Jun SUZUKI
| Department of Computer and Network Engineering | Associate Professor |
| Cluster II (Emerging Multi-interdisciplinary Engineering) | Associate Professor |
| Institute for Advanced Science | Associate Professor |
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Paper
- A Python Based Toolkit for Efficient Computation of Bayesian Nagaoka-Hayashi Bound for Quantum Multiparameter Estima
Zhao Kehan; Jun Suzuki
Last, Proc. of the 24th Asian Quantum Information Science Conference, P2, 50, 380, Aug. 2024, Peer-reviwed
International conference proceedings, English - The gap persistence theorem for quantum multiparameter estimation
Lorcan Conlon; Jun Suzuki; Ping Koy Lam; Syed Assad
Proc. of the 24th Asian Quantum Information Science Conference, P2, 11, 26, Aug. 2024, Peer-reviwed
International conference proceedings, English - A new approach to Bayesian lower bounds for quantum state estimation
Jianchao Zhang; Jun Suzuki
Last, Proc. of the 24th Asian Quantum Information Science Conference, P1, 11, 155, Aug. 2024, Peer-reviwed
International conference proceedings, English - Corrigendum: Quantum state estimation with nuisance parameters (2020 J. Phys. A: Math. Theor. 53 453001)
Jun Suzuki; Yuxiang Yang; Masahito Hayashi
Lead, Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 57, 12, 129501-129501, 11 Mar. 2024, Peer-reviwed, Abstract
This is a correction for Suzuki et al (2020 J. Phys. A: Math. Gen.53 453001).
Scientific journal - Bayesian Nagaoka-Hayashi Bound for Multiparameter Quantum-State Estimation Problem
Jun SUZUKI
Lead, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Institute of Electronics, Information and Communications Engineers (IEICE), E107.A, 3, 510-518, 01 Mar. 2024, Peer-reviwed
Scientific journal, English - Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements
Lorcán O. Conlon; Jun Suzuki; Ping Koy Lam; Syed M. Assad
npj Quantum Information, Springer Science and Business Media LLC, 7, 1, 15 Jul. 2021, Peer-reviwed, Abstract
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 physical quantities. One such bound is the Holevo Cramér–Rao bound on the trace of the mean squared error matrix. The Holevo bound is an asymptotically achievable bound when one allows for any measurement strategy, including collective measurements on many copies of the probe. In this work, we introduce a tighter bound for estimating multiple parameters simultaneously when performing separable measurements on a finite number of copies of the probe. This makes it more relevant in terms of experimental accessibility. We show that this bound can be efficiently computed by casting it as a semidefinite programme. We illustrate our bound with several examples of collective measurements on finite copies of the probe. These results have implications for the necessary requirements to saturate the Holevo bound.
Scientific journal, English - Quantum-state estimation problem via optimal design of experiments
Jun Suzuki
International Journal of Quantum Information, World Scientific Publishing Company, 19, 8, 2040007, 24 Feb. 2021, Peer-reviwed
Scientific journal, English - Non-monotone metric on the quantum parametric model
Jun Suzuki
The European Physical Journal Plus, 136, 90 (26 pages), 17 Jan. 2021, Peer-reviwed, Invited
Scientific journal, English - Efficient computation of the Nagaoka-Hayashi bound for multi-parameter estimation with separable measurements
Lorcan O. Conlon; Jun Suzuki; Ping Koy Lam; Syed M. Assad
Proc. of the 20th Asian Quantum Information Science Conference, Springer Nature, 7, 79-79, 08 Dec. 2020, Peer-reviwed
International conference proceedings, English - Uncertainty relation for estimating the position of an electron in a uniform magnetic field from quantum estimation theory
Shin Funada; Jun Suzuki
Physica A, Elsevier, 558, 124918-49, 15 Nov. 2020, Peer-reviwed
Scientific journal, English - Quantum state estimation with nuisance parameters
Jun Suzuki; Yuxiang Yang; Masahito Hayashi
Journal of Physics A: Mathematical and Theoretical, IOP, 53, 45, 453001 (61 pages), 23 Oct. 2020, Peer-reviwed, Invited
Scientific journal, English - Direct estimation of minimum gate fidelity
Yiping Lu; Jun Yan Sim; Jun Suzuki; Berthold-Georg Englert; Hui Khoon Ng
Physical Review A, American Physical Society, 102, 2, 022410, 18 Aug. 2020, Peer-reviwed
Scientific journal, English - Robust Phase Estimation of Gaussian States in the Presence of Outlier Quantum States
Yukito Mototake; Jun Suzuki
Applied Sciences, MDPI, 10, 16, app10165475, 07 Aug. 2020, Peer-reviwed, Invited
Scientific journal, English - Nuisance parameter problem in quantum estimation theory: Tradeoff relation and qubit examples
Jun Suzuki
Journal of Physics A: Mathematical and theoretical, 53, 26, 264001 (42 pages), 09 Jun. 2020, Peer-reviwed
Scientific journal, English - User-specified random sampling of quantum channels and its applications
Jun Yan Sim; Jun Suzuki; Berthold-Georg Englert; Hui Khoon Ng
Physical Review A, American Physical Society, 101, 2, 022307, 07 Feb. 2020, Peer-reviwed
Scientific journal, English - Optimal estimation of noise asymmetry in the qubit Pauli channel via the theory of optimal design of experiments
Yonatan Gazit; Hui Khoon Ng; Jun Suzuki
Proc. of the 19th Asian Quantum Information Science Conference, 50-56, 20 Aug. 2019, Peer-reviwed
