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Physical Review A

Verification of quantum-gate teleportation based on Bell nonlocality in a black-box scenario

Zi-Qi Wang, Tie-Jun Wang

Published Jul 28, 2023• 12 citations
Publisher

Abstract

Quantum gate teleportation (QGT) is an excellent candidate for implementing remote quantum gate operations in large-scale quantum computer networks as it has the minimum resource demand to realize such computing models. The Bell nonlocality of quantum entanglement channel in QGT can be transformed into the corresponding posterior statistics correlation obtained by local measurements after QGT operation, and this Bell-type-like correlation can be used to check device and measurement loopholes or information leaking in the teleportation systems. In this paper, we propose a verification scheme based on Bell nonlocality for quantum cnot gate teleportation in a black-box scenario where the vendors may not be trusted. The double criteria of high fidelity ($\overline{F}>97.53%$) and high CHSH inequality violation ($\mathrm{CHSH}>2$) are used for assessing a vendor's reliability. The clients can use our scheme to check whether vendors employ classical simulation techniques to forge nonlocal quantum computing processes and it could provide a secure manner for the construction of quantum computer networks in the future.

DOI
10.1103/physreva.108.012434

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Quantum gate teleportation (QGT) is an excellent candidate for implementing remote quantum gate operations in large-scale quantum computer networks as it has the minimum resource demand to realize such computing models. The Bell nonlocality of quantum entanglement channel in QGT can be transformed into the corresponding posterior statistics correlation obtained by local measurements after QGT operation, and this Bell-type-like correlation can be used to check device and measurement loopholes or information leaking in the teleportation systems. In this paper, we propose a verification scheme based on Bell nonlocality for quantum cnot gate teleportation in a black-box scenario where the vendors may not be trusted. The double criteria of high fidelity (F‾>97.53\overline{F}>97.53%F>97.53) and high CHSH inequality violation (CHSH>2\mathrm{CHSH}>2CHSH>2) are used for assessing a vendor's reliability. The clients can use our scheme to check whether vendors employ classical simulation techniques to forge nonlocal quantum computing processes and it could provide a secure manner for the construction of quantum computer networks in the future.
Controlled quantum gate teleportation (CQGT) enables controller-regulated quantum gate transmission in distributed networks. The current CQGT scheme faces security challenges as both genuine tripartite entanglement and insecure classical-quantum hybrid resources can achieve high standard metrics (fidelity or control power). In this paper, we propose a device-independent (DI) CQGT verification scheme using genuine tripartite nonlocality in black-box scenarios. In the quantum cnot gate teleportation, our DI verification scheme based on Svetlichny inequality achieved the maximum inequality violation, which is superior to the traditional Clauser-Horne-Shimony-Holt (CHSH) type scheme. It is crucial that we establish a direct relationship between Svetlichny inequality violation and the effective control power (ECP) of the controller in eavesdropping depolarization channels, where ECP corresponds to the maximum inequality violation. This work addresses critical security verification gaps in CQGT protocols while highlighting the fundamental role of multipartite nonlocality in quantum information processing.
Controlled non-local quantum gate operations reveal the cooperative and supervisory relationships of the controller and the non-local gate operators in a quantum networks, which is an essential feature for building multi-party quantum computing networks, and their security relies on quantum entanglement resources. To understand the behavior of vendors who substitute quantum entanglement resources with classical-quantum hybrid resources, this paper proposes a device-independent verification scheme for controlled non-local CNOT quantum gates. Moreover, it formulates a Svetlichny-type inequality to conduct an effective verification of the utilization of entanglement resources in nonlocal gate operations, particularly in instances where the Svetlichny inequality is not applicable. Our scheme offers a theoretical foundation for constructing secure distributed quantum computing networks in the future.
Large-scale quantum computers possess the capacity to effectively tackle practical problems that can be insurmountable for classical computers. The main challenge in building these quantum computers is to realize scalable modules for remote qubits and entanglement. By assembling small, specialized parts into a larger architecture, the modular approach mitigates complexity and uncertainty. Such a distributed architecture requires non-local quantum gate operations between remote qubits. An essential method for implementing such operations, known as quantum gate teleportation, requires only local operations, classical communication, and shared entanglement. Till today, the quantum gate teleportation using a photonic chip has remained elusive. Here, we experimentally demonstrate the quantum teleportation of an on-chip controlled-NOT (CNOT) gate, implemented via a silicon polarization directional coupler. Assisted