solutions, we calculated the criterion of the qubit entanglement — fidelity. The results of numerical calculations of the fidelity showed that increasing the average number of photons in a mode leads to a decrease in the maximum degree of entanglement. It is shown that the two-qubit entangled state is more stable with respect to external noise than the three-qubit entangled Greenberger — Horne — Zeilinger states (GHZ). Moreover, a genuine entangled GHZ-state is more stable to noise than a GHZ-like entangled state.

Enhancement of multimode entanglement and asymmetric steering by noiseless linear amplification

Quantum entanglement and Einstein-Podolsky-Rosen (EPR) steering is an important resource for quantum information. However, it is very fragile and prone to decoherence. Recently, it has been shown that the noiseless linear amplification (NLA) which can be applied to any channel with loss and noise can effectively counteract the effect of quantum decoherence. Besides, the initial quantum correlation can even be exceed by using this method. Thus, it is a useful tool in enhancing quantum entanglement. In this paper, we apply NLA to the tripartite GHZ entangled state and analyze quantum entanglement and steering after NLA. The results showed that the NLA can effectively improve quantum entanglement and expand the range of quantum steering. Simultaneously, they also provide useful direction for the distillation of quantum state using NLA in practical quantum communication.

Absolutely secure distributed superdense coding: entanglement requirement for optimality

Superdense coding uses entanglement as a resource to communicate classical information efficiently through quantum channels. A superdense coding method is optimal when its capacity reaches Holevo bound. We show that for optimality, maximal entanglement is a necessity across the bipartition of Alice and Bob, but neither absolute nor genuine multipartite entanglement is required. Unlike the previous schemes, which can transmit either even or odd bits of information, we demonstrate a generalized dense coding protocol using the genuine multipartite entangled GHZ state to send arbitrary information bits. Expressed in the eigenbasis of different Pauli operators, GHZ state is characterized by a unique parity pattern which enables us to formulate a security checking technique to ensure absolute security of the protocol. We show this method is better applicable in a scenario, where the initial information is distributed among spatially separated parties. Finally, optimizing the number of qubit(s) sent to Bob, we construct a distributed dense coding method, which completely depicts absolutely secure quantum communication between many to one party.

Probabilistic Quantum Teleportation via 3-Qubit Non-maximally Entangled GHZ State by Repeated Generalized Measurements

We propose a scheme of repeated generalized Bell state measurement (GBSM) for probabilistic quantum teleportation of single qubit state of a particle (say, 0) using 3-qubit non-maximally entangled (NME) GHZ state as a quantum channel. Alice keeps two qubits (say, 1 and 2) of the 3-qubit resource and the third qubit (say, 3) goes to Bob. Initially, Alice performs GBSM on qubits 0 and 1 which may lead to either success or failure. On obtaining success, Alice performs projective measurement on qubit 2 in the eigen basis of $\sigma_{x}$. Both these measurement outcomes are communicated to Bob classically, which helps him to perform a suitable unitary transformation on qubit 3 to recover the information state. On the other hand, if failure is obtained, the next attempt of GBSM is performed on qubits 0 and 2. This process of repeating GBSM on alternate pair of qubits may continue until perfect teleportation with unit fidelity is achieved. We have obtained analytical expressions for success probability up to three repetitions of GBSM. The success probability is shown to be a polynomial function of bipartite concurrence of the NME resource. The variation of success probability with the bipartite concurrence has been plotted which shows the convergence of success probability to unity with GBSM repetitions.

Multi-Party Quantum Secret Sharing Based on GHZ State

In this paper, we propose an efficient multi-party quantum secret sharing scheme based on GHZ entangled state. The participants in this scheme are divided into two groups, and share secrets as a group. There is no need to exchange any measurement information between the two groups, reducing the security problems caused by the communication process. Each participant holds one particle from each GHZ state; it can be found that the particles of each GHZ state are related after measuring them, and the eavesdropping detection can detect external attacks based on this characteristic. Furthermore, since the participants within the two groups encode the measured particles, they can recover the same secrets. Security analysis shows that the protocol can resist the intercept-and-resend attack and entanglement measurement attack, and the simulation results show that the probability of an external attacker being detected is proportional to the amount of information he can obtain. Compared with the existing protocols, this proposed protocol is more secure, has less quantum resources and is more practical.

