Abhishek Shukla

We propose to design a hierarchical quantum secret sharing (HQSS) for multi-node satellite communication network, leveraging the Qline architecture (1), represents unique topology that features a linear quantum network configuration, where qubit generation and measurement occur at the endpoint satellites, with intermediate satellite nodes are limited to single-qubit unitary transforms. In designing a HQSS for multi-node satellite communication network, we consider a group of at least four satellites (A, B, C, D), in linear quantum network configuration, where qubit generation and measurement occur at the endpoint Satellites A and D respectively, with two intermediate satellites B and C limited to single-qubit measurement and unitary transforms. This setting will restrict the two intermediate satellites B and C to allow using lower powers needing the cooperation from the endpoint Satellites A and D, however, endpoint Satellite D utilizes the higher powers to reconstruct the secret without the measurement outcome of one of the lower power intermediate Satellite B or C. The hierarchical structure depends on the trusted (end node Satellite D) or untrusted (intermediate Satellite B, C) locations within a satellite quantum network. Our motivation is to use this hierarchical power for long-distance QSS, allowing leading Satellite A to securely share a quantum secret to Satellite D while bypassing one of the intermediate satellites B or C. Satellite A utlizes a 4-qubit cluster quantum entangled state with Satellites B, C, and D to perform HQSS in Qline architecture. The simplicity of hardware at intermediate nodes in the Qline architecture facilitates easier implementation of proposed HQSS for multi-node satellites. Our HQSS based on Q-line configuration shows that hierarchy (2) with minimal hardware (1, 3) would be the standard requirements in future terrestrial and non-terrestrial quantum networks (2, 3). Further, we also explore the links of our proposed HQSS protocol to semi-quantum (classical) regime (3) operated by intermediate satellite nodes. Moreover, unlike traditional QKD networks, our design based on Qline architecture doesn't require key routing through intermediate nodes, enhancing security by avoiding exposure to these nodes, without consuming established keys for routing security. Rather established keys can be efficiently consumed by a leading Satellite A to securely distributed the entanglement among intermediate Satellites B, C and endpoint Satellite D nodes. As the security of key establishment on Qline networks is composable (1), ensuring that established keys can be utilized for secure entanglement distribution executed by Satellite A among inter-satellite quantum communication network, thereby advancing larger constellations securely. References: 1. Mina Doosti, Lucas Hanouz, Anne Marin, Elham Kashefi and Marc Kaplan, “Establishing shared secret keys on quantum line networks: protocol and security” arXiv:2304.01881v1 2023. 2. C. Shukla, P. Malpani, K. Thapliyal, “Hierarchical Quantum Network using Hybrid Entanglement. Quantum Inf. Process, Vol. 20, 121, 2021. 3. C. Shukla, K. Thapliyal, A. Pathak, “Semi-quantum communication: Protocols for key agreement, controlled secure direct communication and dialogue”, Quantum Inf. Process. 16, 295, 2017.

In a quantum key distribution protocol, an eavesdropper Eve extracts information by performing the measurement on flying qubits. If the measurement basis does not match with the basis in which the qubit is prepared, it leads to a disturbance in the qubit state with 1/2 probability. There is an optimal condition between Information Gain and tolerable disturbance. Leveraging machine learning techniques, several advances have been made in the rapid development of quantum applications. In order to achieve the (upper) bound for Information Gain vs. disturbance trade-off, we investigate this optimal condition for the BB84 protocol using the gradient descent algorithm. By employing such a numerical method, we report an improvisation in the upper bound of the disturbance compare to the existing best threshold reported in Phys. Rev. A, 56 1163 (1997). Interestingly, the Information Gain by Eve at this bound is relatively less than reported in the above paper. It means with our strategy Alice-Bob are in advantageous position in both ways as they do not have to abort the protocol as early as required in Phys. Rev. A, 56 1163 (1997) at d=0.146447, as well as now the information leaked to Eve is also lowered.

We attempt to propose the first orthogonal-state-based (OSB) protocols of measurement-device-independent quantum secure direct communication (MDI-QSDC) using single basis, i.e., Bell basis as decoy qubits for eavesdropping checking, for which OSB protocols are known to achieve unconditional security fundamentally different than the conventional conjugate-coding based protocols. Further, we investigate our proposed OSB MDI-QSDC in the noisy environment and compare it with conjugate coding MDI-QSDC. We aim for achieving superior performance of OSB protocols than conjugate-coding based protocols under certain noisy environment, supported with the existing study of best basis choice of decoy qubits required for secure quantum communication. Furthermore, we have analyzed the security of the proposed protocols under several attacks such as intercept-and-resend attack, entangle-and-measure attack, fake entangled particles attack and flip attack. We show that with some modifications, the proposed OSB MDI-QSDC protocols can also be reduced to OSB MDI versions of QKD protocols.