HIROSHI NAGAOKA
| Emeritus Professor etc. | Emeritus Professor |
Researcher Information
Career
Research Activity Information
Paper
- Information-geometrical characterization of statistical models which are statistically equivalent to probability simplexes
Hiroshi Nagaoka
Proc. of 2017 IEEE International Symposium on Information Theory (ISIT), 1346-1350, Jun. 2017, Peer-reviwed
International conference proceedings, English - A characterization of statistical manifolds on which the relative entropy is a Bregman divergence
Hiroshi Nagaoka
2016 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, IEEE, 1656-1659, 2016, Peer-reviwed, It is well known that the relative entropy (Kullback-Leibler divergence) is represented in the form of Bregman divergence on exponential families and mixture families for some coordinate systems. We give a characterization of the class of statistical manifolds (smooth manifolds of probability mass functions on finite sample spaces) having coordinate systems for which the relative entropy is a Bregman divergence.
International conference proceedings, English - A Two-Step Lniversal VV Code L sing an Asymptotically Sufficient Statistic Extracted from a VF Code
Mitsuharu Arimura; Hiroshi Nagaoka
PROCEEDINGS OF 2016 INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY AND ITS APPLICATIONS (ISITA 2016), IEEE, Proc. of ISITA 2016, 6-10, 2016, Peer-reviwed, In this paper, some theorems which give relationships between a sufficient statistic and the universality of a VV source code are presented. These theorems can be used as a methodology to construct a new two-step universal code using a sufficient statistic. As an example, the parsing tree of LZY code, which is a variation of LZ78 code, is investigated. It is proved that LZY parsing tree is an asymptotically sufficient statistic for the class of finite state sources. Furthermore, a universal two-step VV code for the same class is constructed based on the LZY parsing tree. These results are an extension of the previous results on FV codes to VV codes. Since the type (empirical distribution of symbols) is a sufficient statistic for the class of stationary memoryless sources, an asymptotically sufficient statistic can be regarded as an extension of the type, and the two-step code constructed in this paper can be seen as a generalization of Lynch-Davisson code for sources with memory.
International conference proceedings, English - A Fundamental Inequality for Lower-bounding the Error Probability for Classical and Classical-Quantum Multiple Access Channels and Its Applications,
T. Kubo; H. Nagaoka
IEICE Trans. Fundamentals, The Institute of Electronics, Information and Communication Engineers, E98-A, 12, 2376-2383, Dec. 2015, Peer-reviwed
Scientific journal, English - Lower Bounds on the Error Probability in Classical and Quantum State Discrimination
T. Kubo; H. Nagaoka
Proc. of ISITA2012, 299-302, Oct. 2012, Peer-reviwed
International conference proceedings, English - 量子i.i.d.状態の仮説検定に関する数値的手法とその誤差分析
坂下達哉; 片桐孝洋; 長岡浩司
情報処理学会論文誌 コンピューティングシステム (ACS), 情報処理学会, 4, 4, 214-227, Oct. 2011, Peer-reviwed, 本論文ではテンソル積の既約分解を用いた 2 × 2 サイズの密度行列の量子 i.i.d. 状態に対する仮説検定問題の数値的手法を扱う．特に，誤り確率の計算に現れる数値誤差について分析を行った．その結果，既約成分ごとの寄与の相対関係が重要であることを見い出した．また，多倍長桁数と固有値分解の収束判定に用いる ε を変えたときに，数値誤差がどのように現れるかを考察した．In this paper, we deal with a numerical method for hypothesis testing of quantum i.i.d. states for 2 × 2 density matrices based on the irreducible decomposition of tensor products. Especially, we analyze numerical errors appearing in computation of the error probability. As a result, we found out that the mutual relation among the contributions of irreducible elements is important. In addition, we studied how numerical error appears for different settings of multiple-precision and the convergence criterion ε of eigenvalue routine.
