Detecting unfaithful entanglement by multiple fidelities

• URL: http://arxiv.org/abs/2409.13214v1
• Date: Fri, 20 Sep 2024 04:58:12 GMT
• Title: Detecting unfaithful entanglement by multiple fidelities
• Authors: Ruiqi Zhang, Zhaohui Wei,
• Abstract summary: Certifying entanglement for unknown quantum states experimentally is a fundamental problem in quantum computing and quantum physics. Because of being easy to implement, a most popular approach for this problem in modern quantum experiments is detecting target quantum states with fidelity-based entanglement witnesses. Recently, it has been realized that there exist so-called unfaithful quantum states, which can be entangled, but their entanglement cannot be certified by any fidelity-based entanglement witnesses.
• Score: 7.320365821066744
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Certifying entanglement for unknown quantum states experimentally is a fundamental problem in quantum computing and quantum physics. Because of being easy to implement, a most popular approach for this problem in modern quantum experiments is detecting target quantum states with fidelity-based entanglement witnesses. Specifically, if the fidelity between a target state and an entangled pure state exceeds a certain value, the target state can be guaranteed to be entangled. Recently, however, it has been realized that there exist so-called unfaithful quantum states, which can be entangled, but their entanglement cannot be certified by any fidelity-based entanglement witnesses. In this paper, by specific examples we show that if one makes a slight modification to fidelity-based entanglement witnesses by combining multiple fidelities together, it is still possible to certify entanglement for unfaithful quantum states with this popular technique. Particularly, we will analyze the mathematical structure of the modified entanglement witnesses, and propose an algorithm that can search for the optimal designs for them.

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