Explicit formula for the Holevo bound for two-parameter qubit-state estimation problem
- Graduate School of Information Systems, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585 (Japan)
The main contribution of this paper is to derive an explicit expression for the fundamental precision bound, the Holevo bound, for estimating any two-parameter family of qubit mixed-states in terms of quantum versions of Fisher information. The obtained formula depends solely on the symmetric logarithmic derivative (SLD), the right logarithmic derivative (RLD) Fisher information, and a given weight matrix. This result immediately provides necessary and sufficient conditions for the following two important classes of quantum statistical models; the Holevo bound coincides with the SLD Cramér-Rao bound and it does with the RLD Cramér-Rao bound. One of the important results of this paper is that a general model other than these two special cases exhibits an unexpected property: the structure of the Holevo bound changes smoothly when the weight matrix varies. In particular, it always coincides with the RLD Cramér-Rao bound for a certain choice of the weight matrix. Several examples illustrate these findings.
- OSTI ID:
- 22597055
- Journal Information:
- Journal of Mathematical Physics, Vol. 57, Issue 4; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
Similar Records
Saturating the one-axis twisting quantum Cramér-Rao bound with a total spin readout
Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds