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Zhongguo kexue. Wulixue Lixue Tianwenxue

Device-independent verification of controlled non-local CNOT quantum gate

LI YiNing, GONG NengFei, TIAN YueHan, WANG TieJun

Published Feb 24, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1360/sspma-2024-0575

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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.
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.
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.
Abstract This work presents an extension of the Svetlichny inequality to star-topology quantum networks, enabling the verification of network nonlocality in distributed architectures. The proposed framework uses joint measurements at a central node to certify the entanglement properties between peripheral nodes after their local measurement collapse. We further generalize this methodology to composite quantum networks, constructed from multiple EPR pairs and featuring hybrid star-chain structures, thereby demonstrating its applicability to complex entanglement configurations.
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.
Distant quantum control via quantum gates represents an essential step toward realizing distributed quantum networks. An efficient theoretical protocol for the dual non-local implementation of controlled-not (CNOT) gates between two separated partners is presented in this regard. The suggested protocol requires 1~ebit with local operations and classical communication channels. The efficiency of the teleportation scheme is quantified through an infidelity measure. The numerical results show that the infidelity of performing the CNOT gate between legitimate partners depends on the initial qubit settings. It is also shown that the protocol is performed efficiently if the CNOT control qubit and the auxiliary qubit are prepared in the same direction. Furthermore, we provide a noise analysis for the suggested scheme. We find that by maintaining the noise strengths under the threshold 14\frac{1}{4}41​, one can achieve the dual non-local CNOT gate optimally.
Non-local quantum computation (NLQC) studies how two collaborating players can implement channels on distributed systems using a single simultaneous round of quantum communication and shared entanglement. NLQC has applications in diverse areas, ranging from quantum position-verification to quantum gravity. Recently, it has been realized that the relationships among families of NLQC tasks are highly structured: many seemingly distinct tasks are related by reductions, wherein implementations of one task can be used to efficiently implement a second task. This is analogous to the notion of reduction in complexity theory, and reveals the relative hardness of NLQC tasks. In this work we continue the study of reductions among NLQC tasks. We focus on NLQC examples of the greatest interest in quantum position-verification; in particular examples involving large classical inputs and fixed-size quantum inputs, since these constitute the most feasible protocols for position-verification schemes. Within this setting, we find many new relationships among NLQC tasks. For instance, protocols for the simplest example of redirecting a quantum system based on a classical control imply protocols for controlled single qubit measurements in arbitrary bases, the controlled application of any Clifford unitary, and even the controlled application of any unitary of the form U=C1DC0U=C_1DC_0U=C1​DC0​ with DDD an arbitrary diagonal unitary and C0,C1C_0, C_1C0​,C1​ Clifford circuits. This implies that many feasible position-verification schemes have the same asymptotic scaling for their entanglement cost, and hence a similar level of security. Our techniques rely on ideas from gate teleportation and measurement based quantum computation, among other areas, bringing several new strategies into NLQC which may be of independent interest.