International conference proceedings, English - Quantum process tomography via optimal design of experiments
Yonatan Gazit; Hui Khoon Ng; Jun Suzuki
Physical Review A, American Physical Society, 100, 1, 012350, 01 Jul. 2019, Peer-reviwed
Scientific journal, English - Information Geometrical Characterization of Quantum Statistical Models in Quantum Estimation Theory
Jun Suzuki
Entropy, MDPI, 21, 00703, 01 Jul. 2019, Peer-reviwed
Scientific journal, English - Phase Estimation Problem in the Presence of Nuisance Parameters
Jun Suzuki
XVI International Conference on Quantum Optics and Quantum Information, 95-96, 15 May 2019, Peer-reviwed, Invited
International conference proceedings, English - Classification and characterization of quantum parametric models in quantum estimation theory
Jun Suzuki
Proc. of the 18th Asian Quantum Information Science Conference, 90, Sep. 2018, Peer-reviwed
International conference proceedings, English - Entanglement detection and parameter estimation of quantum channels
Jun Suzuki
PHYSICAL REVIEW A, AMER PHYSICAL SOC, 94, 4, 042306, Oct. 2016, Peer-reviwed, We derive a general criterion to detect entangled states in multipartite systems based on the symmetric logarithmic derivative quantum Fisher information. This criterion is a direct consequence of the fact that separable states do not improve the accuracy upon estimating the one-parameter family of quantum channels. Our result is a generalization of the previously known criterion for the one-parameter unitary channel to any one-parameter quantum channel. Several variants of the proposed criterion are also given, and then the general structure is revealed behind this sort of entanglement criteria based on quantum Fisher information. We discuss several examples to illustrate our criterion. In the last part, we briefly show how the proposed criterion can be extended to a more general setting that is applicable for a certain class of open quantum systems, and we discuss how to detect entangled states even in the presence of decoherence.
Scientific journal, English - Explicit formula for the Holevo bound for two-parameter qubit-state estimation problem
Jun Suzuki
JOURNAL OF MATHEMATICAL PHYSICS, AMER INST PHYSICS, 57, 4, 042201, Apr. 2016, Peer-reviwed, The main contribution of this paper is to derive an explicit expression for the fundamental precision bound, the Holevo bound, for estimating any two-parameter family of qubit mixed-states in terms of quantum versions of Fisher information. The obtained formula depends solely on the symmetric logarithmic derivative (SLD), the right logarithmic derivative (RLD) Fisher information, and a given weight matrix. This result immediately provides necessary and sufficient conditions for the following two important classes of quantum statistical models; the Holevo bound coincides with the SLD Cramer-Rao bound and it does with the RLD Cramer-Rao bound. One of the important results of this paper is that a general model other than these two special cases exhibits an unexpected property: the structure of the Holevo bound changes smoothly when the weight matrix varies. In particular, it always coincides with the RLD Cramer-Rao bound for a certain choice of the weight matrix. Several examples illustrate these findings. Published by AIP Publishing.
Scientific journal, English - Parameter estimation of qubit states with unknown phase parameter
Jun Suzuki
INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, WORLD SCIENTIFIC PUBL CO PTE LTD, 13, 1, 1450044, Feb. 2015, Peer-reviwed, We discuss a problem of parameter estimation for quantum two-level system, qubit system, in presence of unknown phase parameter. We analyze trade-off relations for mean square errors (MSEs) when estimating relevant parameters with separable measurements based on known precision bounds; the symmetric logarithmic derivative (SLD) Cramer-Rao (CR) bound and Hayashi-Gill-Massar (HGM) bound. We investigate the optimal measurement which attains the HGM bound and discuss its properties. We show that the HGM bound for relevant parameters can be attained asymptotically by using some fraction of given n quantum states to estimate the phase parameter. We also discuss the Holevo bound which can be attained asymptotically by a collective measurement.
Scientific journal, English - Creation of excitations from a uniform impurity motion in the condensate
Jun Suzuki
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, ELSEVIER SCIENCE BV, 397, 1 March, 40-53, Mar. 2014, Peer-reviwed, We investigate a phenomenon of creation of excitations in the homogeneous Bose Einstein condensate due to an impurity moving with a constant velocity. A simple model is considered to take into account dynamical effects due to motions of the impurity. Based on this model, we show that there can be a finite amount of excitations created even if velocity of the impurity is below Landau's critical velocity. We also show that the total number of excitations scales differently for large time across the speed of sound. Thus, our result dictates the critical behavior across Landau's one and validates Landau's intuition to the problem. We discuss how Landau's critical velocity emerges and its validity within our model. (C) 2013 Elsevier B.V. All rights reserved.
