An unbounded number of independent observers can share the nonlocality of a single maximally entangled qubit pair

Mengjun Hu, Zhiyuan Zhou, Xiao‐Min Hu +3 more

Shu-Yuan Yang, Jinchuan Hou, Kan He

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.

You-Bang Zhan, PENG-CHENG MA, Qun-Yong Zhang

Tinggui Zhang, Shao-Ming Fei

Recently the authors of Phys. Rev. Lett. 125, 090401 (2020) considered the following scenario: Alice and Bob each have half of a pair of entangled qubit states. Bob measures his half and then passes his part to a second Bob who measures again, and so on. The goal is to maximize the number of Bobs that can have an expected violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality with the single Alice. By taking the maximally entangled pure two-qubit state $|\ensuremath{\phi}\ensuremath{\rangle}=\frac{1}{\sqrt{2}}(|00\ensuremath{\rangle}+|11\ensuremath{\rangle})$ as an example, it has been constructively proved that arbitrarily many independent Bobs can share the nonlocality with the single Alice. Here we demonstrate that arbitrarily many independent observers can share the nonlocality of a single arbitrary dimensional bipartite entangled but not necessary two-qubit entangled state. Furthermore, taking the generalized Greenberger-Horne-Zeilinger (GHZ) states as an example, we show that at most two Charlies can share the genuine nonlocality of a single generalized GHZ state with an Alice and a Bob.

Xiaoping Lou, Zhigang Chen, Zeng Feng

Xin-Miao Yu, Shuyuan Yang, Kan He

The problem of sharing quantum correlations is an interesting problem in the study of quantum information theory. Silva et al. proposed the study of sharing quantum nonlocality at first. They studied the fundamental limits on nonlocality, asking whether a single pair of entangled qubits could generate a long sequence of nonlocal correlations. At the same time, the sequential scenario was also introduced first, in which Alice and Bob each have half of a pair of entangled qubit states. The first Bob measures his half and then passes his part to a second Bob who measures again and so on. Obviously, even partial preservation of entanglement in a shared state in spite of a few sequences of local operations performed by the sharing parties can be important for information processing schemes in which entanglement is utilized as a resource. Thus, the problem of sharing quantum entanglement has also been extensively investigated. Recently, Srivastava et al. proved that there exist a class of T-states whose entanglement can be shared by arbitrarily many independent observers in [ Phys. Rev. A 2022 105 062413 ]. Here, we want to find whether there are other entangled states that can be shared entanglement arbitrarily many times. In this paper, we consider the problem of sharing quantum entanglement when the initial shared state is a two-qubit entangled Werner state. The goal is to maximize the number of Bobs that can share entanglement with a single Alice. By suitably choosing the entanglement witness operator and the unsharp measurement settings by the Bobs, we prove that there exist two-qubit entangled initial shared Werner states whose entanglement can be detected by arbitrarily many sequential observers Bobs with a single Alice. Then, we also consider the special case of the Werner state, that is, the maximally entangled state as the initial shared state. In this case, its entanglement can also be witnessed arbitrarily many times, and the number of Bobs increases with the decrease of parameter.