Generalized Limits for Single-Parameter Quantum Estimation

Generalized limits for single-parameter quantum estimation.

We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multisystem interactions. For a Hamiltonian with k-system parameter-sensitive terms, the quantum limit scales as 1/Nk, where N is the number of systems. These quantum limits remain valid when the Hamiltonian is augmented by any parameter-independent in...

Quantum Limits on Parameter Estimation

We present a new proof of the quantum Cramer-Rao bound for precision parameter estimation [1–3] and extend it to a more general class of measurement procedures. We analyze a generalized framework for parameter estimation that covers most experimentally accessible situations, where multiple rounds of measurements, auxiliary systems or external control of the evolution are available. The proof pr...

Parameter Estimation for Generalized Thurstone Choice Models

We consider the maximum likelihood parameter estimation problem for a generalized Thurstone choice model, where choices are top-1 items from comparison sets of two or more items. We provide tight characterizations of the mean square error, as well as necessary and sufficient conditions for correct classification when each item belongs to one of two classes. These results provide insights into h...

Quantum parameter estimation using general single-mode Gaussian states

Gowers Norm, Function Limits, and Parameter Estimation

Let {fi : Fip → {0, 1}} be a sequence of functions, where p is a fixed prime and Fp is the finite field of order p. The limit of the sequence can be syntactically defined using the notion of ultralimit. Inspired by the Gowers norm, we introduce a metric over limits of function sequences, and study properties of it. One application of this metric is that it provides a characterization of affine-...