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arXiv:2208.02518 · Physical Review Letters

Fundamental Limitation on the Detectability of Entanglement

Pengyu Liu, Zhenhuan Liu, Shu Chen, Xiongfeng Ma

Published Nov 30, 2022• 23 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.129.230503

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Abstract Improvement of the detection ability of quantum entanglement is one of the essential tasks in quantum computing and quantum information. Finite tight frames play a fundamental role in a wide variety of areas and, generally, each application requires a specific class of frames and is closely related to quantum measurement. It is worth noting that a maximal set of complex equiangular vectors is closely related to a symmetric informationally complete measurement. Hence, our goal in this work is to propose a series of separability criteria assigned to a finite tight frame and some well-known inequalities in different quantum systems, respectively. In addition, some tighter criteria to detect entanglement for many-body quantum states are presented in arbitrary dimensions. Finally, the effectiveness of the proposed entanglement detection criteria is illustrated through some detailed examples.