Method for Quantum Denoisers Using Convolutional Neural Network.

In many applications of quantum information science, high-dimensional entanglement is needed. Quantum teleportation is used for transferring information from one place to another using Einstein–Podolsk–Rosen pairs (EPR) and two classical bits of communication in a channel. Since we cannot produce multiple copies of an unknown state for amplification, we will generate multiple EPR pairs. However, after the distribution of the EPR pairs, they will have decreased fidelity with the ideal EPR state. So, to maintain the quantum states and maximize the quantification of the entanglement without losing the strength of the states, we propose to denoise the channel for a few types of noise. We created a random noise source and filtered out the irrelevant information without affecting the relevant information encoded in the quantum states. The proposed model is used for successful denoising of GHZ states from spin flips and bit flip errors. Much of the research work is not carried out by using machine-language-based neural networks for noise-reduction in quantum channels. In this paper, we propose a denoiser called quantum denoiser CNQD, which uses a feedforward convolution neural network model. We tuned our model with highly entangled GHZ states with zero phases and phase between [0, ∏] mixed with different kinds of noise. Finally, the proposed model can be used for optimal quantum communication via noisy quantum channels using GHZ states.

Probabilistic quantum teleportation of shared quantum secret

Very recently, Lee et al. proposed a secure quantum teleportation protocol to transfer shared quantum secret between multiple parties in a network [Phys. Rev. Lett. 124 060501 (2020)]. This quantum network is encoded with a maximally entangled GHZ state. In this paper, we consider a partially entangled GHZ state as the entanglement channel, where it can achieve, probabilistically, unity fidelity transfer of the state. Two kinds of strategies are given. One arises when an auxiliary particle is introduced and a general evolution at any receiver’s location is then adopted. The other one involves performing a single generalized Bell-state measurement at the location of any sender. This could allow the receivers to recover the transmitted state with a certain probability, in which only the local Pauli operators are performed, instead of introducing an auxiliary particle. In addition, the successful probability is provided, which is determined by the degree of entanglement of the partially multipartite entangled state. Moreover, the proposed protocol is robust against the bit and phase flip noise.

The “ER = EPR” Conjecture and Generic Gravitational Properties: A Universal Topological Linking Model of the Correspondence between Tripartite Entanglement and Planck-Scale Wormholes

The “ER = EPR” conjecture, conceived by Maldacena and Susskind, is grounded on the notion that a gravitational theory in the bulk is dual to the corresponding quantum field theory on the boundary in accordance to the AdS/CFT correspondence. The conjecture pertains to the idea that Einstein-Rosen (ER) spacetime bridges and Einstein-Podolsky-Rosen (EPR) quantum entanglement may be considered as dually equivalent. Since ER bridges refer to the connectivity between black holes, the “ER = EPR” conjecture implies that black holes connected by ER bridges are entangled, and conversely, that entangled black holes are connected by ER bridges. However, the instance of the maximally entangled tripartite (GHZ) quantum state points to the necessity of devising a model of non-classical Planck scale ER bridges going beyond the standard description of these bridges in spacetime. Based on the topological structure of the maximally entangled GHZ state, we propose that a universal topological link, called the Borromean rings, furnishes a particular linking structure that is able to unravel the equavalence between entanglement and wormholes, and thus, to address the validity of the “ER = EPR” conjecture beyond the initial context of the AdS/CFT correspondence. As a consequence, we propose the explicit construction of distinguishable extensions of the smooth classical spacetime manifold taking place in the transition to the quantum gravity regime according to a naturally induced physical criterion of gravitational generic properties following from this intrinsic topological qualification of the “ER = EPR” conjecture.

