Related papers: Conciliation of Bayes and Pointwise Quantum State …
A usual assumption in quantum estimation is that the unknown parameter labels the possible states of the system, while it influences neither the sample space of outcomes nor the measurement aimed at extracting information on the parameter…
We consider two variants of a quantum-statistical generalization of the Cramer-Rao inequality that establishes an invariant lower bound on the mean square error of a generalized quantum measurement. The proposed complex variant of this…
The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with…
The Holevo bound is a bound on the mutual information for a given quantum encoding. In 1996 Schumacher, Westmoreland and Wootters [Schumacher, Westmoreland and Wootters, Phys. Rev. Lett. 76, 3452 (1996)] derived a bound which reduces to the…
Quantum metrology protocols are typically designed around the assumption that we have an abundance of measurement data, but recent practical applications are increasingly driving interest in cases with very limited data. In this regime the…
Finding the optimal attainable precisions in quantum multiparameter metrology is a non trivial problem. One approach to tackling this problem involves the computation of bounds which impose limits on how accurately we can estimate certain…
Braunstein and Caves (1994) proposed to use Helstrom's {\em quantum information} number to define, meaningfully, a metric on the set of all possible states of a given quantum system. They showed that the quantum information is nothing else…
We develop a theory of local asymptotic normality in the quantum domain based on a novel quantum analogue of the log-likelihood ratio. This formulation is applicable to any quantum statistical model satisfying a mild smoothness condition.…
In blind compression of quantum states, a sender Alice is given a specimen of a quantum state $\rho$ drawn from a known ensemble (but without knowing what $\rho$ is), and she transmits sufficient quantum data to a receiver Bob so that he…
This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cram\`er-Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are…
We study asymptotically optimal statistical inference concerning the unknown state of $N$ identical quantum systems, using two complementary approaches: a "poor man's approach" based on the van Trees inequality, and a rather more…
Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…
We generalize the approach by Braunstein and Caves [Phys. Rev. Lett. 72, 3439 (1994)] to quantum multi-parameter estimation with general states. We derive a matrix bound of the classical Fisher information matrix due to each measurement…
This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A lower bound on the Bayes risk not only serves as a lower bound…
In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here we propose a theory of quantum…
This paper investigates the {\em nonasymptotic} properties of Bayes procedures for estimating an unknown distribution from $n$ i.i.d.\ observations. We assume that the prior is supported by a model $(\scr{S},h)$ (where $h$ denotes the…
We identify the critical deviation scale governing Bayesian evidence accumulation in regular parametric testing. Under integrated Bayes risk with zero-one loss, the risk-optimal rejection boundary lies in a moderate deviation regime, with a…
This paper presents a general asymptotic theory of sequential Bayesian estimation giving results for the strongest, almost sure convergence. We show that under certain smoothness conditions on the probability model, the greedy information…
This is an English translation of the manuscript which appeared in Surikaiseki Kenkyusho Kokyuroku No. 1055 (1998). The asymptotic efficiency of statistical estimate of unknown quantum states is discussed, both in adaptive and collective…
Regularized system identification is the major advance in system identification in the last decade. Although many promising results have been achieved, it is far from complete and there are still many key problems to be solved. One of them…