Scientific journal, Japanese - A Numerical Study of Hypothesis Testing for Quantum I.I.D. States
T. Sakashita; H. Nagaoka
Proc., 213-214, Aug. 2010, Peer-reviwed
International conference proceedings, English - Information geometrical approach to mean-field approximation for quantum Ising spin models
Y. Nihal; H. Nagaoka
Journal of Physics A: Mathematical and Theoretical, 41, 065005, 2008, Peer-reviwed
Scientific journal, English - Making good codes for classical-quantum channel coding via quantum hypothesis testing
Tomohiro Ogawa; Hiroshi Nagaoka
IEEE TRANSACTIONS ON INFORMATION THEORY, IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 53, 6, 2261-2266, Jun. 2007, Peer-reviwed, In this correspondence, we give an alternative proof of the direct part of the classical-quantum channel coding theorem (the Holevo-Schumacher-Westmoreland (HSW) theorem), using ideas of quantum hypothesis testing. In order to show the existence of good codes, we invoke a limit theorem, relevant to the quantum Stein's lemma, in quantum hypothesis testing as the law of large numbers used in the classical case. We also apply a greedy construction of good codes using a packing procedure of noncommutative operators. Consequently we derive an upper bound on the coding error probability, which is used to give an alternative proof of the HSW theorem. This approach elucidates how the Holevo information applies to the classical-quantum channel coding problems.
Scientific journal, English - An Information-Spectrum Approach to Classical and Quantum Hypothesis Testing for Simple Hypotheses
H. Nagaoka; M. Hayashi
IEEE Transactions on Information Theory, 53, 2, 534-549, 2007, Peer-reviwed
Scientific journal, English - Information geometry of mean field approximation for quantum Boltzmann machines
N. Yapage; H. Nagaoka
Proc., 143-144, 2006, Peer-reviwed
International conference proceedings, English - Some mathematical problems related to quantum hypothesis testing
Hiroshi Nagaoka
General Theory of Information Transfer and Combinatorics, SPRINGER-VERLAG BERLIN, 4123, 1100-1103, 2006, We present two open problems related to the asymptotics of quantum hypothesis testing, together with some discussions about their mutual relation, the classical counterparts and a possible conjecture.
International conference proceedings, English - 量子情報幾何の世界
長岡浩司
電子情報通信学会論文誌, J88-A, 8, 874-885, 2005, Peer-reviwed
Scientific journal, Japanese - An extension of asymptotically sufficient statistic method for pointwise strong universality
M Arimura; H Nagaoka
2005 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), VOLS 1 AND 2, IEEE, Proc., 505-509, 2005, Peer-reviwed, In the previous work in Proc. ISIT2003 and Proc. ISITA2004, we have investigated some relationships between sufficient statistic and weakly universal lossless source coding, and proposed asymptotically sufficient statistic method to evaluate the pointwise redundancy of source codes. This method is an attempt to understand the universality of general lossless source codes from a simple and unified viewpoint. In this paper, we present a new theorem which enables our method to show the pointwise strong universality of lossless source codes. As an example of the theorem, we prove the pointwise strong universality of the original Lynch-Davisson code and conditional Lynch-Davisson code for the class of stationary memoryless and Markov sources, respectively. Moreover, it is shown that this method can be applied to the class of finite state sources. We prove that a blockwise Lynch-Davisson code is pointwise strongly universal for this class. From the viewpoint of our method, all of these algorithms can be seen as examples of a two-step source code using a kind of asymptotically sufficient statistic. The result of this paper gives a unified viewpoint for the universality of context-based algorithms and block-based algorithms, which are typical two types of universal lossless source coding algorithms.
