The Holevo Cramér-Rao bound is at most thrice the Helstrom version

Abstract

In quantum metrology, the Holevo Cramér-Rao bound has attracted renewed interest in recent years due to its superiority over the Helstrom Cramér-Rao bound and its asymptotic attainability for multi-parameter estimation. Its evaluation, however, is often much more difficult than that of the Helstrom version, calling into question the actual improvement offered by the Holevo CRB and whether it is worth the trouble. Here I prove that the Holevo bound is at most thrice the Helstrom version, so the improvement must be limited. The result also shows that the Helstrom version remains a pretty good bound even for multiple parameters and can be approached asymptotically to within a factor of 3.

v2: no change to the paper, just adding a comment here: this work is superseded by Carollo et al., J. Stat. Mech. 094010 (2019); 029902 (2020); Tsang, Albarelli, and Datta, Phys. Rev. X 10, 031023 (2020) [arXiv:1906.09871], which prove a tighter bound

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Cited by in corpus (3)

• A perspective on multiparameter quantum metrology: from theoretical tools to applications in quantum imaging
• Tight bounds on the simultaneous estimation of incompatible parameters
• Bayesian multi-parameter quantum metrology with limited data