Greenberger-Horne-Zeilinger Research Articles

Curvature-enhanced multipartite coherence in the multiverse* *Supported by the National Natural Science Foundation of China (12205133, 1217050862, LJKQZ20222315, JYTMS20231051)

Here, we study the quantum coherence of N-partite Greenberger-Horne-Zeilinger (GHZ) and W states in the multiverse consisting of N causally disconnected de Sitter spaces. Interestingly, N-partite coherence increases monotonically with curvature, whereas the curvature effect destroys quantum entanglement and discord, indicating that the curvature effect is beneficial to quantum coherence and harmful to quantum correlations in the multiverse. We find that with an increase in n expanding de Sitter spaces, the N-partite coherence of the GHZ state increases monotonically for any curvature, whereas the quantum coherence of the W state decreases or increases monotonically depending on the curvature. We find a distribution relationship, which indicates that the correlated coherence of the N-partite W state is equal to the sum of all bipartite correlated coherence in the multiverse. Multipartite coherence exhibits unique properties in the multiverse, suggesting that it may provide some evidence for the existence of the multiverse.

Dissipative stabilization of high-dimensional GHZ states for neutral atoms

High-dimensional quantum entanglement characterizes the entanglement of quantum systems within a larger Hilbert space, introducing more intricate and complex correlations among the entangled particles' states. The high-dimensional Greenberger–Horne–Zeilinger (GHZ) state, symbolic of this type of entanglement, is of significant importance in various quantum information processing applications. This study proposes integrating a neutral atom platform with quantum reservoir engineering to generate a high-dimensional GHZ state deterministically. Leveraging the advantages of neutral atoms in a modified unconventional Rydberg pumping mechanism, combined with controlled dissipation, we achieve a three-dimensional GHZ state with a fidelity surpassing 99% through multiple pump and dissipation cycles. This innovative approach paves the way for experimentally feasible, deterministic preparation of high-dimensional GHZ states in Rydberg atom systems, thereby advancing the capabilities of quantum information processing.

A solvable model for graph state decoherence dynamics

We present an exactly solvable toy model for the continuous dissipative dynamics of permutation-invariant graph states of NN qubits. Such states are locally equivalent to an NN-qubit Greenberger-Horne-Zeilinger (GHZ) state, a fundamental resource in many quantum information processing setups. We focus on the time evolution of the state governed by a Lindblad master equation with the three standard single-qubit jump operators, the Hamiltonian part being set to zero. Deriving analytic expressions for the expectation values of observables expanded in the Pauli basis at all times, we analyze the nontrivial intermediate-time dynamics. Using a numerical solver based on matrix product operators, we simulate the time evolution for systems with up to 64 qubits and verify a numerically exact agreement with the analytical results. We find that the evolution of the operator space entanglement entropy of a bipartition of the system manifests a plateau whose duration increases logarithmically with the number of qubits, whereas all Pauli-operator products have expectation values decaying at most in constant time.

Versatile and controlled quantum teleportation network

A quantum teleportation network involving multiple users is essential for future quantum internet. So far, controlled quantum teleportation has been demonstrated in a three-user network. However, versatile and controlled quantum teleportation network involving more users is in demand, which satisfies different combinations of users for practical requirements. Here we propose a highly versatile and controlled teleportation network that can switch among various combinations of different users. We use a single continuous-variable six-partite Greenberger–Horne–Zeilinger (GHZ) state to realize such a task by choosing the different measurement and feedback operations. The controlled teleportation network, which includes one sub-network, two sub-networks and three sub-networks, can be realized for different application of user combinations. Furthermore, the coherent feedback control (CFC) can manipulate and improve the teleportation performance. Our approach is flexible and scalable, and would provide a versatile platform for demonstrations of complex quantum communication and quantum computing protocols.

Intra‐Cavity Laser Manipulation of High‐Dimensional Non‐Separable States

AbstractNon‐separable states of structured light have the analogous mathematical forms with quantum entanglement, which offer an effective way to simulate quantum process. However, the classical multi‐partite non‐separable states analogue to multi‐particle entanglements can only be controlled by bulky free‐space modulation of light through coupling multiple degrees of freedom (DoFs) with orbital angular momentum (OAM) to achieve high dimensionality and other DoFs to emulate multi‐parties. In this paper, a scheme is proposed to directly emit multi‐partite non‐separable states from a simple laser cavity to mimic multi‐particle quantum entanglement. Through manipulating three DoFs as OAM, polarization, and wavevector inside a laser cavity, the eight‐dimensional (8D) tripartite states and all Greenberger‐Horne‐Zeilinger (GHZ)‐like states can be generated and controlled on demand. In addition, an effective method is proposed to perform state tomography employing convolutional neural network (CNN), for measuring the generated GHZ‐like states with highest fidelity up to 95.11%. This work reveals a feasibility of intra‐cavity manipulation of high‐dimensional multipartite non‐separable states, opening a compact device for quantum‐classical analogy and paving the path for advanced quantum scenarios.