International conference proceedings, English - A Quantum Extension of Boltzmann Machine: An Information Geometrical Approach
N. Yapage; H. Nagaoka
Proc., 204-205, 2005, Peer-reviwed
International conference proceedings, English - Asymptotically Sufficient Statistic Method for Evaluation of Pointwise Redundancy of FV Source Codes
M. Arimura; H. Nagaoka
Proc., 769-774, 2004, Peer-reviwed
International conference proceedings, English - General Formulas for Capacity of Classical-Quantum Channels
M. Hayashi; H. Nagaoka
IEEE Transactions on Information Theory, 49, 7, 1753-1768, Jul. 2003, Peer-reviwed
Scientific journal, English - General Conditions for Existence of Weakly Universal FV Source Codes
M. Arimura; H. Nagaoka
Proc., 110, 2003, Peer-reviwed
International conference proceedings, English - A New Proof of the Channel Coding Theorem via Hypothesis Testing in Quantum Information Theory
T. Ogawa; H. Nagaoka
Proc., 73, 2002, Peer-reviwed
International conference proceedings, English - A General Formula for the Classical Capacity of a General Quantum Channel
M. Hayashi; H. Nagaoka
Proc., 71, 2002, Peer-reviwed
International conference proceedings, English - A Matrix Version of Law of Large Numbers and Its Relation to Quantum Hypothesis Testing
H. Nagaoka
214-217, 2001, Peer-reviwed
International conference proceedings, English - Numerical Experiments on The Capacity of Quantum Channel with Entangled Input States
S. Osawa; H. Nagaoka
IEICE Transactions A, E84-A, 10, 2583-2590, 2001, Peer-reviwed
Scientific journal, English - Strong Converse Theorems in Quantum Information Theory
H. Nagaoka
Proc., 33, 2001, Peer-reviwed
International conference proceedings, English - Strong converse and Stein's lemma in quantum hypothesis testing
T Ogawa; H Nagaoka
IEEE TRANSACTIONS ON INFORMATION THEORY, IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 46, 7, 2428-2433, Nov. 2000, Peer-reviwed, The hypothesis testing problem for two quantum states is treated. We show a new inequality between the errors of the first kind and the second kind, which complements the result of Hiai and Petz to establish the quantum version of Stein's lemma. The inequality is also used to show a bound on the probability of errors of the first kind when the power exponent for the probability of errors of the second kind exceeds the quantum relative entropy, which yields the strong converse in quantum hypothesis testing. Finally, we discuss the relation between the bound and the power exponent derived by Han and Kobayashi in classical hypothesis testing.
Scientific journal, English - Strong converse to the quantum channel coding theorem
T Ogawa; H Nagaoka
IEEE TRANSACTIONS ON INFORMATION THEORY, IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 45, 7, 2486-2489, Nov. 1999, Peer-reviwed, A lower bound on the probability of decoding error for a quantum communication channel is presented, from which the strong converse to the quantum channel coding theorem is immediately shown, The results and their derivations are mostly straightforward extensions of the classical counterparts which were established by Arimoto, except that more careful treatment is necessary here due to the noncommutativity of operators.
Scientific journal, English - An estimation theoretical characterization of coherent states
A Fujiwara; H Nagaoka
JOURNAL OF MATHEMATICAL PHYSICS, AMER INST PHYSICS, 40, 9, 4227-4239, Sep. 1999, Peer-reviwed, We introduce a class of quantum pure state models called the coherent models. A coherent model is an even-dimensional manifold of pure states whose tangent space is characterized by a symplectic structure. In a rigorous framework of noncommutative statistics, it is shown that a coherent model inherits and expands the original spirit of the minimum uncertainty property of coherent states. (C) 1999 American Institute of Physics. [S0022-2488(99)02509-8].
Scientific journal, English - Strong Converse Theorems in the Quantum Information Theory
T. Ogawa; H. Nagaoka
Proc., 54, 1999, Peer-reviwed
International conference proceedings, English - Algorithms of Arimoto-Blahut Type for Computing Quantum Channel Capacity
H. Nagaoka
Proc., 354, Aug. 1998, Peer-reviwed
International conference proceedings, English - Operational capacity and pseudoclassicality of a quantum channel
A Fujiwara; H Nagaoka
IEEE TRANSACTIONS ON INFORMATION THEORY, IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 44, 3, 1071-1086, May 1998, Peer-reviwed, We explore some basic properties of coding theory of a general quantum communication channel and its operational capacity, including: 1) adaptive measurement with feedback code; 2) reconsideration of single-letterized capacity formula; and 3) pseudoclassicality of a channel.
