Greenberger-Horne-Zeilinger Research Articles

Quantum entanglement creation based on quantum scattering in one-dimensional waveguides

We propose two heralded schemes for generating multipartite Greenberger-Horne-Zeilinger (GHZ) and W states. They are realized by photon scattering in one-dimensional waveguides, and the qubits are encoded in the degenerate ground states of the quantum emitters. In our schemes, errors caused by the system imperfections and faulty photon scattering can be turned into detectable photon loss, which is advantageous for quantum information science. That is, our schemes for creating GHZ and W states work in a heralded way. Moreover, the generation of the two entangled states can be theoretically generalized to many-qubit cases in a straightforward way. Our calculations show that both the success probabilities and fidelities of our two schemes are high with current technique on manipulating quantum dots in slow-light photonic crystal waveguides.

Complete hyperentangled Greenberger-Horne-Zeilinger state analysis for polarization and time-bin hyperentanglement

We present an efficient scheme for the complete analysis of hyperentangled Greenberger–Horne–Zeilinger (GHZ) state in polarization and time-bin degrees of freedom with two steps. Firstly, the polarization GHZ state is distinguished completely and nondestructively, resorting to the controlled phase flip (CPF) gate constructed by the cavity-assisted interaction. Subsequently, the time-bin GHZ state is analyzed by using the preserved polarization entanglement. With the help of CPF gate and self-assisted mechanism, our scheme can be directly generalized to the complete N-photon hyperentangled GHZ state analysis, and it may have potential applications in the hyperentanglement-based quantum communication.

Quantum-brachistochrone approach to the conversion from W to Greenberger-Horne-Zeilinger states for Rydberg-atom qubits

Using the quantum-brachistochrone formalism, we address the problem of finding the fastest possible (time-optimal) deterministic conversion between $W$ and Greenberger-Horne-Zeilinger (GHZ) states in a system of three identical and equidistant neutral atoms that are acted upon by four external laser pulses. Assuming that all four pulses are close to being resonant with the same internal (atomic) transition---the one between the atomic ground state and a high-lying Rydberg state---each atom can be treated as an effective two-level system ($gr$-type qubit). Starting from an effective system Hamiltonian, which is valid in the Rydberg-blockade regime and defined on a four-state manifold, we derive the quantum-brachistochrone equations pertaining to the fastest possible $W$-to-GHZ state conversion. By numerically solving these equations, we determine the time-dependent Rabi frequencies of external laser pulses that correspond to the time-optimal state conversion. In particular, we show that the shortest possible $W$-to-GHZ state-conversion time is given by ${T}_{\text{QB}}=6.8\phantom{\rule{0.222222em}{0ex}}\ensuremath{\hbar}/E$, where $E$ is the total laser-pulse energy used, this last time being significantly shorter than the state-conversion times previously found using a dynamical-symmetry-based approach [${T}_{\text{DS}}=(1.33\ensuremath{-}1.66)\phantom{\rule{0.222222em}{0ex}}{T}_{\text{QB}}$].

Dynamical generation of chiral W and Greenberger-Horne-Zeilinger states in laser-controlled Rydberg-atom trimers

Motivated by the significantly improved scalability of optically trapped neutral-atom systems, extensive efforts have been devoted in recent years to quantum-state engineering in Rydberg-atom ensembles. Here we investigate the problem of engineering generalized (``twisted'') $W$ states, as well as Greenberger-Horne-Zeilinger (GHZ) states, in the strongly interacting regime of a neutral-atom system. We assume that each atom in the envisioned system initially resides in its ground state and is subject to several external laser pulses that are close to being resonant with the same internal atomic transition. In particular, in the special case of a three-atom system (Rydberg-atom trimer) we determine configurations of field alignments and atomic positions that enable the realization of chiral $W$ states---a special type of twisted three-qubit $W$ states of interest for implementing noiseless-subsystem qubit encoding. Using chiral $W$ states as an example we also address the problem of deterministically converting twisted $W$ states into their GHZ counterparts in the same three-atom system, thus significantly generalizing recent works that involve only ordinary $W$ states. We show that starting from twisted---rather than ordinary---$W$ states is equivalent to renormalizing downward the relevant Rabi frequencies. While this leads to somewhat longer state-conversion times, we also demonstrate that those times are at least two orders of magnitude shorter than typical lifetimes of relevant Rydberg states.

