Root Estimator of Quantum States

Statistical Inverse Problem: Root Approach

Multiparametric statistical model providing stable reconstruction of parameters by observations is considered. The only general method of this kind is the root model based on the representation of the probability density as a squared absolute value of a certain function, which is referred to as a psi-function in analogy with quantum mechanics. The psi-function is represented by an expansion in terms of an orthonormal set of functions. It is shown that the introduction of the psi-function allows one to represent the Fisher information matrix as well as statistical properties of the estimator of…

Quantum States Estimation: Root Approach

Multiparametric statistical model providing stable reconstruction of parameters by observations is considered. The only general method of this kind is the root model based on the representation of the probability density as a squared absolute value of a certain function, which is referred to as a psi-function in analogy with quantum mechanics. The psi-function is represented by an expansion in terms of an orthonormal set of functions. It is shown that the introduction of the psi-function allows one to represent the Fisher information matrix as well as statistical properties of the estimator of…

Quantum Mechanical Square Root Speedup in a Structured Search Problem

An unstructured search for one item out of N can be performed quantum mechanically in time of order square root of N whereas classically this requires of order N steps. This raises the question of whether square root speedup persists in problems with more structure. In this note we focus on one example of a structured problem and find a quantum algorithm which takes time of order the square root of the classical time.

Generators and Roots of Quantum Logic Gates

This is an exposition of some basic mathematical aspects of quantum logic gates. At first we established some general formulas for the case of arbitrary quantum gate A with unique restriction A^2=I. The explicit form of the generators and roots of matrix A have been found . Then we apply general results to the particular cases of one-qubit and multi-qubit quantum gates. Some interesting properties of square roots of basic Pauli and Hadamard gates are demonstrated.

Valid lower bound for all estimators in quantum parameter estimation

The widely used quantum Cramer-Rao bound (QCRB) sets a lower bound for the mean square error of unbiased estimators in quantum parameter estimation, however, in general QCRB is only tight in the asymptotical limit. With a limited number of measurements biased estimators can have a far better performance for which QCRB cannot calibrate. Here we introduce a valid lower bound for all estimators, either biased or unbiased, which can serve as standard of merit for all quantum parameter estimations.

量子演化作为主方程的平方根

Quantum Evolution as a Square Root of the Master Equation

本文通过强调量子演化的随机性，探讨其与主方程的类比，从而避免量子力学诠释中的概念困难。