Lower Bounds for Quantum Parameter Estimation

Geometric Lower Bounds for Distributed Parameter Estimation under Communication Constraints

We consider parameter estimation in distributed networks, where each node in the network observes an independent sample from an underlying distribution and has k bits to communicate its sample to a centralized processor which computes an estimate of a desired parameter of the distribution. We develop lower bounds for the minimax risk of estimating the underlying parameter under squared l2 loss ...

Lower Bounds for Estimation

Ziv-Zakai error bounds for quantum parameter estimation.

I propose quantum versions of the Ziv-Zakai bounds as alternatives to the widely used quantum Cramér-Rao bounds for quantum parameter estimation. From a simple form of the proposed bounds, I derive both a Heisenberg error limit that scales with the average energy and a limit similar to the quantum Cramér-Rao bound that scales with the energy variance. These results are further illustrated by ap...

General classes of performance lower bounds for parameter estimation: part II: Bayesian bounds

In this paper, a new class of Bayesian lower bounds is proposed. Derivation of the proposed class is performed via projection of each entry of the vector-function to be estimated on a closed Hilbert subspace of L2. This Hilbert subspace contains linear transformations of elements in the domain of an integral transform, applied on functions used for computation of bounds in the Weiss-Weinstein c...

Minimax lower bounds for estimation