Complete analysis of the maximally hyperentangled state via the weak cross-Kerr nonlinearity

We present a simple method for the complete analysis of the maximally hyperentangled state in polarization and spatial-mode degrees of freedom assisted by the weak cross-Kerr nonlinearity. Our method can not only be used for two-photon hyperentangled Bell state analysis and three-photon hyperentangled Greenberger–Horne–Zeilinger (GHZ) state analysis, but is also suitable for N -photon hyperentangled GHZ state analysis. In our protocols, the bit information of hyperentanglement is read out via the nonlinear interaction, and the phase information is obtained by using linear optical element and single photon detector. This approach is achievable with the current technology, and it will be useful for practical high-capacity quantum communication schemes.

Entanglement Property of Tripartite GHZ State in Different Accelerating Observer Frames.

According to the single-mode approximation applied to two different mo des, each associated with different uniformly accelerating reference frames, we present analytical expression of the Minkowski states for both the ground and first excited states. Applying such an approximation, we study the entanglement property of Bell and Greenberger–Horne–Zeilinger (GHZ) states formed by such states. The corresponding entanglement properties are described by studying negativity and von Neumann entropy. The degree of entanglement will be degraded when the acceleration parameters increase. We find that the greater the number of particles in the entangled system, the more stable the system that is studied by the von Neumann entropy. The present results will be reduced to those in the case of the uniformly accelerating reference frame.

Practical multipartite entanglement distribution in noisy channels

Entanglement among multiple parties is vital for practical quantum information applications. As two kinds of typical multipartite entangled state, the W and Greenberger-Horne-Zeilinger (GHZ) states have attracted a lot of attention. In this paper, we propose two practical linear optical schemes for multipartite entanglement distribution in noisy channels. Using the time-bin or spatial-mode degree of freedom (DoF) encoding, the influence of the noise will be eliminated and perfect W or GHZ state can be achieved among different nodes in a deterministic way. Moreover, we construct quantum circuits, which can be implemented with current technology. These results contribute to long-distance quantum communication both in theoretical and experimental points of view.

All-Photonic Architecture for Scalable Quantum Computing with Greenberger-Horne-Zeilinger States

Linear optical quantum computing is beset by the lack of deterministic entangling operations besides photon loss. Motivated by advancements at the experimental front in deterministic generation of various kinds of multiphoton entangled states, we propose an architecture for linear-optical quantum computing that harnesses the availability of three-photon Greenberger-Horne-Zeilinger (GHZ) states. Our architecture and its subvariants use polarized photons in GHZ states, polarization beam splitters, delay lines, optical switches and on-off detectors. We concatenate topological quantum error correction code with three-qubit repetition codes and estimate that our architecture can tolerate remarkably high photon-loss rate of $11.5 \%$; this makes a drastic change that is at least an order higher than those of known proposals. Further, considering three-photon GHZ states as resources, we estimate the resource overheads to perform gate operations with an accuracy of $10^{-6}~(10^{-15})$ to be $2.0\times10^6~(5.6\times10^7)$. Compared to other all-photonic schemes, our architecture is also resource-efficient. In addition, the resource overhead can be even further improved if larger GHZ states are available. Given its striking enhancement in the photon loss threshold and the recent progress in generating multiphoton entanglement, our scheme will make scalable photonic quantum computing a step closer to reality.

When Greenberger, Horne and Zeilinger Meet Wigner’s Friend

A general argument is presented against relativistic, unitary, single-outcome quantum mechanics. This is achieved by combining the Wigner’s Friend thought experiment with measurements on a Greenberger–Horne–Zeilinger (GHZ) state, and describing the evolution of the quantum state in various inertial frames. Assuming unitary quantum mechanics and single outcomes, the result is that the Born rule must be violated in some inertial frame: in that frame, outcomes are obtained for which no corresponding term exists in the pre-measurement wavefunction.

Single-step implementation of a hybrid controlled-not gate with one superconducting qubit simultaneously controlling multiple target cat-state qubits

Hybrid quantum gates have recently drawn considerable attention. They play significant roles in connecting quantum information processors with qubits of different encoding and have important applications in the transmission of quantum states between a quantum processor and a quantum memory. In this work, we propose a single-step implementation of a multi-target-qubit controlled-NOT gate with one superconducting (SC) qubit simultaneously controlling $n$ target cat-state qubits. In this proposal, the gate is implemented with $n$ microwave cavities coupled to a three-level SC qutrit. The two logic states of the control SC qubit are represented by the two lowest levels of the qutrit, while the two logic states of each target cat-state qubit are represented by two quasi-orthogonal cat states of a microwave cavity. This proposal operates essentially through the dispersive coupling of each cavity with the qutrit. The gate realization is quite simple because it requires only a single-step operation. There is no need of applying a classical pulse or performing a measurement. The gate operation time is independent of the number of target qubits, thus it does not increase as the number of target qubits increases. Moreover, because the third higher energy level of the qutrit is not occupied during the gate operation, decoherence from the qutrit is greatly suppressed. As an application of this hybrid multi-target-qubit gate, we further discuss the generation of a hybrid Greenberger-Horne-Zeilinger (GHZ) entangled state of SC qubits and cat-state qubits. As an example, we numerically analyze the experimental feasibility of generating a hybrid GHZ state of one SC qubit and three cat-state qubits within present circuit QED technology.

