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 exponentially many resources with regard to system size or qubit number, 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 evaluate the detection capability of entanglement criteria theoretically. 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 multicopy joint measurements are allowed, the effectiveness of entanglement detection can be exponentially improved, which implies a quantum advantage in entanglement detection problems. Our results may shed light on why quantum phenomena are difficult to observe in large noisy systems.

中文翻译：

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纠缠可检测性的基本限制

纠缠检测在量子信息科学和量子多体物理学中是必不可少的。已经证明，对于随机量子态，纠缠几乎肯定存在，而有效纠缠准则的实现通常会在系统大小或量子比特数方面消耗成指数级的大量资源，而有效准则通常在没有先验知识的情况下表现不佳。这一事实意味着纠缠的可检测性可能存在基本限制。在这项工作中，我们通过系统方法将这种限制形式化为纠缠标准的效率和有效性之间的基本权衡，以从理论上评估纠缠标准的检测能力。对于耦合到环境的系统，我们证明，任何纠缠标准都需要指数级多的可观察量才能在仅限于单副本操作时有效地检测纠缠。否则，标准的检测能力将呈双倍指数衰减。此外，如果允许多副本联合测量，纠缠检测的有效性可以呈指数级提高，这意味着纠缠检测问题具有量子优势。我们的结果可能会阐明为什么在大型嘈杂系统中难以观察到量子现象。这意味着纠缠检测问题中的量子优势。我们的结果可能会阐明为什么在大型嘈杂系统中难以观察到量子现象。这意味着纠缠检测问题中的量子优势。我们的结果可能会阐明为什么在大型嘈杂系统中难以观察到量子现象。