Number of bits returned by a quantum estimation

• URL: http://arxiv.org/abs/2403.17345v2
• Date: Sat, 14 Sep 2024 14:25:17 GMT
• Title: Number of bits returned by a quantum estimation
• Authors: Xi Lu, Wojciech Górecki, Chiara Macchiavello, Lorenzo Maccone,
• Abstract summary: We give two upper bounds to the mutual information in arbitrary quantum estimation strategies. We illustrate the usefulness of these bounds by characterizing the quantum phase estimation algorithm in the presence of noise.
• Score: 1.9865335779110387
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We give two upper bounds to the mutual information in arbitrary quantum estimation strategies. The first is based on some simple Fourier properties of the estimation apparatus. The second is derived using the first but, interestingly, depends only on the Fisher information of the parameter, so it is valid even beyond quantum estimation. We illustrate the usefulness of these bounds by characterizing the quantum phase estimation algorithm in the presence of noise. In addition, for the noiseless case, we extend the analysis beyond applying the bound and we discuss the optimal entangled and adaptive strategies, clarifying inaccuracies appearing on this topic in the literature.

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