arXiv subjects

Fuyuhiko Tanaka

Publications and source records attributed to Fuyuhiko Tanaka.

9 recordsLinked to original sources

arXiv2026

Robust multi-hypothesis quantum-state discrimination under unknown common unitary perturbations via least favorable priors

We study robust K-ary quantum-state discrimination when all candidate states are affected by the same unknown common unitary perturbation. The unknown perturbation does not represent the label to be identified, but acts as a nuisance factor that changes the performance of a fixed measurement. We formulate the problem as a minimax decision problem over the possible perturbations and propose using the Bayes-optimal collective measurement associated with a least favorable prior (LFP) on the nuisance-parameter space. For a finite discretization of this space, we show that the LFP can be computed by a semidefinite program and that the corresponding value coincides with the finite-grid minimax success probability. As numerical demonstrations, we consider a binary nonorthogonal qubit model and a nonorthogonal three-state qutrit model with an unknown common unitary perturbation. The LFP-based measurement substantially flattens the success-probability profile and improves the worst-case success probability compared with a reference-point optimal measurement and a uniform-prior Bayes measurement. The resulting LFP concentrates its weight on regions of the nuisance-parameter space that actively limit the robust discrimination performance, thereby providing both a constructive measurement design and a diagnostic description of the difficult nuisance-parameter regimes.

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arXiv2025

The differential structure shared by probability and moment matching priors on non-regular statistical models via the Lie derivative

In Bayesian statistics, the selection of noninformative priors is a crucial issue. There have been various discussions on theoretical justification, problems with the Jeffreys prior, and alternative objective priors. Among them, we focus on two types of matching priors consistent with frequentist theory: the probability matching priors and the moment matching priors. In particular, no clear relationship has been established between these two types of priors on non-regular statistical models, even though they share similar objectives. Considering information geometry on a one-sided truncated exponential family, a typical example of non-regular statistical models, we find that the Lie derivative along a particular vector field provides the conditions for both the probability and moment matching priors. Notably, this Lie derivative does not appear in regular models. These conditions require the invariance of a generalized volume element with respect to differentiation along the non-regular parameter. This invariance leads to a suitable decomposition of the one-sided truncated exponential family into one-dimensional submodels. This result promotes a unified understanding of probability and moment matching priors on non-regular models.

math.ST↗

arXiv2023

Adaptive quantum state estimation for two optical point sources

In classical optics, there is a well-known resolution limit, called Rayleigh's curse, in the separation of two incoherent optical sources in close proximity. Recently, Tsang et al. revealed that this difficulty may be circumvented in the framework of quantum theory. Following their work, various estimation methods have been proposed to overcome Rayleigh's curse, but none of them enables us to estimate the positions of two point sources simultaneously based on single-photon measurements with high accuracy. In this study, we propose a method to simultaneously estimate the positions of two point sources with the highest accuracy using adaptive quantum state estimation scheme.

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arXiv2020

Reliable Characterization for Improving and Validating Accurate Quantum Operations

A reliable method for characterizing quantum operations that is suitable for improving and validating their accuracies is indispensable for realizing a practical quantum computer. Known methods are still not sufficient because they lack reliability or are not suitable for use in the improvement and validation steps. Here we propose a reliable characterization method that is suitable for the accuracy validation step. First, we introduce a new self-consistent estimator with regularization and physicality constraints that are designed for improvement and validation. Second, we mathematically prove that the method provides estimation results that are stringently physical and converge to the gauge-equivalence class of the quantum operations of interest at the limit of data size going to infinity. The asymptotic convergence guarantees the reliability of the method, and the physical and regularized results ensure the suitability to the validation task. We also derive the asymptotic convergence rate, which would be optimal. Finally, we show numerical results on 1-qubit system, which confirm the theoretical results and prove that the method proposed is practical.

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arXiv2014

Quantum Minimax Theorem

Recently, many fundamental and important results in statistical decision theory have been extended to the quantum system. Quantum Hunt-Stein theorem and quantum locally asymptotic normality are typical successful examples. In the present paper, we show quantum minimax theorem, which is also an extension of a well-known result, minimax theorem in statistical decision theory, first shown by Wald and generalized by LeCam. Our assertions hold for every closed convex set of measurements and for general parametric models of density operator. On the other hand, Bayesian analysis based on least favorable priors has been widely used in classical statistics and is expected to play a crucial role in quantum statistics. According to this trend, we also show the existence of least favorable priors, which seems to be new even in classical statistics.

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arXiv2014

An analytic example of latent information prior

Recently Komaki proposed latent information priors as an objective prior. In this short article, we consider the one-step ahead prediction based on one-sample under the binomial model. In this specific case, the latent information prior is derived analytically and shown to be a discrete prior. It verifies the numerical result by Komaki. As a by-product, we obtain the minimal complete class, the minimax predictive distribution.

math.ST↗

arXiv2009

New derivation of Born's law and parameter estimation based on a relative state formulation

Excluding the concept of probability in quantum mechanics, we derive Born's law from the remaining postulates in quantum mechanics using type method. We also give a way of determining the unknown parameter in a state vector based on an indirect measurement model. While Deutsch adopt a concept of rational decision-maker who introduces probability, we adopt a concept of statistician in our measurement model and clarifies the distinguished feature of quantum measurement. Like many worlds interpretation, our scenario gives a simple solution for problem of measurement.

quant-ph↗

arXiv2006

Generalized Bayesian predictive density operators

Recently the quantum Bayesian prediction problem was formulated by Tanaka and Komaki (2005). It is shown that Bayesian predictive density operators are the best predictive density operators when we evaluate them by using the averaged quantum relative entropy based on a prior distribution. In the present paper, we adopt the quantum alpha-divergence as a wider class of loss function. The generalized Bayesian predictive density operator is defined and shown to be best among all the estimates of the unknown density operator.

quant-ph↗

arXiv2005

Asymptotic Expansion of the Risk Difference of the Bayesian Spectral Density in the ARMA model

The autoregressive moving average (ARMA) model is one of the most important models in time series analysis.We consider the Bayesian estimation of an unknown spectral density in the ARMA model.In the i.i.d. cases, Komaki showed that Bayesian predictive densities based on a superharmonic prior asymptotically dominate those based on the Jeffreys prior.It is shown by using the asymptotic expansion of the risk difference.We obtain the corresponding result in the ARMA model.

math.ST↗