GHZ States Research Articles

GHZ protocols enhance frequency metrology despite spontaneous decay.

The use of correlated states and measurements promises improvements in the accuracy of frequency metrology and the stability of atomic clocks. However, developing strategies robust against dominant noise processes remains challenging. We address the issue of decoherence due to spontaneous decay and show that Greenberger-Horne-Zeilinger (GHZ) states, in conjunction with a correlated measurement and nonlinear estimation strategy, achieve gains of up to 2.25 decibel, comparable to fundamental bounds for up to about 80 atoms in the presence of decoherence. This result is unexpected because GHZ states do not provide any enhancement under dephasing due to white frequency noise compared to the standard quantum limit of uncorrelated states. The gain arises from a veto signal, which allows for the detection and mitigation of errors caused by spontaneous emission events. Through comprehensive Monte Carlo simulations of atomic clocks, we demonstrate the robustness of the GHZ protocol.

Introduction to Bell’s Inequality in Quantum Mechanics

A pedagogical introduction to Bell’s inequality in Quantum Mechanics is presented. Several examples, ranging from spin 1/2 to coherent and squeezed states are worked out. The generalization to Mermin’s inequalities and to GHZ states is also outlined.

Locally distinguishing genuinely nonlocal sets with entanglement resource

A set of orthogonal product states is deemed genuinely nonlocal if they remain locally indistinguishable under any bipartition. In this paper, we first construct a genuinely nonlocal product basis B I(5, 3) in C5⨂C5⨂C5 using a set of nonlocal product states in C3⨂C4 . Then, we obtain a genuinely nonlocal product basis B II(5, 3) by replacing certain states in B I(5, 3) with some superposition states. We achieve perfect discrimination of the constructed genuinely nonlocal product basis, separately employing two EPR states and one GHZ state. Our protocol is more efficient than quantum teleportation.

Creating and controlling global Greenberger-Horne-Zeilinger entanglement on quantum processors

Greenberger-Horne-Zeilinger (GHZ) states, also known as two-component Schrödinger cats, play vital roles in the foundation of quantum physics and the potential quantum applications. Enlargement in size and coherent control of GHZ states are both crucial for harnessing entanglement in advanced computational tasks with practical advantages, which unfortunately pose tremendous challenges as GHZ states are vulnerable to noise. Here we propose a general strategy for creating, preserving, and manipulating large-scale GHZ entanglement, and demonstrate a series of experiments underlined by high-fidelity digital quantum circuits. For initialization, we employ a scalable protocol to create genuinely entangled GHZ states with up to 60 qubits, almost doubling the previous size record. For protection, we take a different perspective on discrete time crystals (DTCs), originally for exploring exotic nonequilibrium quantum matters, and embed a GHZ state into the eigenstates of a tailor-made cat scar DTC to extend its lifetime. For manipulation, we switch the DTC eigenstates with in-situ quantum gates to modify the effectiveness of the GHZ protection. Our findings establish a viable path towards coherent operations on large-scale entanglement, and further highlight superconducting processors as a promising platform to explore nonequilibrium quantum matters and emerging applications.

Multi-qubit gates and Schrödinger cat states in an optical clock.

Many-particle entanglement is a key resource for achieving the fundamental precision limits of a quantum sensor1. Optical atomic clocks2, the current state of the art in frequency precision, are a rapidly emerging area of focus for entanglement-enhanced metrology3-6. Augmenting tweezer-based clocks featuring microscopic control and detection7-10 with the high-fidelity entangling gates developed for atom-array information processing11,12 offers a promising route towards making use of highly entangled quantum states for improved optical clocks. Here we develop and use a family of multi-qubit Rydberg gates to generate Schrödinger cat states of the Greenberger-Horne-Zeilinger (GHZ) type with up to nine optical clock qubits in a programmable atom array. In an atom-laser comparison at sufficiently short dark times, we demonstrate a fractional frequency instability below the standard quantum limit (SQL) using GHZ states of up to four qubits. However, because of their reduced dynamic range, GHZ states of a single size fail to improve the achievable clock precision at the optimal dark time compared with unentangled atoms13. Towards overcoming this hurdle, we simultaneously prepare a cascade of varying-size GHZ states to perform unambiguous phase estimation over an extended interval14-17. These results demonstrate key building blocks for approaching Heisenberg-limited scaling of optical atomic clock precision.

