---
title: "Efficiently evaluating Holevo, RLD and SLD Cramér-Rao bounds for multiparameter quantum estimation with Gaussian states"
url: https://daily.dev/posts/efficiently-evaluating-holevo-rld-and-sld-cram-r-rao-bounds-for-multiparameter-quantum-estimation-w-9geyiwhov
source_url: https://www.nature.com/articles/s42005-026-02550-6
type: article
source: "Nature"
published: 2026-03-02T06:13:12.909Z
updated: 2026-03-02T06:13:38.067Z
tags: ["python", "quantum-computing"]
reading_time: 15
upvotes: 0
comments: 0
language: en
---

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# Efficiently evaluating Holevo, RLD and SLD Cramér-Rao bounds for multiparameter quantum estimation with Gaussian states

**[Nature](https://daily.dev/sources/nature)** · 15 min read · 0 upvotes · 0 comments

## Summary

A unified framework is introduced for computing the Holevo Cramér-Rao bound (HCRB) for arbitrary multimode Gaussian states in multiparameter quantum metrology. By reformulating the HCRB as a semidefinite program (SDP) that depends only on first and second moments of the state and their parametric derivatives, the approach avoids the intractable optimization over Hermitian operators in infinite-dimensional systems. The same phase-space formulation also yields SDP forms for the symmetric logarithmic derivative (SLD) and right logarithmic derivative (RLD) bounds, plus analytical results for two-parameter single-mode covariance matrix estimation. The method is demonstrated on simultaneous estimation of phase and loss, and joint estimation of displacement and squeezing. Python code via CVXPY is available on GitHub.

## Full article

daily.dev links to this article rather than hosting it. Read it at the original source: <https://www.nature.com/articles/s42005-026-02550-6>

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Tags: [#python](https://daily.dev/tags/python), [#quantum-computing](https://daily.dev/tags/quantum-computing)

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