arXiv subjects

Akio Fujiwara

Publications and source records attributed to Akio Fujiwara.

12 recordsLinked to original sources

arXiv2026

A game-theoretic probability approach to loopholes in CHSH experiments

We study the CHSH inequality from an informational, timing-sensitive viewpoint using game-theoretic probability, which avoids assuming an underlying probability space. The locality loophole and the measurement-dependence (``freedom-of-choice'') loophole are reformulated as structural constraints in a sequential hidden-variable game between Scientists and Nature. We construct a loopholes-closed game with capital processes that test (i) convergence of empirical conditional frequencies to the CHSH correlations and (ii) the absence of systematic correlations between measurement settings and Nature's hidden-variable assignments, and prove that Nature cannot satisfy both simultaneously: at least one capital process must diverge. This yields an operational winning strategy for Scientists and a game-theoretic probabilistic interpretation of experimentally observed CHSH violations.

quant-ph↗

arXiv2025

A coding theoretic study of homogeneous Markovian predictive games

This paper explores a predictive game in which a Forecaster announces odds based on a time-homogeneous Markov kernel, establishing a game-theoretic law of large numbers for the relative frequencies of occurrences of all finite strings. A key feature of our proof is a betting strategy built on a universal coding scheme, inspired by the martingale convergence theorem and algorithmic randomness theory, without relying on a diversified betting approach that involves countably many operating accounts. We apply these insights to thermodynamics, offering a game-theoretic perspective on Le\'o Szil\'ard's thought experiment.

cs.IT↗

arXiv2024

Efficiency of estimators for locally asymptotically normal quantum statistical models

We herein establish an asymptotic representation theorem for locally asymptotically normal quantum statistical models. This theorem enables us to study the asymptotic efficiency of quantum estimators such as quantum regular estimators and quantum minimax estimators, leading to a universal tight lower bound beyond the i.i.d. assumption. This formulation complements the theory of quantum contiguity developed in the previous paper [Fujiwara and Yamagata, Bernoulli 26 (2020) 2105-2141], providing a solid foundation of the theory of weak quantum local asymptotic normality.

quant-ph↗

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.

quant-ph↗

arXiv2023

Autoparallelity of Quantum Statistical Manifolds in Light of Quantum Estimation Theory

In this paper we study the autoparallelity w.r.t. the e-connection for an information-geometric structure called the SLD structure, which consists of a Riemannian metric and mutually dual e- and m-connections, induced on the manifold of strictly positive density operators. Unlike the classical information geometry, the e-connection has non-vanishing torsion, which brings various mathematical difficulties. The notion of e-autoparallel submanifolds is regarded as a quantum version of exponential families in classical statistics, which is known to be characterized as statistical models having efficient estimators (unbiased estimators uniformly achieving the equality in the Cramer-Rao inequality). As quantum extensions of this classical result, we present two different forms of estimation-theoretical characterizations of the e-autoparallel submanifolds. We also give several results on the e-autoparallelity, some of which are valid for the autoparallelity w.r.t. an affine connection in a more general geometrical situation.

quant-ph↗

arXiv2021

Noise-induced degeneration in online learning

In order to elucidate the plateau phenomena caused by vanishing gradient, we herein analyse stability of stochastic gradient descent near degenerated subspaces in a multi-layer perceptron. In stochastic gradient descent for Fukumizu-Amari model, which is the minimal multi-layer perceptron showing non-trivial plateau phenomena, we show that (1) attracting regions exist in multiply degenerated subspaces, (2) a strong plateau phenomenon emerges as a noise-induced synchronisation, which is not observed in deterministic gradient descent, (3) an optimal fluctuation exists to minimise the escape time from the degenerated subspace. The noise-induced degeneration observed herein is expected to be found in a broad class of machine learning via neural networks.

nlin.AO↗

arXiv2019

Noncommutative Lebesgue decomposition and contiguity with applications in quantum statistics

We herein develop a theory of contiguity in the quantum domain based upon a novel quantum analogue of the Lebesgue decomposition. The theory thus formulated is pertinent to the weak quantum local asymptotic normality introduced in the previous paper [Yamagata, Fujiwara, and Gill, \textit{Ann. Statist.}, \textbf{41} (2013) 2197-2217.], yielding substantial enlargement of the scope of quantum statistics.

math.OA↗

arXiv2017

Noncommutative Lebesgue decomposition with application to quantum local asymptotic normality

We develop a theory of local asymptotic normality in the quantum domain based on a noncommutative extension of the Lebesgue decomposition. This formulation gives a substantial generalization of the previous paper [Yamagata, Fujiwara, and Gill (2013). Ann. Statist., 41, 2197-2217.], extending the scope of the quantum local asymptotic normality to a wider class of quantum statistical models that comprise density operators of mixed ranks.

quant-ph↗

arXiv2016

Data processing for qubit state tomography: An information geometric approach

A statistically feasible data post-processing method for the conventional qubit state tomography is studied from an information geometrical point of view. It is shown that the space $(-1,1)^3$ of the Stokes parameters $(ξ_1, ξ_2,ξ_3)$ that specify qubit states should be regarded as a Riemannian manifold endowed with a metric $g_{ij}:=δ_{ij}/(1-(ξ_i)^2)$, and that the data processing based on the maximum likelihood method is realized by the orthogonal projection from the empirical distribution onto the Bloch sphere with respect to the metric $g_{ij}$. An efficient algorithm for computing the maximum likelihood estimate is also proposed.

quant-ph↗

arXiv2016

Information geometry of sandwiched Rényi $α$-divergence

Information geometrical structure $(g^{(D_α)}, \nabla^{(D_α)},\nabla^{(D_α)*})$ induced from the sandwiched Rényi $α$-divergence $D_α(ρ\|σ):=\frac{1}{α(α-1)}\log\,{\rm Tr} \left(σ^{\frac{1-α}{2α}}ρ\,σ^{\frac{1-α}{2α}}\right)^α$ on a finite quantum state space $\mathcal{S}$ is studied. It is shown that the Riemannian metric $g^{(D_α)}$ is monotone if and only if $α\in(-\infty, -1]\cup [\frac{1}{2},\infty)$, and that the quantum statistical manifold $({\mathcal{S}}, g^{(D_α)}, \nabla^{(D_α)},\nabla^{(D_α)*})$ is dually flat if and only if $α=1$.

quant-ph↗

arXiv2013

Quantum local asymptotic normality based on a new quantum likelihood ratio

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. As an application, we prove the asymptotic achievability of the Holevo bound for the local shift parameter.

quant-ph↗

arXiv2012

Experimental Demonstration of Adaptive Quantum State Estimation

The first experimental demonstration of an adaptive quantum state estimation (AQSE) is reported. The strong consistency and asymptotic efficiency of AQSE have been mathematically proven [ A. Fujiwara J. Phys. A 39 12489 (2006)]. In this Letter, the angle of linear polarization of single photons, the phase parameter between the right and the left circularly polarization, is estimated using AQSE, and the strong consistency and asymptotic efficiency are experimentally verified. AQSE will provide a general useful method in both quantum information processing and metrology.

quant-ph↗