Approximate bang-bang control assisted rapid switching feedback stabilization for stochastic qubit systems

For stochastic qubit systems under measurement feedback, an approximate bang-bang control assisted rapid switching control scheme with fewer switching times between the two subsets of state space is proposed in this paper. An eigenstate for single-qubit systems and any GHZ entangled state for multi-qubit systems are prepared successfully. In our control scheme, the state space is partitioned into two parts: a subset S1 containing the target state and its complementary set S2. On each subset, a Lyapunov function is selected and the corresponding control law is designed, where the control laws in S1 are of approximate bang-bang form and therefore can speed up the control process and the control laws in S2 ensure the strictly monotonic descent of the corresponding Lyapunov function and therefore can reduce the switching times. In particular, for multi-qubit systems with degenerate measured observables, we use two control channels to distinguish the target state from other isospectral eigenstates. By properly constructing the control Hamiltonians and using stochastic Lyapunov stability theory, we prove that the switching control laws in this paper render the system trajectory to switch at most twice on the boundary of S1 and S2 and to converge to the target state contained in S1 rapidly. Numerical simulations verify the effectiveness and rapidity of the proposed rapid control scheme.

A novel dynamic quantum secret sharing in high-dimensional quantum system

This paper proposed a novel dynamic quantum secret sharing protocol in high-dimensional quantum system. Via transmitting the particles circularly and local unitary operations, the dealer and all agents can share the multi-particle entangled GHZ state in high-dimensional quantum system. The proposed protocol allows a dealer to share the predetermined dits without directly distributing any piece of shares to agents. To recover the secrets, dealer and all agents only need to perform the single-particle measurement operation and then implement the simple modular arithmetic operation according to their corresponding measurement results. Besides, in the proposed protocol, only a little fraction of entangled GHZ states are employed for eavesdropping check instead of lots of decoy (or detecting) particles used in previous protocols. Since the protocol is designed in the high-dimensional quantum system, it makes our protocol have higher resource capacity and better security in detecting the illegal eavesdropper than former protocols designed in two-dimensional quantum system. Security analyses indicate that the proposed protocol is immune to general attacks of intercept-and-resend, entangle-and-measure, collusion, and revoked a dishonest agent. Furthermore, the efficiency of proposed DQSS protocol in noise environment is deduced through quantum fidelity. The obtained results indicate that the efficiency of proposed protocol decreases with the increase in channel noise parameter and it has a quite different efficiency in four types of noise, i.e., dit-flip, d-phase-flip, amplitude-damping and depolarizing.

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.

Bayesian Optimal Control of Greenberger-Horne-Zeilinger States in Rydberg Lattices

The ability to prepare nonclassical states in a robust manner is essential for quantum sensors beyond the standard quantum limit. We demonstrate that Bayesian optimal control is capable of finding control pulses that drive trapped Rydberg atoms into highly entangled Greenberger-Horne-Zeilinger states. The control sequences have a physically intuitive functionality based on the quasi-integrability of the Ising dynamics. They can be constructed in laboratory experiments, resulting in preparation times that scale very favorably with the system size.

Coherent transport of spin by adiabatic passage in quantum dot arrays

We introduce an adiabatic transfer protocol for spin states in large quantum dot arrays that is based on time-dependent modulation of the Heisenberg exchange interaction in the presence of a magnetic field gradient. We refer to this protocol as spin-CTAP (coherent transport by adiabatic passage) in analogy to a related protocol developed for charge state transfer in quantum dot arrays. The insensitivity of this adiabatic protocol to pulse imperfections has potential advantages for reading out extended spin qubit arrays. When the static exchange interaction varies across the array, a quantum-controlled version of spin-CTAP is possible, where the transfer process is conditional on the spin states in the middle of the array. This conditional operation can be used to generate N-qubit entangled GHZ states. Using a realistic noise model, we analyze the robustness of the spin-CTAP operations and find that high-fidelity (>95%) spin eigenstate transfer and GHZ state preparation is feasible in current devices.

Detection of genuine N-Qubit W state, GHZ state and Twin-Fock state via Quantum Fisher information

We study the entanglement detection of three classes of state in the white noise model: N-qubit W state, Greenberger-Horne-Zeilinger state and Twin-Fock state. Taking advantage of Quantum Fisher information, we first present how to witness M-separable W state (M≤N) in the ideal situation, and then derive the criteria for detecting genuine W state, Greenberger-Horne-Zeilinger state and Twin-Fock state in the noisy model. Meanwhile, the bounds for M-separable W state, k-partite entangled GHZ state and k-partite entangled Twin-Fock state are also investigated. The results show that with the increase of the number of particles, the requirement of visibility V for genuine multipartite entanglement becomes more and more stringent, while it is relaxed for partial entanglement. Specially, an extremum value of VWN=1/3 is found in the limit of large N.