Scientific journal, English
MISC
- 量子状態空間の幾何学
長岡浩司
Feb. 2009, 数理科学, 548, 22-28, Japanese, Introduction other - 量子推定と不確定性原理
長岡浩司
Oct. 2005, 数理科学, 508, 26-34, Japanese, Introduction other - 量子情報科学の来し方行く末
長岡浩司
現在ブームともいえる活況にある量子情報科学の成立過程を,様々な学問領域の交流の歴史に焦点を当てながら解説する.また,現在のブームの持つ性格を分析し,将来に向けての提言を試みる., The Institute of Electronics, Information and Communication Engineers, Aug. 2002, 電子情報通信学会誌, 85, 8, 576-579, Japanese, Introduction other, 0913-5693, 110003230947, AN1001339X - 量子情報理論における極限定理について
長岡浩司
2001, 数理科学, 456, 47-55, Japanese, Introduction other
Books and other publications
- Asymptotic Theory of Quantum Statistical Inference
Masahito Hayashi
English, Joint work, chapters 2, 4, 8, 9, 10, 11, 17, 19, 27, World Scientific, 2005 - Methods of Information Geometry
S. Amari; H. Nagaoka
English, American Mathematical Society /Oxford University Press, 2000 - 情報幾何の方法
甘利俊一; 長岡浩司
Japanese, 岩波書店, 1993
Lectures, oral presentations, etc.
- 情報スペクトルをめぐる初期の思い出と若干の考察
長岡 浩司
Public discourse, Japanese, 2018年電子情報通信学会総合大会, Invited, 電子情報通信学会, 東京電機大学 東京千住キャンパス, Domestic conference
22 Mar. 2018 - 勾配法を用いた通信路容量計算法について
福 先伶; 長岡 浩司
Oral presentation, Japanese, 第40回情報理論とその応用シンポジウム, 新潟県新発田市 泉慶, Domestic conference
01 Dec. 2017 - 確率単体とマルコフ同型な統計モデルの特徴付け
長岡浩司
Oral presentation, Japanese, 第39回情報理論とその応用シンポジウム, Domestic conference
Dec. 2016 - Revisit to the autoparallelity and the canonical divergence for dually at spaces
Hiroshi Nagaoka
Invited oral presentation, English, Information Geometry and its Applications (IGAIA) IV, Invited, Liblice, Czech Republic, http://igaia.utia.cz, International conference
16 Jun. 2016 - Random coding exponent function の数値計算における有本アルゴリズムの高速化
渡邉広樹; 長岡浩司
Oral presentation, Japanese, 電子情報通信学会情報理論研究会／技術研究報告, 電子情報通信学会, Domestic conference
Mar. 2016 - 古典量子多重アクセス通信路における弱逆性に関する考察
久保卓也; 長岡浩司
Oral presentation, Japanese, 第38回情報理論とその応用シンポジウム, Domestic conference
Nov. 2015 - 十分統計量と VF 符号のユニバーサル性の関係
有村光晴; 長岡浩司
Oral presentation, Japanese, 第38回情報理論とその応用シンポジウム, Domestic conference
Nov. 2015 - 量子情報理論黎明期の歴史と巨人 Holevo の足跡
長岡浩司
Others, Japanese, 第38回情報理論 とその応用シン ポジウム, Domestic conference
Nov. 2015 - Some Remarks on Lower Bounds on the Error Probability for Classical and Quantum Multiple Access Channels
Takuya Kubo; Hiroshi Nagaoka
Oral presentation, Japanese, 37th Symposium on Information Theory and Its Applications, Domestic conference
12 Dec. 2014 - Acceleration of an Arimoto-Blahut-type Algorithm for Channels with Memories
Naoki Tominaga; Hiroshi Nagaoka
Oral presentation, Japanese, 37th Symposium on Information Theory and Its Applications, Domestic conference
11 Dec. 2014 - Classical and quantum simple hypothesis testing revisited
Hiroshi Nagaoka
