Sub-Quantum Fisher Information

• URL: http://arxiv.org/abs/2101.10144v2
• Date: Thu, 24 Jun 2021 15:22:08 GMT
• Title: Sub-Quantum Fisher Information
• Authors: M. Cerezo, Akira Sone, Jacob L. Beckey, Patrick J. Coles
• Abstract summary: We analyze a lower bound on the Quantum Fisher Information (QFI) The sub-QFI is based on the super-fidelity, an upper bound on Uhlmann's fidelity. We provide additional meaning to the sub-QFI as a measure of coherence, asymmetry, and purity loss.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Quantum Fisher Information (QFI) plays a crucial role in quantum information theory and in many practical applications such as quantum metrology. However, computing the QFI is generally a computationally demanding task. In this work we analyze a lower bound on the QFI which we call the sub-Quantum Fisher Information (sub-QFI). The bound can be efficiently estimated on a quantum computer for an $n$-qubit state using $2n$ qubits. The sub-QFI is based on the super-fidelity, an upper bound on Uhlmann's fidelity. We analyze the sub-QFI in the context of unitary families, where we derive several crucial properties including its geometrical interpretation. In particular, we prove that the QFI and the sub-QFI are maximized for the same optimal state, which implies that the sub-QFI is faithful to the QFI in the sense that both quantities share the same global extrema. Based on this faithfulness, the sub-QFI acts as an efficiently computable surrogate for the QFI for quantum sensing and quantum metrology applications. Finally, we provide additional meaning to the sub-QFI as a measure of coherence, asymmetry, and purity loss.

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