Multi-User Measurement-Device-Independent Quantum Key Distribution Based on GHZ Entangled State.

As a multi-particle entangled state, the Greenberger–Horne–Zeilinger (GHZ) state plays an important role in quantum theory and applications. In this study, we propose a flexible multi-user measurement-device-independent quantum key distribution (MDI-QKD) scheme based on a GHZ entangled state. Our scheme can distribute quantum keys among multiple users while being resistant to detection attacks. Our simulation results show that the secure distance between each user and the measurement device can reach more than 280 km while reducing the complexity of the quantum network. Additionally, we propose a method to expand our scheme to a multi-node with multi-user network, which can further enhance the communication distance between the users at different nodes.

Locality of three-qubit Greenberger-Horne-Zeilinger-symmetric states

The hierarchy of nonlocality and entanglement in multipartite systems is one of the fundamental problems in quantum physics. We study this topic in three-qubit systems considering the entanglement classification of stochastic local operations and classical communication (SLOCC). The equivalence under SLOCC divides threequbit states into separable, biseparable, W, and Greenberger-Horne-Zeilinger (GHZ) classes. The W and GHZ are two subclasses of genuine tripartite entanglement.We adopt the family of GHZ-symmetric states as a research subject, which share the symmetries of the GHZ state and have a complete characterization of SLOCC classes. In the biseparable region (with bipartite entanglement), there exist GHZ-symmetric states that are found to be fully local. In addition, there are bilocal states in both theW and GHZ classes. That is, neither of the subclasses of genuine tripartite entanglement can ensure genuinely tripartite nonlocality.

Generation of the GHZ and the W State in a Series of Rydberg Atoms Trapped in Optical Lattices

In this work, we present a quantum control methodology to create multi-particle entangled states of two typical classes, the W and the Greenberger-Horne-Zeilinger (GHZ). The methodology is demonstrated on a generation of the W and GHZ three-atomic states via the mechanism of two-photon passage using overlapping chirped pulses and the interplay of the chirp rate, the one-photon and two-photon detuning, the peak Rabi frequency and the strength of the Rydberg-Rydberg interactions. A chain of N alkali 87Rb atoms in an optical lattice interacting with two laser fields is modeled within a semi-classical theory. The strategy to create different classes of multiparticle entangled states was revealed through performed dressed state analysis

Double-server blind quantum computation based on the GHZ state

We propose a new double-server blind quantum computation protocol based on the Greenberger–Horne–Zeilinger (GHZ) state. In this protocol, the correlation of the GHZ triplets has been utilized to deal with the existing double-server blind quantum computation protocol’s limitation, in which two servers cannot communicate with each other. Moreover, although the two servers in this protocol can obtain different parts of the particles in different GHZ states, they cannot match every GHZ state particle correctly, and this is because the positions of the particles are kept secret. Therefore, the protocol is still secure, in which two servers can communicate with each other. Furthermore, the client can make authentication requests to the trusted center, determining if the first server is honest or not by calculating measurements of part of the GHZ particles. After analyzing the security of the protocol, the protocol is found to be unconditionally secure.

Quantifying tripartite spatial and energy-time entanglement in nonlinear optics

In this work, we provide a means to quantify genuine tripartite entanglement in arbitrary (pure and mixed) continuous-variable states as measured by the Tripartite Entanglement of formation -- a resource-based measure quantifying genuine multi-partite entanglement in units of elementary Greenberger-Horne-Zeilinger (GHZ) states called gebits. Furthermore, we predict its effectiveness in quantifying the tripartite spatial and energy-time entanglement in photon triplets generated in cascaded spontaneous parametric down-conversion (SPDC), and find that ordinary nonlinear optics can be a substantial resource of tripartite entanglement.