New multiparty measurement-device-independent quantum secret sharing protocol based on entanglement swapping

A new multiparty measurement-device-independent quantum secret sharing (MDI-QSS) protocol is proposed based on entanglement swapping. All the measurement tasks are delegated to an untrusted party, eliminating all detector-side-channel loopholes. Only Einstein–Podolsky–Rosen (EPR) pairs, single photons and Bell-state measurements are required irrespective of the number of participants. Compared with existing MDI-QSS protocols, no additional unitary operations or Greenberger–Horne–Zeilinger (GHZ)-state measurements are needed. Our protocol is feasible experimentally and holds inspiring potential for the application in practical multiparty quantum communication networks.

GHZ distillation protocols in the presence of decoherence

In this paper, we introduce a novel heuristic approach designed to optimize the performance of Greenberger-Horne- Zeilinger (GHZ) creation and distillation protocols under decoherence. Our methodology converts these protocols into a practical set of instructions, demonstrating, through simulations, the production of higher-quality GHZ states than previously known protocols. This advancement contributes to the field of distributed quantum computing by addressing the need for high-quality entanglement required for operations between different quantum computers.

QSMAH: A novel quantum-based secure cryptosystem using mutual authentication for healthcare in the internet of things

Healthcare in IoT provides many benefits, such as real-time data transfer and decision-making based on the information received from the patient's Body Sensor Nodes (BSNs). Many healthcare centers have adopted IoT-based devices such as heart monitoring implants and Electrocardiograms (ECG) for continuous patient monitoring in and out of hospitals. However, due to open Internet connectivity and lack of authentication, these devices may lead to several life-threatening risks. Recent advancements in Quantum Computing threatened the security of classical cryptographic primitives such as the RSA algorithm. The security and privacy of patient data are of utmost importance and are to be protected from existing vulnerabilities and futuristic Quantum attacks. Motivated by the abovementioned issues, we proposed the QSMAH protocol which ensures secure Key Agreement (KA) and Mutual Authentication (MA) based on Quantum Cryptography. Unlike classical authentication schemes, in our protocol, Quantum Teleportation and Quantum Entanglement are effectively utilized for secure data transfer among entities. The security of the proposed QSMAH protocol relies on a Quantum Key and Greenberger–Horne–Zeilinger (GHZ) states to achieve strong authentication. An extensive formal security analysis using BAN logic is provided to prove the goal of our protocol. The simulation of the proposed protocol is provided using Automated Validation of Internet Security Protocols and Applications (AVISPA). The results reflect that the security of our protocol cannot be tampered with by Quantum Shor's and Grover's algorithms. The security analysis proves that QSMAH is also resistant to classical attacks and futuristic Quantum attacks on cryptographic schemes.

Pairwise‐Parallel Entangling Gates on Orthogonal Modes in a Trapped‐Ion Chain

AbstractParallel operations are important for both near‐term quantum computers and larger‐scale fault‐tolerant machines because they reduce execution time and qubit idling. This study proposes and implements a pairwise‐parallel gate scheme on a trapped‐ion quantum computer. The gates are driven simultaneously on different sets of orthogonal motional modes of a trapped‐ion chain. This work demonstrates the utility of this scheme by creating a Greenberger‐Horne‐Zeilinger (GHZ) state in one step using parallel gates with one overlapping qubit. It also shows its advantage for circuits by implementing a digital quantum simulation of the dynamics of an interacting spin system, the transverse‐field Ising model. This method effectively extends the available gate depth by up to two times with no overhead when no overlapping qubit is involved, apart from additional initial cooling. This scheme can be easily applied to different trapped‐ion qubits and gate schemes, broadly enhancing the capabilities of trapped‐ion quantum computers.

Conference key agreement in a quantum network

Quantum conference key agreement (QCKA) allows multiple users to establish a secure key from a shared multi-partite entangled state. In a quantum network, this protocol can be efficiently implemented using a single copy of a N-qubit Greenberger-Horne-Zeilinger (GHZ) state to distil a secure N-user conference key bit, whereas up to N-1 entanglement pairs are consumed in the traditional pair-wise protocol. We demonstrate the advantage provided by GHZ states in a testbed consisting of a photonic six-user quantum network, where four users can distil either a GHZ state or the required number of Bell pairs for QCKA using network routing techniques. In the asymptotic limit, we report a more than two-fold enhancement of the conference key rate when comparing the two protocols. We extrapolate our data set to show that the resource advantage for the GHZ protocol persists when taking into account finite-key effects.

