Entanglement detection is essential in quantum information science and quantum many-body physics. It has been proved that entanglement exists almost surely for a random quantum state, while the realizations of effective entanglement criteria usually consume exponential resources, and efficient criteria often perform poorly without prior knowledge. This fact implies a fundamental limitation might exist in the detectability of entanglement. In this work, we formalize this limitation as a fundamental trade-off between the efficiency and effectiveness of entanglement criteria via a systematic method to theoretically evaluate the detection capability of entanglement criteria. For a system coupled to an environment, we prove that any entanglement criterion needs exponentially many observables to detect the entanglement effectively when restricted to single-copy operations. Otherwise, the detection capability of the criterion will decay double-exponentially. Furthermore, if multi-copy joint measurements are allowed, the effectiveness of entanglement detection can be exponentially improved, which implies a quantum advantage in entanglement detection problems.
(Ref: Pengyu Liu, Zhenhuan Liu, Shu Chen, Xiongfeng Ma. arXiv:2208.02518)
Zhenhuan Liu is a PhD candidate in the Institute for Interdisciplinary Information Science, Tsinghua University. He got his bachelor’s degree from the School of Physics, Peking University, in 2020 and started doctoral research on quantum information science. His research interests include quantum foundation, entanglement detection, and quantum system benchmarking.