Universal quantum operations and ancilla-based read-out for tweezer clocks

Enhancing the precision of measurements by harnessing entanglement is a long-sought goal in quantum metrology1,2. Yet attaining the best sensitivity allowed by quantum theory in the presence of noise is an outstanding challenge, requiring optimal probe-state generation and read-out strategies3–7. Neutral-atom optical clocks8, which are the leading systems for measuring time, have shown recent progress in terms of entanglement generation9–11 but at present lack the control capabilities for realizing such schemes. Here we show universal quantum operations and ancilla-based read-out for ultranarrow optical transitions of neutral atoms. Our demonstration in a tweezer clock platform9,12–16 enables a circuit-based approach to quantum metrology with neutral-atom optical clocks. To this end, we demonstrate two-qubit entangling gates with 99.62(3)% fidelity—averaged over symmetric input states—through Rydberg interactions15,17,18 and dynamical connectivity19 for optical clock qubits, which we combine with local addressing16 to implement universally programmable quantum circuits. Using this approach, we generate a near-optimal entangled probe state1,4, a cascade of Greenberger–Horne–Zeilinger states of different sizes, and perform a dual-quadrature5 Greenberger–Horne–Zeilinger read-out. We also show repeated fast phase detection with non-destructive conditional reset of clock qubits and minimal dead time between repetitions by implementing ancilla-based quantum logic spectroscopy20 for neutral atoms. Finally, we extend this to multi-qubit parity checks and measurement-based, heralded, Bell-state preparation21–24. Our work lays the foundation for hybrid processor–clock devices with neutral atoms and more generally points to a future of practical applications for quantum processors linked with quantum sensors25.

Bosonic and fermionic coherence of N-partite states in the background of a dilaton black hole

We study the N-partite coherences of GHZ and W states for free bosonic and fermionic fields when any n observers hover near the event horizon of a Garfinkle-Horowitz-Strominger (GHS) dilaton black hole. We derive the more general analytical expressions for N-partite coherence, encompassing both physically accessible and inaccessible coherences in the context of the dilaton black hole. It has been found that the coherence of the bosonic field is greater than that of the fermionic field, while the entanglement of the fermionic field is greater than that of the bosonic field in dilaton spacetime. Additionally, the coherence of the W state is greater than that of the GHZ state, whereas the entanglement of the GHZ state is greater than that of the W state in curved spacetime. These results suggest that we should utilize suitable quantum resources and different types of particles for relativistic quantum information tasks.

A Novel Authenticated Quantum Anonymous Secret Sharing for Classical and Quantum Information

AbstractAnonymous secret sharing (ASS) is an essential cryptographic concept that facilitates the sharing and reconstruction of secret information while safeguarding the identity of the involved secret receivers, which has broad applications in key management, data backup, and distributed systems. In this study, a novel authenticated quantum anonymous secret sharing (QASS) protocol that emphasizes information privacy and identity anonymity protection is proposed. Employing ‐level multipartite GHZ states as a quantum resource, one‐sided anonymous entanglement (AE) is innovatively established between the dealer and anonymous receivers, enabling the dealer to distribute a random share of secret information. Additionally, by establishing a one‐sided AE between anonymous receivers and restorer, the restorer can securely collect and reconstruct the secret information using quantum teleportation (QT). Rigorous security analysis demonstrates that protocol can resist attacks from active adversaries and potentially dishonest users. Quantum experiments on IBM Qiskit validate the correctness and feasibility of the proposed QASS protocol. This work contributes to the advancement of quantum anonymous communication, addressing the requirements for information privacy and identity anonymity in practical application environments.

An exponential reduction in training data sizes for machine learning derived entanglement witnesses

Abstract We propose a support vector machine (SVM) based approach for generating an entanglement witness that requires exponentially less training data than previously proposed methods. SVMs generate hyperplanes represented by a weighted sum of expectation values of local observables whose coefficients are optimized to sum to a positive number for all separable states and a negative number for as many entangled states as possible near a specific target state. Previous SVM-based approaches for entanglement witness generation used large amounts of randomly generated separable states to perform training, a task with considerable computational overhead. Here, we propose a method for orienting the witness hyperplane using only the significantly smaller set of states consisting of the eigenstates of the generalized Pauli matrices and a set of entangled states near the target entangled states. With the orientation of the witness hyperplane set by the SVM, we tune the plane's placement using a differential program that ensures perfect classification accuracy on a limited test set as well as maximal noise tolerance. For \(N\) qubits, the SVM portion of this approach requires only \(O(6^N)\) training states, whereas an existing method needs \(O(2^{4^N})\). We use this method to construct witnesses of 4 and 5 qubit GHZ states with coefficients agreeing with stabilizer formalism witnesses to within 3.7 percent and 1 percent, respectively. We also use the same training states to generate novel 4 and 5 qubit W state witnesses. Finally, we computationally verify these witnesses on small test sets and propose methods for further verification.