with the scalable silicon chip platform, high-fidelity local quantum logic gates, linear optical components, post-selected entanglement, and coincidence measurements from photonic qubits, we first measure and characterize our teleported chip-scale CNOT gate with an average truth table fidelity of 93.1 ± 0.3%. Second, for different input polarization states, we obtain an average quantum state fidelity of 87.0 ± 2.2% with our teleported on-chip CNOT gate. Third, we use our non-local CNOT gate for remote entanglement creation of four Bell states, with an average quantum state fidelity of 86.2 ± 0.8%. Fourth, we fully characterize our teleported on-chip CNOT gate with a quantum process fidelity of 83.1 ± 2.0%, and an average non-local CNOT gate fidelity of 86.5 ± 2.2%. Our teleported photonic on-chip quantum logic gate could be extended both to multiple qubits and chip-scale modules towards fault-tolerant and large-scale distributed quantum computation.
Developing reliable methods for certifying the dimension of a given quantum system or process is essential to ensure the validity of claimed realization of high-dimensional (HD) quantum advantages. The existing criteria for certifying genuine HD quantum teleportation (HDQT) mainly focus on demonstrating the successful transmission of genuine HD quantum states. However, a complete certification of HDQT must also identify the entanglement dimension of resource, which is critical for verifying whether the transmission capacity and noise resilience meet the necessary thresholds. Here we propose two universal criteria (based on fidelity and robustness, respectively) for certifying genuine HDQT behaviors that can close this gap by fully identifying the dimension of the entanglement. Both criteria require only the input and output teleportation data and remain feasible under partial Bell-state measurements. Furthermore, the robustness-based criterion has stronger noise resistance and it requires no prior assumptions about local operations, making it robust even in black-box scenario. Our results establish a universal and reliable theoretical framework for validating the core quantum advantage in HDQT, pivotal for ensuring the reliable links in HD quantum networks.
Quantum teleportation, a cornerstone of quantum information science, enables the transfer of an unknown quantum state from one location to another without physically moving the state itself. Its efficacy is primarily quantified by fidelity, a measure of how closely the teleported state resembles the original. Achieving high-fidelity teleportation is paramount for practical applications in quantum communication and computation. This paper explores the intricate relationship between non-locality, the no-cloning theorem, and the pursuit of high-fidelity quantum teleportation. We introduce the concept of "unclonable non-locality" to describe scenarios where the inherent non-local correlations of entangled states are leveraged in a manner that inherently resists illicit copying, thereby enhancing the integrity and security of the teleportation process. We review current state-of-the-art teleportation protocols, analyzing their fidelity limitations and the impact of various noise models, such as those arising from Bell-diagonal resource states and local amplitude-damping channels. Our framework emphasizes that protocols exhibiting identical average fidelities can conceal distinct statistical behaviors and asymmetries introduced by local noise, stressing the need for a comprehensive statistical assessment beyond simple average fidelity. We propose methods for constructing and utilizing entangled resources that maximize non-local correlations while inherently enforcing the no-cloning principle, thereby offering a robust pathway to deterministic, high-fidelity quantum state transfer. The discussion highlights the potential for designing tailored teleportation benchmarks based on prior importance functions, unifying moment-based criteria and threshold-based success probabilities into a single figure of merit, and clarifying the role of entanglement strength in certifying high-fidelity teleportation. We also acknowledge the ethical implications associated with the development of powerful quantum technologies that could have significant societal impacts.
Quantum gate teleportation enables distant parties to implement nonlocal quantum operations without physically transferring the participating qubits, making it a promising primitive for distributed quantum computing. We introduce a general framework for deterministic quantum gate teleportation based on path superposition, in which the target nonlocal operation is specified through the phase of a preshared maximally entangled resource and a suitable family of path-dependent local unitary operators. The framework establishes general design conditions that guarantee deterministic teleportation after measurement of the control qubits and the application of local correction operations. As representative realizations, we construct teleportation protocols for controlled-NOT (CNOT) and controlled-Z (CZ) gates, demonstrating that different nonlocal operations can be implemented within the same protocol architecture through appropriate choices of the design parameters. We further outline a proof-of-concept photonic realization based on spatial-path and polarization degrees of freedom. The proposed framework identifies path superposition as a versatile resource for quantum gate teleportation and distributed quantum information processing.