GHZ States Research Articles

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.

Ab-initio tree-tensor-network digital twin for quantum computer benchmarking in 2D

Large-scale numerical simulations of the Hamiltonian dynamics of a noisy intermediate scale quantum computer—a digital twin—could play a major role in developing efficient and scalable strategies for tuning quantum algorithms for specific hardware. Via a two-dimensional tensor network digital twin of a Rydberg atom quantum computer, we demonstrate the feasibility of such a program. In particular, we quantify the effects of gate crosstalks induced by the van der Waals interaction between Rydberg atoms: according to an 8×8 digital twin simulation based on the current state-of-the-art experimental setups, the initial state of a five-qubit repetition code can be prepared with a high fidelity, a first indicator for a compatibility with fault-tolerant quantum computing. The preparation of a 64-qubit Greenberger–Horne–Zeilinger state with about 700 gates yields a 99.9% fidelity in a closed system while achieving a speedup of 35% via parallelization.

The maximal violation of the Svetlichny inequality for “X” states and the extended GHZ states

For a quantum system, violation of a Svetlichny inequality indicates the existence of genuine nonlocality. Through the same mathematical analysis approach, we derive the analytical expressions of the maximal violation of the Svetlichny inequality for certain three-qubit pure states and mixed “X” states. These pure states represented in the five-parameter form belong to extended GHZ states. It is convenient to use the obtained expression to distinguish the genuine nonlocal states in these states. We also obtain the analytical expression of the maximal violation of Svetlichny inequality for a subclass of four-qubit “X” states. We show the application potentiality of these expressions by designing two schemes where quantum resources are converted from less qubits “X” states to more qubits “X” states.

Efficient high-dimensional cyclic quantum teleportation via a 3-dimensional GHZ state in a noisy environment

This paper studies the novel efficient protocol for teleporting two-qutrit states using a quantum system operating in a noisy environment. A novel Cyclic Quantum Teleportation (CYQT) protocol facilitates the exchange of unknown two-qutrit states among three users, using the quantum channel of a nine-qutrits entangled state. The specialty of the proposed protocol is that the users can only apply a few three-dimensional GHZ-state measurements on their particles and can transmit more quantum information. After that, we analyze the protocol's performance in the presence of a noisy environment, including trit-flip noise, phase-flip noise, and amplitude-damping noise on the teleported state between users where they share an entangled quantum channel. We found that the protocol's fidelity is influenced by the initial state of the amplitude coefficient and the noise intensity. Further, we subjected the protocol to various attacks to ensure its security. This evaluation clearly shows that CYQT is robust in ensuring secure communication.

Parameterized Multipartite Entanglement and Genuine Entanglement Measures Based on q-Concurrence.

We study genuine multipartite entanglement (GME) and multipartite k-entanglement based on q-concurrence. Well-defined parameterized GME measures and measures of multipartite k-entanglement are presented for arbitrary dimensional n-partite quantum systems. Our GME measures show that the GHZ state is more entangled than the W state. Moreover, our measures are shown to be inequivalent to the existing measures according to entanglement ordering. Detailed examples show that our measures characterize the multipartite entanglement finer than some existing measures, in the sense that our measures identify the difference of two different states while the latter fail.

Stabilization of approximate GHZ state with quasi-local couplings

We propose a reservoir design, composed of fixed dissipation operators acting each on few local subsystems, to stabilize an approximate GHZ state on n qubits. The main idea is to work out how a previously proposed sequence of two stabilization steps can be applied instead in appropriate (probabilistic) superposition. We examine various alternatives to synchronize the superposition using local couplings only, thanks to a chain of ‘clock’ ancillas or to additional levels on the data subsystems. The practical value of these alternatives depends on experimental constraints. They all feature a design tradeoff between approximate stabilization fidelity and protection against perturbations. These proposals illustrate how simple autonomous automata can be implemented in quantum reservoir engineering to replace sequential state preparation procedures. Encoding automaton actions via additional data levels only, appears particularly efficient in this context. Our analysis method, reducing the Lindblad master equation to a Markov chain on virtual output signals, may be of independent interest.

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

Secure two-party computation via measurement-based quantum computing

Secure multiparty computation (SMC) provides collaboration among multiple parties, ensuring the confidentiality of their private information. However, classical SMC implementations encounter significant security and efficiency challenges. Resorting to the entangled Greenberger–Horne–Zeilinger (GHZ) state, we propose a quantum-based two-party protocol to compute binary Boolean functions, with the help of a third party. We exploit a technique in which a random Z-phase rotation on the GHZ state is performed to achieve higher security. The security and complexity analyses demonstrate the feasibility and improved security of our scheme compared to other SMC Boolean function computation methods. Additionally, we implemented the proposed protocol on the IBM QisKit and found consistent outcomes that validate the protocol’s correctness.

