Bipartite and multipartite entangled states are basic ingredients for constructing quantum networks and their accurate verification is crucial to the functioning of the networks, especially for untrusted networks. Here we propose a simple approach for verifying the Bell state in an untrusted network in which one party is not honest. Only local projective measurements are required for the honest party. It turns out each verification protocol is tied to a probability distribution on the Bloch sphere and its performance has an intuitive geometric meaning. This geometric picture enables us to construct the optimal and simplest verification protocols, which are also very useful to detecting entanglement in the untrusted network. Moreover, we show that our verification protocols can achieve almost the same sample efficiencies as protocols tailored to standard quantum state verification. Furthermore, we establish an intimate connection between the verification of Greenberger–Horne–Zeilinger states and the verification of the Bell state. By virtue of this connection we construct the optimal protocol for verifying Greenberger–Horne–Zeilinger states and for detecting genuine multipartite entanglement.

Self-testing refers to a device-independent way to uniquely identify an unknown quantum device based only on the observed statistics. Earlier results on self-testing of multipartite state were restricted either to Dicke states or Graph states. In this paper, we propose self-testing schemes for a large family of symmetric three-qubit states, namely the superposition of W state and GHZ state. We first propose and analytically prove a self-testing criterion for the special symmetric state with equal coefficients of the canonical bases, by designing subsystem self-testing of partially and maximally entangled state simultaneously. Then we demonstrate for the general case, the states can be self-tested numerically by the swap method combining semidefinite programming (SDP) in high precision.

Self-testing, which refers to device-independent characterization of the state and the measurement, enables the security of a quantum information processing task certified independently of the operation performed inside the devices. Quantum states lie at the core of self-testing as key resources. However, for different entangled states, usually, different measurement settings should be taken in self-testing recipes. This may lead to the redundancy of measurement resources. In this work, we use fixed two-binary measurements and answer the question of which states can be self-tested with the same settings. By investigating the structure of generalized tilted-Clauser-Horne-Shimony-Holt Bell operators with the sum-of-squares decomposition method, we show that a family of two-qubit entangled states can be self-tested with the same measurement settings. The robustness analysis indicates that our scheme is feasible for practical experiment instruments. Moreover, our results can be applied to various quantum information processing tasks.

Quantum secret sharing enables participants to share secrets grounded in the principles of quantum mechanics, ensuring the secrets recovery solely through collaborative efforts within an authorized subset of participants. Quantum anonymous secret sharing fulfills the fundamental requirements of quantum secret sharing while also ensuring the anonymity of the secret receivers. In order to address the turnover of personnel in practical scenarios, this paper propose a secure dynamic quantum anonymous secret sharing protocol utilizing Greenberger-Horne-Zeilinger states. In our scheme, on the premise of not reveal the identities of participants, the dynamic update of the participants can be realized, and the shared secret will not be altered. Furthermore, an identity authentication mechanism using single particles is introduced in this protocol, ensuring that only authenticated participants can engage in the sharing process. The proposed protocol is secure and can resist both internal and external attacks. Experimental validation conducted on the IBM quantum computing platform demonstrates the feasibility of our scheme.