Scientific journal, English - Creation of excitations from subcritical velocity motion of impurity in BEC
Jun Suzuki
Abstract for Finite-Temperature Non-Equilibrium Superfluid Systems, page 36, Feb. 2013
International conference proceedings, English - Symmetric coupling of four spin-1/2 systems
Jun Suzuki; Berthold-Georg Englert
Journal of Physics A: Mathematical and theoretical, 45, 25, 255301 (17 pages), May 2012, Peer-reviwed
Scientific journal, English - Encoding many qubits in a rotor
Philippe Raynal; Amir Kalev; Jun Suzuki; Berthold-Georg Englert
QUANTUM AFRICA 2010: THEORETICAL AND EXPERIMENTAL FOUNDATIONS OF RECENT QUANTUM TECHNOLOGY, AMER INST PHYSICS, 1469, 63-81, 2012, Peer-reviwed, We propose a scheme for encoding many qubits in a single rotor, that is, a continuous and periodic degree of freedom. A key feature of this scheme is its ability to manipulate and entangle the encoded qubits with a single operation on the system. We also show, using quantum error-correcting codes, how to protect the qubits against small errors in angular position and momentum which may affect the rotor. We then discuss the feasibility of this scheme and suggest several candidates for its implementation. The proposed scheme is immediately generalizable to qudits of any finite dimension.
International conference proceedings, English - Long-lived qubit from three spin-1/2 atoms
Rui Han; Niels Loerch; Jun Suzuki; Berthold-Georg Englert
PHYSICAL REVIEW A, AMER PHYSICAL SOC, 84, 1, 012322, Jul. 2011, Peer-reviwed, A system of three spin-1/2 atoms allows the construction of a reference-frame-free (RFF) qubit in the subspace with total angular momentum j = 1/2. The RFF qubit stays coherent perfectly as long as the spins of the three atoms are affected homogeneously. The inhomogeneous evolution of the atoms causes decoherence, but this decoherence can be suppressed efficiently by applying a bias magnetic field of modest strength perpendicular to the plane of the atoms. The resulting lifetime of the RFF qubit can be many days, making RFF qubits of this kind promising candidates for quantum information storage units. Specifically, we examine the situation of three (6)Li atoms trapped in a CO(2)-laser-generated optical lattice and find that, with conservatively estimated parameters, a stored qubit maintains a fidelity of 0.9999 for two hours.
Scientific journal, English - Radiation from accelerated impurities in a Bose-Einstein Condensate
Jun Suzuki
Physics Letters A, 375, 1396-1401, Feb. 2011, Peer-reviwed
Scientific journal, English - Encoding qubits in a rotor
Amir Kalev; Philippe Raynal; Jun Suzuki; Berthold-Georg Englert
QUANTUM COMMUNICATION, MEASUREMENT AND COMPUTING (QCMC): THE TENTH INTERNATIONAL CONFERENCE, AMER INST PHYSICS, 1363, 69-72, 2011, Peer-reviwed, We present a scheme for encoding many qubits in a single rotor, that is, a continuous and periodic degree of freedom. A key feature of this scheme is its ability to manipulate and entangle the encoded qubits with a single operation on the system. We also show, using quantum error-correcting codes, how to protect the qubits against small errors in angular position and momentum which may affect the rotor. Finally, we propose a possible realization of qubits encoded in orbital angular momentum of a single photon.
International conference proceedings, English - Entanglement detection from interference fringes in atom-photon systems
Jun Suzuki; Christian Miniatura; Kae Nemoto
Updating Quantum Cryptography and Communications 2010, 88, Oct. 2010, Peer-reviwed
International conference proceedings, English - Radiation from accelerated impurities in Bose-Einstein Condensates
Jun Suzuki
Proc. of the 10th Asian Conference on Quantum Information Science, 159-160, Aug. 2010, Peer-reviwed
International conference proceedings, English - Entanglement detection from interference fringes in atom-photon systems
Jun Suzuki; Christian Miniatura; Kae Nemoto
International Conference on Atomic Physics 2010, 527, Jul. 2010
International conference proceedings, English - Entanglement detection from interference fringes in atom-photon systems
Jun Suzuki; Christian Miniatura; Kae Nemoto
PHYSICAL REVIEW A, AMER PHYSICAL SOC, 81, 6, 062307, Jun. 2010, Peer-reviwed, A measurement scheme of atomic qubits pinned at given positions is studied by analyzing the interference pattern obtained when they emit photons spontaneously. In the case of two qubits, a well-known relation is revisited in which the interference visibility is equal to the concurrence of the state in the infinite spatial separation limit of the qubits. By taking into account the superradiant and subradiant effects, it is shown that a state tomography is possible when the qubit spatial separation is comparable to the wavelength of the atomic transition. In the case of three qubits, the relations between various entanglement measures and the interference visibility are studied, where the visibility is defined from the two-qubit case. A qualitative correspondence among these entanglement relations is discussed. In particular, it is shown that the interference visibility is directly related to the maximal bipartite negativity.