Bidirectional Quantum Teleportation with GHZ States and EPR Pairs via Entanglement Swapping

A novel bidirectional quantum teleportation schema with GHZ states and EPR pairs via entanglement swapping is proposed. Two GHZ states and two pure EPR pairs build the quantum physical system. Within this quantum system, two entangled GHZ states serve for the quantum channel, and via the entanglement swapping the new entanglements are generated from the involved qbuits after the measurements are performed on both sides. CNOT operation, single qubit measurement and the appropriate unitary transformation are executed on each side, the pure EPR states are simultaneously teleported to each other. The presented protocol bears the economical and efficient advantage compared with the conventional protocols.

A controlled multi-party quantum dialogue protocol in the network

A controlled multi-party quantum dialogue scheme in the network based on high dimensional multi-qudit entangled GHZ states is proposed. In our scheme, a semi-honest third party (TP) is introduced to assist the implementation of the scheme. Each user can be thought of as one node in the network and is connected by classical links and quantum links. In the network, multiple users can exchange their private messages with each other simultaneously under the control of TP. With the aid of secure classical channels and quantum channels, the proposed protocol can be ensured with unconditionally security. In addition, our protocol requires single-qudit measurements only which weakens the hardware requirements of network nodes. Compared with previous quantum dialogue protocols, our scheme demonstrates a large operating flexibility.

Self-testing multipartite entangled states through projections onto two systems

Finding ways to test the behaviour of quantum devices is a timely enterprise, especially in light of the rapid development of quantum technologies. Device-independent self-testing is one desirable approach, as it makes minimal assumptions on the devices being tested. In this work, we address the question of which states can be self-tested. This has been answered recently in the bipartite case (Coladangelo et al 2017 Nat. Commun. 8 15485), while it is largely unexplored in the multipartite case, with only a few scattered results, using a variety of different methods: maximal violation of a Bell inequality, numerical SWAP method, stabiliser self-testing etc. In this work, we investigate a simple, and potentially unifying, approach: combining projections onto two-qubit spaces (projecting parties or degrees of freedom) and then using maximal violation of the tilted CHSH inequalities. This allows one to obtain self-testing of Dicke states and partially entangled GHZ states with two measurements per party, and also to recover self-testing of graph states (previously known only through stabiliser methods). Finally, we give the first self-test of a class of multipartite qudit states: we generalise the self-testing of partially entangled GHZ states by adapting techniques from (Coladangelo et al 2017 Nat. Commun. 8 15485), and show that all multipartite states which admit a Schmidt decomposition can be self-tested with few measurements.

Teleportation of two-qubit entangled state via non-maximally entangled GHZ state

Quantum teleportation is of significant meaning in quantum information. We study the probabilistic teleportation of unknown two-qubit entangled state utilizing non-maximally entangled GHZ state as quantum channel. We formulate it as unambiguous state discrimination problem and derive exact optimal POVM operator for maximizing the success probability of unambiguous state discrimination. Only one three-qubit POVM for the sender, one two-qubit unitary operation for the receiver and two cbits for outcome notification are required in this scheme. The unitary operation is given in the form of concise formula and average fidelity is calculated. We show that our scheme is applicable in the situation where the information of quantum channel is only available for the sender.

Cabello’s nonlocality for generalized three-qubit GHZ states

In this paper, we study Cabello’s nonlocality argument (CNA) for three-qubit systems configured in the generalized GHZ state. For this class of states, we show that CNA runs for almost all entangled ones, and that the maximum probability of success of CNA is 14 % (approx.), which is attained for the maximally entangled GHZ state. This maximum probability is slightly higher than that achieved for the standard Hardy’s nonlocality argument (HNA) for three qubits, namely, 12.5 %. In addition, we show that the success probability of both HNA and CNA for three-qubit systems can reach a maximum of $$50~\%$$ in the framework of generalized no-signaling theory.