Invited oral presentation, English, Beyond IID Conference 2014, Invited, Centre for Quantum Technologies (CQT), National University of Singapore, Singapore, http://beyondiid.quantumlah.org, International conference
19 May 2014 - 情報幾何の方法
長岡浩司
Invited oral presentation, Japanese, 日本物理学会 第69回年次大会, Invited, Domestic conference
27 Mar. 2014 - Complexification of Information Geometry in view of Quantum Estimation Theory
Hiroshi Nagaoka
Invited oral presentation, English, GSI2013 --- Geometric Science of Information, Invited, Paris, France, http://www.see.asso.fr/gsi2013, International conference
29 Aug. 2013 - 一般化Poor-Verdu不等式に関するいくつかの考察
久保卓也; 長岡浩司
Oral presentation, Japanese, 第３５回情報理論とその応用シンポジウム,第３５回情報理論とその応用シンポジウム
Dec. 2012 - 指数型分布族、混合型分布族、そして相対エントロピー： ある情報幾何学的考察
長岡浩司
Oral presentation, Japanese, 第35回情報理論とその応用シンポジウム,第35回情報理論とその応用シンポジウム
Dec. 2012 - 量子仮説検定、大数の法則、そして大偏差
長岡浩司
Invited oral presentation, Japanese, 統計関連学会連合大会, Invited, 北海道大学, Domestic conference
10 Sep. 2012 - The Inheritance Condition for the Canonical Divergence
Hiroshi Nagaoka
Invited oral presentation, English, International Workshop on Anomalous Statistics, Generalized Entropies, and Information Geometry, International Workshop on Anomalous Statistics, Generalized Entropies, and Information Geometry, Nara, Japan, International conference
Mar. 2012 - 量子仮説検定における大偏差問題について
長岡浩司
Others, Japanese, RIMS研究集会「独立性と従属性の数理 ---代数と確率の出会い---」, 京都大学数理解析研究所
Dec. 2011 - 古典・量子状態推定における誤り確率の下界について
久保卓也; 長岡浩司
Oral presentation, Japanese, 電子情報通信学会・量子情報技術時限研究専門委員会, 量子情報技術研究会,第25回・量子情報技術研究会(QIT25)
Nov. 2011 - Information Geometry of Quantum Relative Entropy and Some Extension
H. Nagaoka
Invited oral presentation, English, Information Geometry and Its Applications III, Information Geometry and Its Applications (IGAIA) III, Leipzig, Germany, International conference
Aug. 2010 - Qubit通信路における量子Arimoto-Blahutアルゴリズムに関する考察
安藤裕太; 長岡浩司
Oral presentation, Japanese, 第３２回情報理論とその応用シンポジウム,第３２回情報理論とその応用シンポジウム
Dec. 2009 - VF および VV符号化の符号化レートに関する情報スペクトル的考察
平井和也; 長岡浩司
Oral presentation, Japanese, 第３２回情報理論とその応用シンポジウム,第３２回情報理論とその応用シンポジウム
Dec. 2009 - 量子情報理論の地下を流れる数学的水脈について
長岡浩司
Invited oral presentation, Japanese, 第２１回量子情報技術研究会 (QIT), 電子情報通信学会
Nov. 2009 - 情報幾何から見たベキ乗構造 --- α接続の幾何 ---
長岡浩司
Others, Japanese, summer school 数理物理 2009「ベキ乗則の数理」, summer school 数理物理 2009 「ベキ乗則の数理」
Aug. 2009 - 情報スペクトルを通してみた確率・情報・エントロピー
長岡浩司
Invited oral presentation, Japanese, ソサイエティ大会（基礎・境界ソサイエティ）, 電子情報通信学会
Sep. 2008 - 量子情報幾何学概論
長岡浩司
Public symposium, Japanese, 量子論の諸問題と今後の発展, 高エネルギー加速器研究機構, 筑波
Mar. 2008 - 統計力学と量子情報の数理
長岡浩司
Oral presentation, Japanese, 日本物理学会2007年春季大会,日本物理学会2007年春季大会
Mar. 2007 - 量子 i.i.d. 状態における仮説検定の漸近特性に関する数値的アプローチ
堂嶋隆幸; 片桐孝洋; 長岡浩司