Scientific journal, English - Encoding many qubits in a rotor
Philippe Raynal; Amir Kalev; Jun Suzuki; Berthold-Georg Englert
Physical Review A - Atomic, Molecular, and Optical Physics, 81, 5, 20 May 2010, Peer-reviwed, We propose a scheme for encoding many qubits in a single rotor, that is, a continuous and periodic degree of freedom. A key feature of this scheme is its ability to manipulate and entangle the encoded qubits with a single operation on the system. We also show, using quantum error-correcting codes, how to protect the qubits against small errors in angular position and momentum which may affect the rotor. We then discuss the feasibility of this scheme and suggest several candidates for its implementation. The proposed scheme is immediately generalizable to qudits of any finite dimension. © 2010 The American Physical Society.
Scientific journal, English - Encoding many qubits in a rotor
Philippe Raynal; Amir Kalev; Jun Suzuki; Berthold-Georg Englert
PHYSICAL REVIEW A, AMER PHYSICAL SOC, 81, 5, 052327, May 2010, Peer-reviwed, We propose a scheme for encoding many qubits in a single rotor, that is, a continuous and periodic degree of freedom. A key feature of this scheme is its ability to manipulate and entangle the encoded qubits with a single operation on the system. We also show, using quantum error-correcting codes, how to protect the qubits against small errors in angular position and momentum which may affect the rotor. We then discuss the feasibility of this scheme and suggest several candidates for its implementation. The proposed scheme is immediately generalizable to qudits of any finite dimension.
Scientific journal, English - Symmetric construction of reference-frame-free qudits
Jun Suzuki; Gelo Noel Macuja Tabia; Berthold-Georg Englert
PHYSICAL REVIEW A, AMER PHYSICAL SOC, 78, 5, 052328, Nov. 2008, Peer-reviwed, By exploiting a symmetric scheme for coupling N spin-1/2 constituents (the physical qubits) to states with total angular momentum N/2-1, we construct rotationally invariant logical qudits of dimension d=N-1. One can encode all qudit states, and realize all qudit measurements, by this construction. The rotational invariance of all relevant objects enables one to transmit quantum information without having aligned reference frames between the parties that exchange the qudits. We illustrate the method by explicit constructions of reference-frame-free qubits and qutrits and, for the qubit case, comment on possible experimental implementations.
Scientific journal, English - Raw-data attacks in quantum cryptography with partial tomography
Syed M. Assad; Jun Suzuki; Berthold-Georg Englert
INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, WORLD SCIENTIFIC PUBL CO PTE LTD, 4, 6, 1003-1012, Dec. 2006, Peer-reviwed, We consider a variant of the BB84 protocol for quantum cryptography, the prototype of tomographically incomplete protocols, where the key is generated by one-way communication rather than the usual two-way communication. Our analysis, backed by numerical evidence, establishes thresholds for eavesdropping attacks on the raw data and on the generated key at quantum bit error rates of 10% and 6.15%, respectively. Both thresholds are lower than the threshold for unconditional security in the standard BB84 protocol.
Scientific journal, English - Individual Raw Data Attacks in the Bennett Brassard 1984 Protocol with Incomplete Tomography
Syed M. Assad; Jun Suzuki; Berthold-Georg Englert
Proc. of the 8th International Conference on Quantum Communication, Measurement and Computing, 8, 221-224, Nov. 2006, Peer-reviwed
International conference proceedings, English - Critical Velocities for Energy Dissipation from Periodic Motions of Impurity in Bose-Einstein Condensates
Jun Suzuki
Proc. of the 13th Central European Workshop on Quantum Optics, Acta Physica Hungarica A, 26, 149-156, May 2006, Peer-reviwed
International conference proceedings, English - Model for entangled states with spin-spin interaction
Y Aharonov; J Anandan; GJ Maclay; J Suzuki
PHYSICAL REVIEW A, AMER PHYSICAL SOC, 70, 5, 052114, Nov. 2004, Peer-reviwed, A system consisting of two neutral spin-1/2 particles is analyzed for two magnetic field perturbations: (1) an inhomogeneous magnetic field over all space, and (2) external fields over a half space containing only one of the particles. The field is chosen to point from one particle to the other, which results in essentially a one-dimensional problem. A number of interesting features are revealed for the first case: the singlet, which has zero potential energy in the unperturbed case, remains unstable in the perturbing field. The spin-zero component of the triplet evolves into a bound state with a double well potential, with the possibility of tunneling. Superposition states can be constructed which oscillate between entangled and unentangled states. For the second case, we show that changes in the magnetic field around one particle affect measurements of the spin of the entangled particle not in the magnetic field nonlocally. By using protective measurements, we show it is possible in principle to establish a nonlocal interaction using the two particles, provided the dipole-dipole potential energy does not vanish and is comparable to the potential energy of the particle in the external field.
