Separation between Entanglement Criteria and Entanglement Detection
Protocols
- URL: http://arxiv.org/abs/2403.01664v1
- Date: Mon, 4 Mar 2024 01:23:46 GMT
- Title: Separation between Entanglement Criteria and Entanglement Detection
Protocols
- Authors: Zhenhuan Liu, Fuchuan Wei
- Abstract summary: Entanglement detection is one of the most fundamental tasks in quantum information science.
We show the relationship between a good entanglement criterion and an effective entanglement detection protocol (EDP)
Our results can be used to prove the exponential speedups achieved through quantum memory.
- Score: 1.1471584747312693
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Entanglement detection is one of the most fundamental tasks in quantum
information science, playing vital roles in theoretical studies and quantum
system benchmarking. Researchers have proposed many powerful entanglement
criteria with high detection capabilities and small observable numbers.
Nonetheless, entanglement criteria only represent mathematical rules deciding
the existence of entanglement. The relationship between a good entanglement
criterion and an effective experimental entanglement detection protocol (EDP)
is poorly understood. In this study, we introduce postulates for EDPs about
their detection capabilities and robustness and use them to show the difference
between entanglement criteria and EDPs. Specifically, we design an entanglement
detection task for unknown pure bipartite states and demonstrate that the
sample complexity of any EDP and the number of observables for a good
entanglement criterion can have exponential separation. Furthermore, we
discover that the optimal EDP with the lowest sample complexity does not
necessarily correspond to the optimal entanglement criterion with the fewest
observables. Our results can be used to prove the exponential speedups achieved
through quantum memory and be generalized to multipartite entanglement
detection. By highlighting the significance and independence of EDP design, our
work holds practical implications for entanglement detection experiments.
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