Fundamental Limitation on the Detectability of Entanglement
- URL: http://arxiv.org/abs/2208.02518v2
- Date: Thu, 1 Dec 2022 12:21:51 GMT
- Title: Fundamental Limitation on the Detectability of Entanglement
- Authors: Pengyu Liu, Zhenhuan Liu, Shu Chen, Xiongfeng Ma
- Abstract summary: Entanglement detection is essential in quantum information science and quantum many-body physics.
We formalize this limitation as a fundamental trade-off between the efficiency and effectiveness of entanglement criteria.
If multi-copy joint measurements are allowed, the effectiveness of entanglement detection can be exponentially improved.
- Score: 2.5295602849229875
- License: http://creativecommons.org/licenses/by/4.0/
- 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 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.
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