Scientific journal, English - A linear chemical cycle and oscillations
J Suzuki; A Morita
JOURNAL OF PHYSICAL CHEMISTRY A, AMER CHEMICAL SOC, 105, 31, 7321-7325, Aug. 2001, Peer-reviwed, We have found that for a simple first-order successive irreversible cyclic reaction, there exist oscillations in time for the concentrations of chemical species for a certain range in the number of reaction steps. If the steps are too small or too large, we do not obtain the oscillations, which has been thought to be the case previously.
Scientific journal, English
MISC
- Role of the extended Hilbert space in the attainability of the Quantum Cramer-Rao bound for multiparameter estimation
Lorcan O. Conlon; Jun Suzuki; Ping Koy Lam; Syed M. Assad
Apr. 2024, Preprint arXiv, 2404.01520, 18 pages, English, Technical report - QestOptPOVM: An iterative algorithm to find optimal measurements for quantum parameter estimation
Jianchao Zhang; Jun Suzuki
Last, Mar. 2024, Preprint arXiv, 2403.20131, 31 pages, English, Technical report - The gap persistence theorem for quantum multiparameter estimation
Lorcan O. Conlon; Jun Suzuki; Ping Koy Lam; Syed M. Assad
15 Aug. 2022, Preprint arXiv, 2208.07386, 10 pages, English, Technical report - Error trade-off relations for two-parameter unitary model with commuting generators
Shin Funada; Jun Suzuki
02 Oct. 2020, Preprint arXiv, 2010.00789, 7 pages, English, Technical report
Books and other publications
- Quantum Paths: Festschrift in Honor of Berge Englert on His 60th Birthday
Jun Suzuki
Scholarly book, English, Contributor, Chapter 6, World Scientific Publisher, 23 May 2015, 9789814651837 - Mathematical Horizons for Quantum Physics
Huzihiro Araki; Berthold-Georg Englert; Leong-Chuan Kwek; Jun Suzuki
English, Supervisor, World Scientific Publishing, Aug. 2010 - Mathematics of Quantum Computation and Quantum Technology
Jun Suzuki; Syed M. Assad; Berthold-Georg Englert
English, Joint work, Accessible information about quantum states: An open optimization problem, Chapman & Hall/CRC, 2007 - Relativity in Rotating Frames
Jeeva S. Anandan; Jun Suzuki
English, Joint work, Quantum Mechanics in a Rotating Frame, Kluwer Academic Publishers, 2004
Lectures, oral presentations, etc.
- 量子推定理論
鈴木 淳
Public discourse, Japanese, QIH・MS6・Q-LEAPサマースクール2024, Invited, https://www.qst.go.jp/site/2024qih-ss/20240709.html, サマースクール全体のプログラムとしては50分講義を3回実施
03 Sep. 2024
02 Sep. 2024- 05 Sep. 2024 - On Minimum D-invariant Extension of rank-deficient statistical models in Quantum Estimation Theory
Jun Suzuki
Oral presentation, English, 電子情報通信学会 IT研究会
07 Aug. 2024
06 Aug. 2024- 07 Aug. 2024 - Bayesian Nagaoka-Hayashi Bound for Multiparameter Quantum-State Estimation Problem
Jun Suzuki
Invited oral presentation, English, Quantum TUT workshop 2024 on quantum statistics and quantum information theory, Invited
22 Feb. 2024
22 Feb. 2024- 22 Feb. 2024 - Tightness of the Nagaoka-Hayashi bound in i.i.d. qubit-state estimation
Jianchao Zhang; Jun Suzuki
Poster presentation, English, Quantum Information Processing 2024 (qip2024), Peer-reviewed
16 Jan. 2024
13 Jan. 2024- 19 Jan. 2024 - Numerical computation of Bayesian Nagaoka-Hayashi bound for three-parameter qubit-state estimation
Zhao Kehan; Suzuki Jun
Poster presentation, English, 第49回量子情報技術研究会(QIT49)
18 Dec. 2023
17 Dec. 2023- 19 Dec. 2023 - Optimal POVM with minimal size in two-parameter qubit-state estimation
Jianchao Zhang; Jun Suzuki
Poster presentation, English, 第49回量子情報技術研究会(QIT49)
18 Dec. 2023
17 Dec. 2023- 19 Dec. 2023 - Introduction to Optimal Design of Experiments (DoE) and its Applications to Quantum Estimation
Jun Suzuki
Invited oral presentation, English, Quantum Information, Quantum Matter and Quantum Gravity, Invited
28 Sep. 2023
04 Sep. 2023- 06 Oct. 2023 - The Gap Persistence Theorem Between Nagaoka-Hayashi Bound and Holevo Bound for Quantum Multiparameter Estimation
Lorcan O CONLON; Jun SUZUKI; Ping K LAM; Syed M ASSAD
Oral presentation, English, 電子情報通信学会 EMM-IT合同研究会
12 May 2023
11 May 2023- 12 May 2023 - 最適な量子測定に基づく量子ニューラルネットワーク分類器の性能特性
山田 優作、鈴木 淳
Oral presentation, Japanese, RCC・ISEC・IT・WBS合同研究会, 電子情報通信学会 情報理論研究会, 山口大学
14 Mar. 2023 - Nagaoka-Hayashi bound in multi-parameter estimation
Jun Suzuki
Invited oral presentation, English, Japan-Singapore(NUS) Joint seminar, Invited, http://jsps-seminar.org, International conference
