Abstract
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.
Highlights
Entanglement is the characteristic of quantum mechanics and key resource in quantum information processing[1,2,3]
We propose a simple approach for verifying the Bell state over an untrusted network in the semi-deviceindependent (SDI) scenario in which one party is not honest
We proposed a simple and practical approach for verifying the Bell state in an untrusted quantum network in which one party is not honest
Summary
Entanglement is the characteristic of quantum mechanics and key resource in quantum information processing[1,2,3]. To guarantee the proper functioning of a quantum network, it is essential to verify the entangled state deployed in the network accurately and efficiently, especially for untrusted networks[21,22,23,24,25,26,27,28,29] This scenario has wide applications in quantum information processing, such as one-sided device-independent (DI) quantum key distribution[30], anonymous communication[31,32], and verifiable quantum secure modulo summation[33]. We establish a simple connection between verification protocols of the Bell state and probability distributions on the Bloch sphere and reveal an intuitive geometric interpretation of the performance of each verification protocol By virtue of this geometric picture, we construct the optimal and simplest protocols for verifying the Bell state, which can be applied to detecting entanglement in the untrusted network.
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