Violation of Bell Inequality by Four‐Photon Greenberger‐Horne‐Zeilinger State with a Phase from a Warm Atomic Ensemble

AbstractA Greenberger–Horne–Zeilinger (GHZ) entangled state with a phase is crucial for realizing desired multipartite quantum states for practical applications. Here, it is reported that the violations of the general Bell inequality (GBI) introduced in using the four‐photon polarization‐entangled phase‐GHZ state realized via intrinsic polarization correlation and collective two‐photon coherence in the 5S1/2–5P3/2–5D5/2 transition of 87Rb atoms. The phase‐GHZ state can be achieved by the unitary transformation of only one local phase of the four photons. Theoretically, the GHZ state with the π/4 phase affords maximal violation of the GBI of 2√2 at the local measurement settings of the Pauli operators σx and σy. Strong violations of the GBI of the phase‐GHZ state by 47 standard deviations are experimentally demonstrated. In addition to the entanglement witness for the phase‐GHZ state, the results represent a genuine four‐photon entanglement of the phase‐GHZ state, thereby providing a novel resource for realizing photonic quantum computation, magic‐state distillation from entangled states, and quantum networks based on atom–photon interactions.

Proposal for the complete high-dimensional Greenberger–Horne–Zeilinger state measurement

Abstract A theoretical proposal for the complete analysis of high-dimensional Greenberger–Horne–Zeilinger (GHZ) state is presented in this Letter. We first demonstrate the approach for the complete three-photon GHZ state measurement in three dimensions, and then generalize it to the situation of N-photon system in d dimensions. In our approach, the photonic hyperentanglement and quantum Fourier transform are both utilized. The presented proposal will be useful for the high-dimensional multi-photon quantum computation and quantum communication.

Tripartite Entanglement Extraction from the Black Hole Vacuum

AbstractThe first investigation of tripartite entanglement harvesting in the vicinity of a black hole is carried out. Working in the context of a static Bañados–Teitelboim–Zanelli (BTZ) black hole spacetime the authors find that it is possible to harvest tripartite entanglement in regions where harvesting of bipartite entanglement is known to be impossible due to intense Hawking radiation. In these situations, it implies that the harvested entanglement is of the Greenberger–Horne–Zeilinger (GHZ) type.

The power of qutrits for non-adaptive measurement-based quantum computing

Non-locality is not only one of the most prominent quantum features but can also serve as a resource for various information-theoretical tasks. Analysing it from an information-theoretical perspective has linked it to applications such as non-adaptive measurement-based quantum computing (NMQC). In this type of quantum computing the goal is to output a multivariate function. The success of such a computation can be related to the violation of a generalised Bell inequality. So far, the investigation of binary NMQC with qubits has shown that quantum correlations can compute all Boolean functions using at most qubits, whereas local hidden variables (LHVs) are restricted to linear functions. Here, we extend these results to NMQC with qutrits and prove that quantum correlations enable the computation of all three-valued logic functions using the generalised qutrit Greenberger–Horne–Zeilinger (GHZ) state as a resource and at most qutrits. This yields a corresponding generalised GHZ type paradox for any three-valued logic function that LHVs cannot compute. We give an example for an n-variate function that can be computed with only n + 1 qutrits, which leads to convenient generalised qutrit Bell inequalities whose quantum bound is maximal. Finally, we prove that not all functions can be computed efficiently with qutrit NMQC by presenting a counterexample.

Genuine entanglement under squeezed generalized amplitude damping channels with memory

We study genuine entanglement among three qubits undergoing a noisy process that includes dissipation, squeezing, and decoherence. We obtain a general solution and analyze the asymptotic quantum states. We find that most of these asymptotic states can be genuinely entangled depending upon the parameters of the channel, memory parameter, and the parameters of the initial states. We study Greenberger–Horne–Zeilinger (GHZ) states and W states, mixed with white noise, and determine the conditions for them to be genuinely entangled at infinity. We find that for these mixtures, it is possible to start with a bi-separable state (with a specific mixture of white noise) and end with genuine entangled states. However, the memory parameter μ must be very high. We find that in contrast to the two-qubit case, none of the three-qubit asymptotic states for n → ∞ are genuinely entangled.

Efficient quantum secret sharing scheme based on monotone span program

How to efficiently share secrets among multiple participants is a very important problem in key management. In this paper, we propose a multi-secret sharing scheme based on the Greenberger Horne Zeilinger (GHZ) state. First, the distributor uses monotone span program to encode the secrets and generate the corresponding secret shares to send to the participants. Then, each participant uses the generalized Pauli operator to embed its own secret share into the transmitted particle. The participant who wants to get the secrets can get multiple secrets at the same time by performing a GHZ-state joint measurement. Furthermore, since this scheme is based on a monotone span program, its access structure is more general than the access structure (t, n) threshold. Compared with other schemes, our proposed scheme is more efficient, less computational cost.