22 Feb. 2023 - Information geometry of the qutrit system based on the Bloch vector representation
Yutaro Fukuda and Jun Suzuki
Poster presentation, English, Japan-Singapore(NUS) Joint seminar
20 Feb. 2023 - Improvement of the performance for quantum neural networks based on optimal quantum measurement
Yusaku Yamada and Jun Suzuki
Poster presentation, English, Japan-Singapore(NUS) Joint seminar
20 Feb. 2023 - Phase Error Correction in OAM Qubits Encoding
Yoshiharu Minagawa and Jun Suzuki
Oral presentation, English, Japan-Singapore(NUS) Joint seminar
20 Feb. 2023 - QestOptPOVM: Numerical search for finding an optimal POVM for multiparameter estimation
Jianchao Zhang and Jun Suzuki
Oral presentation, English, Japan-Singapore(NUS) Joint seminar
20 Feb. 2023 - Error trade-off relation for estimating momentum shift of relativistic spin-1/2 particle
Shin Funada and Jun Suzuki
Oral presentation, English, The 47th Quantum Information Technology Symposium (QIT47)
09 Dec. 2022 - QestOptPOVM: Numerical search for finding an optimal POVM for multiparameter estimation
Jianchao Zhang and Jun Suzuki
Poster presentation, English, The 47th Quantum Information Technology Symposium (QIT47)
08 Dec. 2022 - On Local Attainability of Quantum Cramer-Rao Bound
Jun Suzuki
Oral presentation, English, The 45th Symposium on Information Theory and its Applications (SITA2022)
01 Dec. 2022 - OAM 量子ビット符号化における位相誤り訂正の検討
皆川 善晴、鈴木 淳
Oral presentation, Japanese, The 45th Symposium on Information Theory and its Applications (SITA2022)
30 Nov. 2022 - Nagaoka-Hayashi bound in multi-parameter estimation
Jun Suzuki
Public discourse, English, CQT Seminar, Invited, Centre for Quantum Technologies, NUS, Singapore, Centre for Quantum Technologies, NUS, Singapore
16 Aug. 2022 - Introduction to Quantum Information Geometry and its Application to Qutrit system
福田優太朗; 鈴木 淳
Public discourse, Japanese, 芝浦 - 量子基礎論・量子情報オンラインセミナー, Invited, 芝浦工業大学 量子基礎論研究室
12 Jul. 2022 - 量子3準位系における量子Fisher計量の凸結合族のBlochベクトルに基づく解析
福田優太朗; 鈴木 淳
Poster presentation, Japanese, The 46th Quantum Information Technology Symposium (QIT46), Domestic conference
30 May 2022 - Optimal measurement preserving map for quantum state estimation and hypothesis testing
Jun Suzuki
Oral presentation, English, IT EMM 合同研究会, 電子情報通信学会 情報理論研究会, 岐阜大学, Domestic conference
18 May 2022 - Effect of Wigner rotation on estimating momentum shift of relativistic spin-1/2 particle
Shin Funada; Jun Suzuki
Poster presentation, English, 25th Annual Conference on Quantum Information Processing (QIP 2022), International conference
11 Mar. 2022 - Bayesian Holevo and Nagaoka-Hayashi bounds for quantum-state estimation
Jun Suzuki
Oral presentation, English, Information and communication engineers, Domestic conference
21 Jan. 2022 - Quantum Information Geometry of Weakly Contaminated Models
Jun Suzuki
Oral presentation, English, The 44th Symposium on Information Theory and its Applications (SITA2021), Domestic conference
09 Dec. 2021 - Effect of Wigner rotation on estimating momentum shift of relativistic spin-1/2 particle
Shin Funada; Jun Suzuki
Oral presentation, English, The 45th Quantum Information Technology Symposium (QIT45), Domestic conference
01 Dec. 2021 - Non-monotone metric on the quantum parametric model
Jun Suzuki
Poster presentation, English, The 45th Quantum Information Technology Symposium (QIT45), Domestic conference
30 Nov. 2021 - Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements
Lorcan O. Conlon; Jun Suzuki; Ping Koy Lam; Syed M. Assad
Oral presentation, English, Quantum Information and Measurement VI, https://www.optica.org/en-us/meetings/topical_meetings/quantum_information_and_measurement_vi/, International conference
05 Nov. 2021 - Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements
Lorcan O. Conlon; Jun Suzuki; Ping Koy Lam; Syed M. Assad
Oral presentation, English, The 44th Quantum Information Technology Symposium (QIT44), Domestic conference
25 May 2021 - Error trade-off relations for two-parameter unitary model with commuting generators
Shin Funada; Jun Suzuki
Poster presentation, English, Quantum 2020, https://www.iopconferences.org/iop/frontend/reg/thome.csp?pageID=978476&eventID=1552&traceRedir=2, International conference