Error‐Heralded and Deterministic Interconversion Between W State and Greenberger–Horne–Zeilinger State with Faithful Quantum Gates in Decoherence‐Free‐Subspace

Error‐Heralded and Deterministic Interconversion Between W State and Greenberger–Horne–Zeilinger State with Faithful Quantum Gates in Decoherence‐Free‐Subspace

Verification of quantum networks using the GHZ paradox

The Greenberger–Horne–Zeilinger (GHZ) paradox shows that it is possible to create a multipartite state involving three or more particles in which the measurement outcomes of the particles are correlated in a way that cannot be explained by classical physics. We extend it to witness quantum networks. We first extend the GHZ paradox to simultaneously verify the GHZ state and Einstein–Podolsky–Rosen states on triangle networks. We then extend the GHZ paradox to witness the entanglement of chain networks consisting of multiple GHZ states. All the present results are robust against the noise.

Quantum multicast based on joint remote state preparation

Effective propagation of information among multiple users is the purpose of realizing large-scale quantum communication networks. In this paper, multicast protocols for any single, two and three qubits with real amplitude and complex phase information are presented. They were realized using a composite of Greenberger–Horne–Zeilinger states as shared channels. Joint remote state preparation was the main method for completing quantum multicast. At the same time, quantum state tomography of the schemes was carried out on the IBM Quantum platform. The obtained states were compared with the target states by fidelity. The analysis of communication efficiency and noise effects shows that our protocol has advantages in the case of complex coefficients.

Characterization of entanglement on superconducting quantum computers of up to 414 qubits

As quantum technology advances and the size of quantum computers grow, it becomes increasingly important to understand the extent of quality in the devices. As large-scale entanglement is a quantum resource crucial for achieving quantum advantage, the challenge in its generation makes it a valuable benchmark for measuring the performance of universal quantum devices. In this paper, we study entanglement in Greenberger-Horne-Zeilinger (GHZ) and graph states prepared on the range of IBM Quantum devices. We generate GHZ states and investigate their coherence times with respect to state size and dynamical decoupling techniques. A GHZ fidelity of 0.519±0.014 is measured on a 32-qubit GHZ state, certifying its genuine multipartite entanglement (GME). We show a substantial improvement in GHZ decoherence rates for a seven-qubit GHZ state after implementing dynamical decoupling, and observe a linear trend in the decoherence rate of α=(7.13N+5.54)×10−3µs−1 for up to N=15 qubits, confirming the absence of superdecoherence. Additionally, we prepare and characterize fully bipartite entangled native-graph states on 22 superconducting quantum devices with qubit counts as high as 414 qubits, all active qubits of the 433-qubit IBM Osprey device. Analysis of the decay of two-qubit entanglement within the prepared states shows suppression of coherent noise signals with the implementation of dynamical decoupling techniques. Additionally, we observe that the entanglement in some qubit pairs oscillates over time, which is likely caused by residual ZZ-interactions. Characterizing entanglement in native-graph states, along with detecting entanglement oscillations, can be an effective approach to low-level device benchmarking that encapsulates two-qubit error rates along with additional sources of noise, with possible applications to quantum circuit compilation. We develop several tools to automate the preparation and entanglement characterization of GHZ and graph states. In particular, a method to characterize graph state bipartite entanglement using just 36 circuits, constant with respect to the number of qubits. Published by the American Physical Society 2024

The iteration formula of (n, 2, d) full-correlated multi-component Bell function and its applications

No matter for a scientific or technological reason, constructing Bell inequalities for multi-partite and high-dimensional systems is a significant task. The Mermin-Ardehali-Belinskiĭ-Klyshko (MABK) inequality is expressed in the form of iteration formula and correlation functions, and is the generalization of the Clauser-Horne-Shimony-Holt (CHSH) inequality to multi-partite cases. In the sense of detecting the nonlocality of the noisy maximally entangled states with the most white noises for the corresponding quantum system, the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality, expressed in the joint probabilities form, is the high-dimensional analogue of the Clauser-Horne (CH) inequalities on joint probabilities. In the sense of detecting the nonlocality of the noisy Greenberger-Horne-Zeilinger(GHZ) states with the most white noises for the n-qudit system, it is a challenging task to construct the multi-partite analogue of the CGLMP inequality with iteration formula and correlation functions. In this paper, we generalize the multi-component correlation functions [Phys. Rev. A 71, 032 107 (2005)] for bipartite d-dimensional systems to n-partite d-dimensional ones, introduce the general full-correlated multi-component Bell function In,d , and construct the corresponding Bell inequality. By this way, we can reproduce both the CGLMP inequality and the Bell inequality in [Phys. Rev. A 71, 032 107 (2005)] for the case n = 2, and the MABK inequality for the case d = 2. Inspired by the iteration formula form of the MABK inequality, we prove that for prime d the general Bell function In,d can be reformulated by iterating two Bell functions In−1,d . As applications, for prime d, confined to the unbiased symmetric (d × 2)-port beam splitters and the noisy n-qudit GHZ states, we recover the most robust Bell inequalities for small n and d, such as for the (3, 2, 3), (4, 2, 3), (5, 2, 3), and (3, 2, 5) Bell scenarios, with the iteration formula and the most robust Bell inequalities for the (2, 2, d) scenario. This implies that the iteration formula is an efficient way of constructing the multi-partite analogues of the CGLMP inequality with correlation functions. In addition, we also give some new Bell inequalities with the same robustness but inequivalent to the known ones.