An Elementary Proof That Everett’s Quantum Multiverse Is Nonlocal: Bell-Locality and Branch-Symmetry in the Many-Worlds Interpretation

Everett’s many-worlds or multiverse theory is an attempt to find an alternative to the standard Copenhagen interpretation of quantum mechanics. Everett’s theory is often claimed to be local in the Bell sense. Here, we show that this is not the case and debunk the contradictions by analyzing in detail the Greenberger–Horne–Zeilinger (GHZ) nonlocality theorem. We discuss and compare different notions of locality often mixed in the Everettian literature and try to explain the nature of the confusion. We conclude with a discussion of probability and statistics in the many-worlds theory and stress that the strong symmetry existing between branches in the theory prohibits the definition of probability and that the theory cannot recover statistics. The only way out from this contradiction is to modify the theory by adding hidden variables à la Bohm and, as a consequence, the new theory is explicitly Bell-nonlocal.

Multi-party simultaneous quantum identity authentication based on Greenberger-Horne-Zeilinger states

A successful implementation of any secure communication protocols requires the identity authentication as a prerequisite. Quantum identity authentication (QIA) can ensure the unconditional security of identity code. In this paper, we propose a multi-party simultaneous quantum identity authentication (MSQIA) protocol based on the Greenberger-Horne-Zeilinger (GHZ) state. In the protocol, N certified users can directly send their identity codes to the authenticator Alice simultaneously through quantum channels without classical communication, which enables Alice to authenticate their identity at the same time. Our protocol only requires Alice to perform the single-photon measurement. In theory, this protocol is unconditionally secure and one pair of (N + 1)-photon GHZ state can transmit N bits of identity codes. Our MSQIA protocol has application potential in the quantum communication field in the near future.

Bipartite entanglement distillation by unilateral and bilateral local filters using polarizing Mach–Zehnder interferometers

The extraordinary correlation seen in entangled states in space-like separated regions is one of the most intriguing aspects of quantum states. Practical utility of entanglement as a resource for quantum key distribution, dense coding, or teleportation generally requires maximally entangled states. In practice, entanglement quality degrades substantially due to channel noise. The problem may be mitigated by entanglement distillation. The simplest distillation protocol is enforced by local filtering operations and classical communication. The local filtering operations are merely generalized positive operator valued measures utilizing additional degrees of freedom (DoFs) as ancillary qubits. In this work, we experimentally show that filtering on a single channel (unilateral) is equally effective as filtering on both channels (bilateral) for distillation of pure non-maximally entangled bipartite states. This result holds for a non-maximally entangled multi-qubit Greenberger-Horne-Zeilinger (GHZ) like states as well, as they show a straightforward extension of the Bell state structure. Further, we provide a theoretical comparison of the efficacy of unilateral and bilateral filtering for the case of mixed states resulting from local depolarizing noise introduced either in one or both of the non-maximally entangled pairs. Surprisingly, when noise is introduced in either one of the channels, we find that unilateral filtering on the noise-free channel outperforms the filtering on the noisy channel and bilateral filtering on both channels. We also find that bilateral filtering is more effective when both channels are noisy. A reduction in the number of local operations, in general, has the advantage of reducing the complexity of the experimental apparatus and the reduction of measurement related errors.

Preparing maximally entangled states by monitoring the environment–system interaction

A common assumption in an open quantum system is that the noise induced by the environment, due to the interaction between a quantum system and its environment, is responsible for the disappearance of quantum properties. Interestingly, Barreiro et al. (2011) show, experimentally, using an open-system quantum ion traps simulator, an environment state can be engineered and controlled to pump an arbitrary quantum system toward a maximally entangled state and thus can be considered a resource for quantum information processing. Here, we demonstrate this idea to pump an arbitrary maximally mixed state into Greenberger–Horne–Zeilinger (GHZ) state by simulating our quantum circuit using one of the IBM Q processors. Barreiro et al. (2011) offer the circuits for the execution of the GHZ pumping. Nevertheless, those are collected gates that are suitable to the trapped-ions platform, so their circuits implementation on the IBM Q devices would result in large depth circuits and thus requires many gates. Consequently, we suggest a different circuit structure that follow similar goals, but have been considered the features of the IBM Q platform.Moreover, we run the simulation of our circuit using the QASM simulator and free-web based interface, IBM Quantum Experience, with and without error mitigation, to investigate the effect of the noise on the preparation of the initial mixed states of the qubits in addition to the population of the target state of the system.