12 Oct. 2020 - ロバスト統計を用いた外れ値を含むコヒーレント状態の位相推定
本武行人; 鈴木淳
Oral presentation, Japanese, 2020年電子情報通信学会総合大会, Domestic conference
27 Mar. 2020 - Characterization of Quantum Parametric Models Based on One-Parameter Family of Quantum Fisher Metric
Jun Suzuki
Oral presentation, English, The 42nd Symposium on Information Theory and its Applications (SITA2019), Domestic conference
27 Nov. 2019 - Error trade-off relations for two-parameter unitary model with commuting generators
Shin Funada; Jun Suzuki
Poster presentation, English, The 41st Quantum Information Technology Symposium (QIT41), Domestic conference
18 Nov. 2019 - Phase Estimation Problem in the Presence of Nuisance Parameters
Jun Suzuki
Invited oral presentation, English, XVI International Conference on Quantum Optics and Quantum Information (ICQOQI2019), Invited, Minsk, Belarus, International conference
15 May 2019 - Equivalence theorem and comparison of optimal designs in qubit systems
Jun Suzuki
Oral presentation, English, ISEC IT WBS 合同研究会, 名古屋大学, Domestic conference
08 Mar. 2019 - Parameter Estimation Problems in Quantum Systems and Optimal Design of Experiments
Jun Suzuki
Oral presentation, English, The 41st Symposium on Information Theory and its Applications (SITA2018), Domestic conference
20 Dec. 2018 - Uncertainty relation from parameter estimation of the position of an electron in a uniform magnetic field
Shin Funada; Jun Suzuki
Poster presentation, English, The 39th Quantum Information Technology Symposium (QIT39), Domestic conference
26 Nov. 2018 - Quantum Information Geometry of a Qubit System: Parameter Es- timation View
Jun Suzuki
Oral presentation, English, International Workshop on Quantum Information, Quantum Computing and Quantum Control (IWQIQC2018), Invited, International conference
07 Nov. 2018 - Classification and characterization of quantum parametric models in quantum estimation theory
Jun Suzuki
Poster presentation, English, 18th Asian Conference on Quantum Information Science (AQIS2018), International conference
09 Sep. 2018 - On Simulation of Unruh Effect by Accelerating an Impurity in the Bose-Einstein Condensate
鈴木淳
Poster presentation, Japanese, 物性研短期研究会 量子情報・物性の新潮流, Domestic conference
02 Aug. 2018 - Characterization of classical statistical model for quantum parametric model
Jun Suzuki
Oral presentation, English, The 38th Quantum Information Technology Symposium (QIT38), Domestic conference
04 Jun. 2018 - Phase estimation of a qubit state interacting with unknown noise parameters
Jun Suzuki
Poster presentation, English, International Conference on challenges in Quantum Information Science, CQIS2018, National Institute of Informatics, International conference
09 Apr. 2018 - Parameter Orthogonalization Method in Quantum Parameter Estimation Problem
Jun Suzuki
Oral presentation, English, ISEC IT WBS, IEICE Tech. Rep, 名古屋大学, Domestic conference
09 Mar. 2018 - Ultimate precision limit in quantum estimation theory: Explicit formula for the Holevo bound for qubit-state estimation problem
Jun Suzuki
Public discourse, English, CQT seminar, Invited, Centre for Quantum Technologies, National University of Singapore
22 Feb. 2018 - Advances in Quantum Estimation Theory: Invitation to Quantum Information Science
Jun Suzuki
Public discourse, English, 706th Advanced Science Research Center seminar, Invited
18 Jan. 2018 - Channel-parameter estimation problem in quantum systems from optimal design of experiments
Jun Suzuki
Oral presentation, English, The 40th Symposium on Information Theory and its Applications (SITA2017), Domestic conference
29 Nov. 2017 - Parameter Estimation of Quantum States from Optimal Design of Experiments
Jun Suzuki
Oral presentation, English, The 37th Quantum Information Technology Symposium (QIT37), Domestic conference
17 Nov. 2017 - Encoding, manipulation, and decoding of multiple qubits with orbital angular momentum of single photons
Jun Suzuki
Public discourse, English, Seminar, Invited, Prof. Englert, Centre for Quantum Technologies, National University of Singapore
23 Aug. 2017 - On simulation of Unruh effect using accelerated impurities in the Bose–Einstein condensate
鈴木淳
Poster presentation, English, 第14回原子・分子・光科学（AMO）討論会, 原子・分子・光科学（AMO）討論会実行委員会, 電気通信大学, Domestic conference