Control power of high-dimensional controlled dense coding

We quantitatively analyze and evaluate the control power in a high-dimensional noisy quantum channel for transmitting classical information. We calculate the control power of the controlled dense coding scheme in a four-dimensional extended Greenberger-Horne-Zeilinger (GHZ) class state channel. Different from controlled teleportation, there is no tradeoff between the control power and the classical capacity of the optimal four-dimensional GHZ state quantum channel. Only when the channel is noisy and the sender is allowed to gain some control authority can the tradeoff between the control power and the classical capacity be activated, and the overall control power for transmitting classical information will be enhanced by reducing the classical capacity of the high-dimensional quantum channel. This noise induced characteristic is very different from that of transmitting quantum information, and it may provide new ideas and methods to develop the resource theory of quantum channels.

Entanglement generation in a quantum network at distance-independent rate

AbstractWe develop a protocol for entanglement generation in the quantum internet that allows a repeater node to use n-qubit Greenberger-Horne-Zeilinger (GHZ) projective measurements that can fuse n successfully entangled links, i.e., two-qubit entangled Bell pairs shared across n network edges, incident at that node. Implementing n-fusion, for n ≥ 3, is in principle not much harder than 2-fusions (Bell-basis measurements) in solid-state qubit memories. If we allow even 3-fusions at the nodes, we find—by developing a connection to a modified version of the site-bond percolation problem—that despite lossy (hence probabilistic) link-level entanglement generation, and probabilistic success of the fusion measurements at nodes, one can generate entanglement between end parties Alice and Bob at a rate that stays constant as the distance between them increases. We prove that this powerful network property is not possible to attain with any quantum networking protocol built with Bell measurements and multiplexing alone. We also design a two-party quantum key distribution protocol that converts the entangled states shared between two nodes into a shared secret, at a key generation rate that is independent of the distance between the two parties.

Multi-qubit entanglement and algorithms on a neutral-atom quantum computer.

Gate-model quantum computers promise to solve currently intractable computational problems if they can be operated at scale with long coherence times and high-fidelity logic. Neutral-atom hyperfine qubits provide inherent scalability owing to their identical characteristics, long coherence times and ability to be trapped in dense, multidimensional arrays1. Combined with the strong entangling interactions provided by Rydberg states2-4, all the necessary characteristics for quantum computation are available. Here we demonstrate several quantum algorithms on a programmable gate-model neutral-atom quantum computer in an architecture based on individual addressing of single atoms with tightly focused optical beams scanned across a two-dimensional array of qubits. Preparation of entangled Greenberger-Horne-Zeilinger (GHZ) states5 with up to six qubits, quantum phase estimation for a chemistry problem6 and the quantum approximate optimization algorithm (QAOA)7 for the maximum cut (MaxCut) graph problem are demonstrated. These results highlight the emergent capability of neutral-atom qubit arrays for universal, programmable quantum computation, as well as preparation of non-classical states of use for quantum-enhanced sensing.

Self-testing of multipartite Greenberger-Horne-Zeilinger states of arbitrary local dimension with arbitrary number of measurements per party

Device independent certification schemes have gained a lot of interest lately, not only for their applications in quantum information tasks but also their implications towards foundations of quantum theory. The strongest form of device independent certification, known as self-testing, often requires for a Bell inequality to be maximally violated by specific quantum states and measurements. In this work, using the techniques developed recently in [S. Sarkar et al., npj Quantum Inf. 7, 151 (2021)], we provide the first self-testing scheme for the multipartite Greenberger-Horne-Zeilinger (GHZ) states of arbitrary local dimension that does not rely on self-testing results for qubit states and that exploits the minimal number of two measurements per party. This makes our results interesting as far as practical implementation of device-independent certification methods is concerned. Our self-testing statement relies on maximal violation of a Bell inequality proposed recently in [R. Augusiak et al., New J. Phys. 21, 113001 (2019)].

Quantum-Memory-Enhanced Preparation of Nonlocal Graph States.

Graph states are an important class of multipartite entangled states. Previous experimental generation of graph states and in particular the Greenberger-Horne-Zeilinger (GHZ) states in linear optics quantum information schemes is subjected to an exponential decay in efficiency versus the system size, which limits its large-scale applications in quantum networks. Here, we demonstrate an efficient scheme to prepare graph states with only a polynomial overhead using long-lived atomic quantum memories. We generate atom-photon entangled states in two atomic ensembles asynchronously, retrieve the stored atomic excitations only when both sides succeed, and further project them into a four-photon GHZ state. Wemeasure the fidelity of this GHZ state and further demonstrate its applications in the violation of Bell-type inequalities and in quantum cryptography. Our work demonstrates the prospect of efficient generation of multipartite entangled states in large-scale distributed systems with applications in quantum information processing and metrology.