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Physical Review A

Device-independent verification of controlled quantum controlled-not-gate teleportation

Yi-Ning Li, Neng-Fei Gong, Ru-Qing Zhang, Jing-Wei Wen, Tie-Jun Wang

Published Oct 29, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1103/g2r8-q6m5

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•Feb 6, 2013•1 citation
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.
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.
We present a device-independent analysis of controlled quantum teleportation where the receiver is not trusted. We show that the notion of genuine tripartite nonlocality allows us to certify control power in such a scenario. By considering a specific adversarial attack strategy on a device characterized by depolarizing noise, we find that control power is a monotonically increasing function of genuine tripartite nonlocality. These results are relevant for building practical quantum communication networks and also shed light on the role of nonlocality in multipartite quantum information processing.
Quantum nonlocality is an important resource for ensuring the security of quantum communication, which plays an indispensable role in building quantum networks. From bipartite to multipartite quantum systems, various inequalities are constructed as tools to unearth the quantum nonlocality. Control power is a crucial indicator for evaluating supervision, control, and collaboration in quantum networks. However, there is currently no exploration of the relevance between the control power and the quantum nonlocality in continuous variable quantum networks. In this work, based on the Mermin−Klyshko (MK) inequality with rotated quantum-number parity operators, we reveal the quantum nonlocality of general Greenberger−Horne−Zeilinger-type (GHZ-type) entangled coherent states, which can be extended to arbitrary multi-mode states. And then, we evaluate the control power through quantum nonlocality in continuous variable controlled quantum teleportation via a 3-mode GHZ-type entangled coherent state as channel. The results show that the control power of continuous variable quantum networks is a monotonically increasing function of genuine tripartite nonlocality. This quantitative dependence of control power on quantum nonlocality remains robust even with decoherence. The advantages of the MK inequality are simplicity in computation and scalability into arbitrary multi-mode channels. In addition, maximal violation of the MK inequality can be achieved more easily in the experiment. Our work proves that, compared with the Bell−Mermin inequality, the MK inequality performs better in experimental measurements of complete control power; compared with the Svetlichny inequality, the MK inequality avoids negative and unreasonable control power when inequalities exceed the classical upper bound. Therefore, the MK inequality is found to be a more reliable tool to reveal the quantum nonlocality in multipartite systems. This work illuminates the important application of nonlocality in multipartite continuous variable quantum communications and is of significance for the construction of practical quantum protocols.
Entanglement and nonlocality are two of the features demonstrated by quantum systems which give rise to new possibilities in a variety of fields such as communication technology, cryptography and the study of fundamental physics. In this thesis, we explore three such applications of entanglement and nonlocality. \n \n In the first problem, we show that currently available noisy intermediate-scale quantum (NISQ) computers can be used for versatile quantum simulations of chaotic systems. We introduce a novel classical-quantum hybrid approach for exploring the dynamics of the chaotic quantum kicked top (QKT) on a universal quantum computer. The programmability of this approach allows us to experimentally explore the complete range of QKT chaoticity parameter regimes inaccessible to previous studies. Furthermore, the number of gates in our simulation does not increase with the number of kicks, thus making it possible to study the QKT evolution for an arbitrary number of kicks without fidelity loss. Using a publicly accessible NISQ computer (IBMQ), we observe periodicities in the evolution of the 2-qubit QKT, as well as signatures of chaos in the time-averaged 2-qubit entanglement. We also demonstrate a connection between entanglement and delocalization in the 2-qubit QKT, confirming theoretical predictions. \n \n In the second problem, we perform a device independent study of controlled teleportation of a qubit with an untrusted receiver. We construct a device independently testable scenario in a way that allows us to certify in the context of controlled teleportation, whether quantum resources are being used by the device despite the receiver being untrusted. We find in this case that the well known Svetlichny inequality must be violated to certify quantum correlations. While a maximal violation of Mermin's inequality guarantees maximum control power in controlled teleportation with trusted parties, we find that the Svetlichny inequality must be maximally violated to guarantee maximal control power with an untrusted receiver. This indicates that a stronger form of nonlocality is required to device independently test the controlled quantum teleportation with an untrusted receiver. By taking the example of the total depolarized and the qubit depolarized GHZ states, we show that controller's authority is a monotonically increasing function of the Svetlichny inequality violation. We find a window of non-maximal Svetlichny inequality violation where the controller's authority is non-zero. This shows that the controlled teleportation scheme with an untrusted receiver is robust to depolarizing noise present in the device. \n \n In the third problem, we study the quantum circuit implementation of a cryptographic object called quantum lightning. Quantum lightning is a strengthening of the public key quantum money scheme. We review an existing construction of quantum lightning, build the quantum circuit implementing an important step of the scheme and identify the difficulties in realizing others.
We present a general method to quantify both bipartite and multipartite entanglement in a device-independent manner, meaning that we put a lower bound on the amount of entanglement present in a system based on observed data only but independently of any quantum description of the employed devices. Some of the bounds we obtain, such as for the Clauser-Horne-Shimony-Holt Bell inequality or the Svetlichny inequality, are shown to be tight. Besides, device-independent entanglement quantification can serve as a basis for numerous tasks. We show in particular that our method provides a rigorous way to construct dimension witnesses, gives new insights into the question whether bound entangled states can violate a Bell inequality, and can be used to construct device independent entanglement witnesses involving an arbitrary number of parties.