Comment and improvement on the “semi-quantum ring signature protocol based on multi-particle GHZ state”

Comment and improvement on the “semi-quantum ring signature protocol based on multi-particle GHZ state”

Quantum broadcasting of the generalized GHZ state: quantum noise analysis using quantum state tomography via IBMQ simulation

This study focuses on the challenges posed by quantum noise to communication protocols, with a particular emphasis on the vulnerabilities of current quantum broadcast protocols. The research employs the generalized GHZ state, known for its multipartite entangled cluster state with real-value coefficients, as a diagnostic tool to understand and address the impact of quantum noise on transmitted information. Implementing two novel controlled quantum broadcast schemes on the IBM Quantum (IBMQ) Experience platform, using the Qiskit library and the QASM simulator, the investigation evaluates the effects of four different types of quantum noise through Kraus operator models. A notable aspect of the study is the pioneering use of quantum state tomography for a comprehensive analysis of quantum noise effects, providing novel insights into the resilience of quantum communication protocols.

The silicon vacancy centers in SiC: determination of intrinsic spin dynamics for integrated quantum photonics

The negatively charged silicon vacancy center (VSi−\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\rm{V}}}_{{\\rm{Si}}}^{-}$$\\end{document}) in silicon carbide (SiC) is an emerging color center for quantum technology covering quantum sensing, communication, and computing. Yet, limited information currently available on the internal spin-optical dynamics of these color centers prevents us from achieving the optimal operation conditions and reaching the maximum performance especially when integrated within quantum photonics. Here, we establish all the relevant intrinsic spin dynamics of the VSi−\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\rm{V}}}_{{\\rm{Si}}}^{-}$$\\end{document} center at cubic lattice site (V2) in 4H-SiC by an in-depth electronic fine structure modeling including the intersystem-crossing and deshelving mechanisms. With carefully designed spin-dependent measurements, we obtain all the previously unknown spin-selective radiative and non-radiative decay rates. To showcase the relevance of our work for integrated quantum photonics, we use the obtained rates to propose a realistic implementation of time-bin entangled multi-photon GHZ and cluster state generation. We find that up to three-photon GHZ or cluster states are readily within reach using the existing nanophotonic cavity technology.

Fast generation of GHZ state with Rydberg superatom by transitionless quantum driving

Fast generation of GHZ state with Rydberg superatom by transitionless quantum driving

Shortcut to multipartite entanglement generation: A graph approach to boson subtractions

We propose a graph method for systematically searching for schemes that can generate multipartite entanglement in linear bosonic systems with heralding. While heralded entanglement generation offers more tolerable schemes for quantum tasks than postselected ones, it is generally more challenging to find appropriate circuits for multipartite systems. We show that our graph mapping from boson subtractions provides handy tactics to overcome the limitations in circuit designs. Within our graph framework, we identify enhanced schemes for qubit N-partite GHZ, W, and the superposition of N = 3 GHZ and W states. Furthermore, we have found a qudit N-partite GHZ state generation scheme, which requires substantially fewer particles than previous proposals. These results demonstrate the power of our approach in discovering optimized solutions for the generation of intricate heralded entangled states. We expect our method to serve as a promising tool in generating diverse entanglement.

Quantum states generation and manipulation in a programmable silicon-photonic four-qubit system with high-fidelity and purity

We present a programmable silicon photonic four-qubit integrated circuit for the generation and manipulation of diverse quantum states. The silicon photonic chip integrates photon-pair sources, pump-reducing filters, wavelength-division-multiplexing filters, Mach–Zehnder interferometer switches, and single-qubit arbitrary gates, enabling versatile state preparation and tomography. We measure Hong–Ou–Mandel interference with an impressive 98% visibility using four-photon coincidence, laying the foundation for high-purity qubits. Our analysis involves estimating the fidelity and purity of distinct quantum states through maximum-likelihood estimation applied to tomographic measurements. In our experimental results, we showcase the following achievements: a heralded single qubit achieving 98.2% fidelity and 98.3% purity, a Bell state reaching 95.2% fidelity and 94.8% purity, and a four-qubit system with two simultaneous Bell states exhibiting 87.4% fidelity and 84.6% purity. Finally, a four-qubit Greenberger–Horne–Zeilinger (GHZ) state demonstrates 85.4% fidelity and 81.7% purity. In addition, we certify the entanglement of the four-photon GHZ state through Bell’s inequality violations and a negative entanglement witness.