Realizing quantum nonlocal operations is important in quantum computing, quantum information, and quantum cryptography. This study explores probabilistic protocols to achieve high-fidelity nonlocal operation \(U_{AB}(\lambda )=e^{i\lambda \sigma _{n_{A}}\sigma _{n_{B}}}\) , \(\lambda \in (0,\frac{\pi }{2})\) particularly investigating their applicability to more general quantum entangled states. This involves collaborative efforts between Alice and Bob, employing local unitary operations and measurements to implement nonlocal gates effectively. What’s more, we also extend the general technique to the case when the entangled quantum state is many-body, and we find that it is possible to realize a many-body nonlocal operation \(U_{A_{1}A_{2}\cdots A_{N}C}(\xi )=e^{i\xi \sigma _{n_{A_{1}}}\sigma _{n_{A_{2}}}\cdots \sigma _{n_{A_{N}}}\sigma _{n_{C}}}\) , \(\xi \in (0,\frac{\pi }{2})\) . What’s more, we expect to encounter the effects generated by quantum noise in practical applications, but for specific applications we can find appropriate ways to mitigate the effects of quantum noise. In a word, advances in this area suggest promising results, demonstrating the potential to realize complex quantum operations using minimal resources.
