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Quantum Algorithms

Measuring quantum relative entropy with finite-size effect

arXiv
Authors: Masahito Hayashi

Year

2024

Paper ID

66125

Status

Preprint

Abstract Read

~2 min

Abstract Words

78

Citations

N/A

Abstract

We study the estimation of relative entropy D(ρ\|σ) when σ is known. We show that the Cramér-Rao type bound equals the relative varentropy. Our estimator attains the Cramér-Rao type bound when the dimension d is fixed. It also achieves the sample complexity O\(d2\) when the dimension d increases. This sample complexity is optimal when σ is the completely mixed state. Also, it has time complexity O\(d6 polylog d\). Our proposed estimator unifiedly works under both settings.

Why This Paper Matters

  • It adds a 2024 reference point for readers tracking recent quantum research.
  • We study the estimation of relative entropy D(ρ|σ) when σ is known.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2406.17299 [2] arXiv https://arxiv.org/abs/2406.17299 [3] Publisher https://arxiv.org/abs/2406.17299

Local Citation Graph (Related-Paper Links)

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