Recently, a class of innovative notions on quantum network nonlocality(QNN), called full quantum network nonlocality(FQNN), have been proposed in Phys. Rev. Lett. 128 010403(2022). As the generalization of full networ...Recently, a class of innovative notions on quantum network nonlocality(QNN), called full quantum network nonlocality(FQNN), have been proposed in Phys. Rev. Lett. 128 010403(2022). As the generalization of full network nonlocality(FNN), l-level quantum network nonlocality(l-QNN) was defined in arxiv. 2306.15717 quant-ph(2024). FQNN is a NN that can be generated only from a network with all sources being non-classical. This is beyond the existing standard network nonlocality, which may be generated from a network with only a non-classical source. One of the challenging tasks is to establish corresponding Bell-like inequalities to demonstrate the FQNN or l-QNN. Up to now, the inequality criteria for FQNN and l-QNN have only been established for star and chain networks. In this paper, we devote ourselves to establishing Bell-like inequalities for networks with more complex structures. Note that star and chain networks are special kinds of tree-shaped networks. We first establish the Bell-like inequalities for verifying l-QNN in k-forked tree-shaped networks. Such results generalize the existing inequalities for star and chain networks. Furthermore, we find the Bell-like inequality criteria for l-QNN for general acyclic and cyclic networks. Finally, we discuss the demonstration of l-QNN in the well-known butterfly networks.展开更多
It was showed in [Phys. Rev. Lett. 125 090401(2020)] that there exist unbounded number of independent Bobs who can share quantum nonlocality with a single Alice by performing sequentially measurements on the Bob's...It was showed in [Phys. Rev. Lett. 125 090401(2020)] that there exist unbounded number of independent Bobs who can share quantum nonlocality with a single Alice by performing sequentially measurements on the Bob's half of the maximally entangled pure two-qubit state. However, from practical perspectives, errors in entanglement generation and noises in quantum measurements will result in the decay of nonlocality in the scenario. In this paper, we analyze the persistency and termination of sharing nonlocality in the noisy scenario. We first obtain the two sufficient conditions under which there exist n independent Bobs who can share nonlocality with a single Alice under noisy measurements and the noisy initial two qubit entangled state. Analyzing the two conditions, we find that the influences on persistency under different kinds of noises can cancel each other out. Furthermore, we describe the change patterns of the maximal nonlocality-sharing number under the influence of different noises. Finally, we extend our investigation to the case of arbitrary finite-dimensional systems.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12271394 and 12071336)the Key Research and Development Program of Shanxi Province(Grant No.202102010101004)。
文摘Recently, a class of innovative notions on quantum network nonlocality(QNN), called full quantum network nonlocality(FQNN), have been proposed in Phys. Rev. Lett. 128 010403(2022). As the generalization of full network nonlocality(FNN), l-level quantum network nonlocality(l-QNN) was defined in arxiv. 2306.15717 quant-ph(2024). FQNN is a NN that can be generated only from a network with all sources being non-classical. This is beyond the existing standard network nonlocality, which may be generated from a network with only a non-classical source. One of the challenging tasks is to establish corresponding Bell-like inequalities to demonstrate the FQNN or l-QNN. Up to now, the inequality criteria for FQNN and l-QNN have only been established for star and chain networks. In this paper, we devote ourselves to establishing Bell-like inequalities for networks with more complex structures. Note that star and chain networks are special kinds of tree-shaped networks. We first establish the Bell-like inequalities for verifying l-QNN in k-forked tree-shaped networks. Such results generalize the existing inequalities for star and chain networks. Furthermore, we find the Bell-like inequality criteria for l-QNN for general acyclic and cyclic networks. Finally, we discuss the demonstration of l-QNN in the well-known butterfly networks.
基金supported by the National Natural Science Foundation of China (Grant Nos.12271394 and 12071336)the Key Research and Development Program of Shanxi Province (Grant No.202102010101004)。
文摘It was showed in [Phys. Rev. Lett. 125 090401(2020)] that there exist unbounded number of independent Bobs who can share quantum nonlocality with a single Alice by performing sequentially measurements on the Bob's half of the maximally entangled pure two-qubit state. However, from practical perspectives, errors in entanglement generation and noises in quantum measurements will result in the decay of nonlocality in the scenario. In this paper, we analyze the persistency and termination of sharing nonlocality in the noisy scenario. We first obtain the two sufficient conditions under which there exist n independent Bobs who can share nonlocality with a single Alice under noisy measurements and the noisy initial two qubit entangled state. Analyzing the two conditions, we find that the influences on persistency under different kinds of noises can cancel each other out. Furthermore, we describe the change patterns of the maximal nonlocality-sharing number under the influence of different noises. Finally, we extend our investigation to the case of arbitrary finite-dimensional systems.