Multi-party semi-quantum secret sharing protocol based on measure-flip and reflect operations

Semi-quantum secret sharing (SQSS) protocols serve as fundamental frameworks in quantum secure multi-party computations, offering the advantage of not requiring all users to possess intricate quantum devices. However, current SQSS protocols mainly cater to bipartite scenarios, with few protocols suitable for multi-party scenarios. Moreover, the multi-party SQSS protocols face limitations such as low qubit efficiency and inability to share deterministic secret information. To address this gap, this paper proposes a multi-party SQSS protocol based on multi-particle GHZ states. In this protocol, the quantum user can distribute the predetermined secret information to multiple classical users with limited quantum capabilities, and only through mutual cooperation among all classical users can the correct secret information be reconstructed. By utilizing measure-flip and reflect operations, the transmitted multi-particle GHZ states can all contribute keys, thereby improving the utilization of transmitted particles. Then, security analysis shows that the protocol’s resilience against prevalent external and internal threats. Additionally, employing IBM Qiskit, we conduct quantum circuit simulations to validate the protocol’s accuracy and feasibility. Finally, compared to similar studies, the proposed protocol has advantages in terms of protocol scalability, qubit efficiency, and shared message types.

Bidirectional Quantum Teleportation of GHZ and EPR States Through Entanglement Swapping Utilizing a Pre-established GHZ Channel

Bidirectional Quantum Teleportation of GHZ and EPR States Through Entanglement Swapping Utilizing a Pre-established GHZ Channel

A new quantum group blind signature scheme based on GHZ states

With the development of quantum computers, traditional communication security based on classical computers can no longer guarantee unconditional security. At the same time, a series of encrypted communication solutions that rely on quantum mechanical properties have been spawned. This article focuses on the field of quantum signatures, based on the entangled Greenberger–Horne–Zeilinger state, combining group signatures (any member of the group can sign on behalf of the group) and blind signatures (the signer cannot know the accuracy of the signature content) proposed a new quantum group blind signature scheme that utilizes quantum key distribution to achieve unconditional security. By splitting the original message, the scheme strengthens the relevance of the signature participants and makes the signature to have stronger binding. Then, the security of the scheme against internal and external attacks is analyzed. In this scheme, a pleasing efficiency has been achieved, and the non-repudiation of signatures has been enhanced. At the same time, disputed signatures can be traced back to the signer.

Correction to: Unilateral protection scheme for N-qubit GHZ states against decoherence: a resource-efficient approach

Correction to: Unilateral protection scheme for N-qubit GHZ states against decoherence: a resource-efficient approach

Activation of Einstein–Podolsky–Rosen steering sharing with unsharp nonlocal measurements

Einstein–Podolsky–Rosen (EPR) steering is commonly shared among multiple observers by utilizing unsharp measurements. Nevertheless, their usage is restricted to local measurements and does not encompass all nonlocal measurement-based cases. In this work, a method for finding beneficial local measurement settings has been expanded to include nonlocal measurement cases. This method is applicable for any bipartite state and offers benefits even in scenarios with a high number of measurement settings. Using the Greenberger–Horne–Zeilinger state as an illustration, we show that employing unsharp nonlocal measurements can activate the phenomenon of steering sharing in contrast to using local measurements. Furthermore, our findings demonstrate that nonlocal measurements with unequal strength possess a greater activation capability compared to those with equal strength. Our activation method generates fresh concepts for conservation and recycling quantum resources.

Efficient Quantum Private Comparison Based on GHZ States.

Quantum private comparison (QPC) is a fundamental cryptographic protocol that allows two parties to compare the equality of their private inputs without revealing any information about those inputs to each other. In recent years, QPC protocols utilizing various quantum resources have been proposed. However, these QPC protocols have lower utilization of quantum resources and qubit efficiency. To address this issue, we propose an efficient QPC protocol based on GHZ states, which leverages the unique properties of GHZ states and rotation operations to achieve secure and efficient private comparison. The secret information is encoded in the rotation angles of rotation operations performed on the received quantum sequence transmitted along the circular mode. This results in the multiplexing of quantum resources and enhances the utilization of quantum resources. Our protocol does not require quantum key distribution (QKD) for sharing a secret key to ensure the security of the inputs, resulting in no consumption of quantum resources for key sharing. One GHZ state can be compared to three bits of classical information in each comparison, leading to qubit efficiency reaching 100%. Compared with the existing QPC protocol, our protocol does not require quantum resources for sharing a secret key. It also demonstrates enhanced performance in qubit efficiency and the utilization of quantum resources.