Oral presentation, Japanese, 第２９回情報理論とその応用シンポジウム,第２９回情報理論とその応用シンポジウム
2006 - A Quantum/Complex Extension of Information Geometry
H. Nagaoka
Invited oral presentation, English, The 2nd International Symposium on Information Geometry and Its Applications, The 2nd International Symposium on Information Geometry and Its Applications, Tokyo, Japan, International conference
Dec. 2005 - Differential Geometrical Aspects of Quantum Estimation Theory
H. Nagaoka
Invited oral presentation, English, COE-Kakenhi workshop on Quantum Information Theory and Quantum Statistical Inference, Tokyo, Japan, International conference
Nov. 2005 - The Exponential Family of Markov Chains and Its Information Geometry
H. Nagaoka
Oral presentation, Japanese, 第２８回情報理論とその応用シンポジウム,第２８回情報理論とその応用シンポジウム
2005 - Around the Quantum Relative Entropy --- Some Basic Considerations on the Quantization of Information Theory ---
H. Nagaoka
Keynote oral presentation, English, 2003 IEEE International Symposium on Information Theory, 2003 IEEE International Symposium on Information Theory, Yokohama, Japan, International conference
Jun. 2003 - 量子情報幾何学の世界
長岡浩司
Invited oral presentation, Japanese, ２００２年度日本数学会年会「総合講演・企画特別講演アブストラクト」
Mar. 2002 - 一般情報源の仮説検定及び情報源固定長符号化での正しい確率の指数
林正人; 長岡浩司
Oral presentation, Japanese, 第24回情報理論とその応用シンポジウム,第24回情報理論とその応用シンポジウム
Dec. 2001 - 可変長符号化の符号化レートに関する情報スペクトル的考察
平井和也; 長岡浩司
Oral presentation, Japanese, 第24回情報理論とその応用シンポジウム,第24回情報理論とその応用シンポジウム
Dec. 2001 - A new proof of the channel coding theorem via hypothesis testing in quantum information theory
T. Ogawa; H. Nagaoka
Oral presentation, English, 第24回情報理論とその応用シンポジウム,第24回情報理論とその応用シンポジウム
Dec. 2001 - 量子系の情報幾何学について
長岡浩司
Oral presentation, Japanese, 第４回情報論的学習理論ワークショップ,第４回情報論的学習理論ワークショップ
2001 - 量子系の情報幾何学について
長岡浩司
Invited oral presentation, Japanese, 第４回情報論的学習理論ワークショップ予稿集
2001 - A Matrix Version of Law of Large Numbers and Its Relation to Quantum Hypothesis Testing
H. Nagaoka
Invited oral presentation, English, IWSDA2001, IWSDA2001, Chengdu, China, International conference
2001 - 情報スペクトル的方法について―古典および量子情報理論におけるその役割―
長岡浩司
Oral presentation, Japanese, 情報理論研究会（IT）, 熊本（電子情報通信学会技術研究報告),情報理論研究会（IT）, 熊本（電子情報通信学会技術研究報告)
2000 - 情報スペクトル的方法について―古典および量子情報理論におけるその役割―
長岡浩司
Invited oral presentation, Japanese, 情報理論研究会（IT）,熊本, 2000.（予稿集：電子情報通信学会技術研究報告)
2000 - 量子仮説検定の情報スペクトル理論
長岡浩司
Oral presentation, Japanese, 第22回情報理論とその応用シンポジウム,第22回情報理論とその応用シンポジウム
Dec. 1999 - 量子Arimoto-Blahutアルゴリズムとその応用
長岡浩司; 大沢 進
Oral presentation, Japanese, 第２回量子情報技術研究会（電子情報通信学会・量子情報技術時限研究専門委員会）,第２回量子情報技術研究会（電子情報通信学会・量子情報技術時限研究専門委員会）
Nov. 1999 - 量子仮説検定の漸近論について
長岡浩司
Oral presentation, Japanese, シンポジウム「統計的推測理論とその情報論的側面」,シンポジウム「統計的推測理論とその情報論的側面」
Nov. 1998