Quantum homomorphic aggregation signature scheme based on GHZ states

A quantum homomorphic aggregation signature scheme is proposed based on GHZ states, combined with homomorphic aggregation techniques. The scheme has the following features: Firstly, by changing the existing quantum homomorphic signature scheme which generally uses Bell state as the signature particle, and choosing GHZ state as the signature particle, it can realize the signature of the multi-bit messages by preparing fewer quantum resources; Secondly, the idea of classical aggregated signature is introduced, where multiple message signatures are aggregated into a single signature by quantum entanglement swapping technique, and the verifier can determine the validity of all signatures by only one verification; At the same time, the verification of individual signatures by the aggregator is realized, and dishonest behaviors among the signature members can be detected in time; Finally, the whole signature process satisfies the basic homomorphic property. Compared with the existing quantum homomorphic signature scheme, this scheme can effectively reduce the consumption of quantum resources, improving the efficiency of signature verification and enhancing the reliability of the signature. The security analysis shows that the scheme has the verifiability, unforgeability and non-repudiation.

Custom Bell inequalities from formal sums of squares

Bell inequalities play a key role in certifying quantum properties for device-independent quantum information protocols. It is still a major challenge, however, to devise Bell inequalities tailored for an arbitrary given quantum state. Existing approaches based on sums of squares provide results in this direction, but they are restricted by the necessity of first choosing measurement settings suited to the state. Here, we show how the sum of square property can be enforced for an arbitrary target state by making an appropriate choice of nullifiers, which is made possible by leaving freedom in the choice of measurement. Using our method, we construct simple Bell inequalities for several families of quantum states, including partially entangled multipartite GHZ states and qutrit states. In most cases we are able to prove that the constructed Bell inequalities achieve self-testing of the target state. We also use the freedom in the choice of measurement to self-test partially entangled two-qubit states with a family of settings with two parameters. Finally, we show that some statistics can be self-tested with distinct Bell inequalities, hence obtaining new insight on the shape of the set of quantum correlations.

Unilateral protection scheme for N-qubit GHZ states against decoherence: a resource-efficient approach

Unilateral protection scheme for N-qubit GHZ states against decoherence: a resource-efficient approach

A, B, C of three-qubit entanglement: three vectors to control it all

In this paper we are focusing on entanglement control problem in a three-qubit system. We demonstrate that vector representation of entanglement, associated with SO(6) representation of SU(4) two-qubit group, can be used to solve various control problems analytically including (i) the transformation between a W- type states and GHZ state, and (ii) manipulating bipartite concurrences and three-tangle under a restricted access to only two qubits, and (iii) designing USp(4)- type quaternionic operations and quantum states.

Optimal distributed multi-parameter estimation in noisy environments

We consider the task of multiple parameter estimation in the presence of strong correlated noise with a network of distributed sensors. The signals and the noises have different spatial dependence but are encoded with the same local generators. We study how to find and improve noise-insensitive strategies. We show that sequentially probing with GHZ states from the decoherence-free subspace that we identify is asymptotically optimal up to a factor of at most 4 in the limit of many repetitions. The implementation of such strategies only requires local read-out and ‘passive’ resources—an initially entangled state of the sensors and tunable local interaction strength.

Observation of quantum nonlocality in Greenberger-Horne-Zeilinger entanglement on a silicon chip

Nonlocality is the defining feature of quantum entanglement. Entangled states with multiple particles are of crucial importance in fundamental tests of quantum physics as well as in many quantum information tasks. One of the archetypal multipartite quantum states, Greenberger-Horne-Zeilinger (GHZ) state, allows one to observe the striking conflict of quantum physics to local realism in the so-called all-versus-nothing way. This is profoundly different from Bell’s theorem for two particles, which relies on statistical predictions. Here, we demonstrate an integrated photonic chip capable of generating and manipulating the four-photon GHZ state. We perform a complete characterization of the four-photon GHZ state using quantum state tomography and obtain a state fidelity of 0.729±0.006. We further use the all-versus-nothing test and the Mermin inequalities to witness the quantum nonlocality of GHZ entanglement. Our work paves the way to perform fundamental tests of quantum physics with complex integrated quantum devices.