30 Jun. 2017 - Phase estimation problem in open quantum systems with nuisance parameters: An analysis on the memory effect and achievability of the quantum Cramer-Rao bound
Jun Suzuki
Oral presentation, English, The 36th Quantum Information Technology Symposium (QIT36), Domestic conference
30 May 2017 - Ultimate precision limit in quantum estimation theory: Explicit formula for the Holevo bound for qubit-state estimation problem
Jun Suzuki
Invited oral presentation, English, JSAP Wrokshop on Quantum Inforamtion and Related Fields, Invited, International conference
02 Mar. 2017 - On the problem of optimal channel-parameter estimation for discrete memoryless channels
Jun Suzuki
Oral presentation, English, The 39th Symposium on Information Theory and its Applications (SITA2016), Domestic conference
14 Dec. 2016 - Wave-Particle Duality from Parameter Estimation Perspective: An example of nuisance parameter problem in quantum estimation theory
Public discourse, English, QuLink Seminar
13 Jul. 2016 - Nuisance parameter problem in quantum parameter estimation theory
Jun Suzuki
Oral presentation, English, The 33rd Quantum Information Technology Symposium (QIT33), Domestic conference
25 Nov. 2015 - Encoding, manipulation, and decoding of multiple qubits with orbital angular momentum of single photons
Jun Suzuki
Invited oral presentation, English, Interdisciplinary Workshop on Quantum Device--towards development of the quantum information device--2015, Invited, 国立情報学研究所, https://www.qis.ex.nii.ac.jp/iwqd2015/index.html, International conference
13 Oct. 2015 - Encoding, manipulation, and decoding of multiple qubits with orbital angular momentum of single photons
Jun Suzuki
Invited oral presentation, English, Interdisciplinary Workshop on Quantum Device--towards development of the quantum information device--2015, Invited, https://www.qis.ex.nii.ac.jp/iwqd2015/index.html, International conference
13 Oct. 2015 - Explicit formula for the Holevo bound for two-parameter qubit estimation problems
Jun Suzuki
Oral presentation, English, The 32nd Quantum Information Technology Symposium (QIT32), 大阪大学, Domestic conference
26 May 2015 - Nuisance parameter problem in quantum estimation theory
Jun Suzuki
Invited oral presentation, English, QI Workshop 2015–Mathematics, Physics, and Information in Quantum Information Science at NII in Tokyo, Invited, International conference
17 Feb. 2015 - Parameter estimation of quantum two-dimensional system with unknown phase
Jun Suzuki
Oral presentation, English, 第37回情報理論とその応用シンポジウム, Domestic conference
10 Dec. 2014 - Parameter estimation of qubit states with unknown phase parameter
Jun Suzuki
Oral presentation, English, The 31st Quantum Information Technology Symposium (QIT31), Domestic conference
18 Nov. 2014 - Entanglement detection from channel parameter estimation problem
Jun Suzuki
Poster presentation, English, 14th Asian Conference on Quantum Information Science, International conference
21 Aug. 2014 - Creation of excitations from uniform impurity motion in the homogeneous condensate
Jun Suzuki
Poster presentation, English, The 24th International Conference on Atomic Physics, International conference
03 Aug. 2014 - Wave-particle duality in quantum estimation theory
Jun Suzuki
Invited oral presentation, English, BERGEFEST: Singapore Workshop on Quantum Information, Quantum Optics and Foundations of Quantum Mechanics, Invited, International conference
22 Apr. 2014 - Separability criterion for multi-partite systems based on SLD Fisher information
Jun Suzuki
Poster presentation, Japanese, New Horizon in Quantum Information Science, http://quantphys.org/NHQIS/top.html, Domestic conference
23 Mar. 2014 - Numerical analysis of optimal quantum cloning machines for trine states
Akira Koyama; Jun Suzuki
Oral presentation, Japanese, ISEC IT WBS, IEICE Tech. Rep, 名古屋大学, Domestic conference
03 Mar. 2014 - Qubit subalgebra from Weyl algebra of quantum angular momentum system
Jun Suzuki
Poster presentation, Japanese, The 29th Quantum Information Technology Symposium (QIT29), https://staff.aist.go.jp/s-kawabata/qit/qit29/, Domestic conference
18 Nov. 2013 - Encoding many qubits in Orbital Angular Momentum of Single Photons and Application to Quantum Error Correction
Jun Suzuki
Oral presentation, Japanese, Symposium on New Frontiers of Quantum Photonic Network, 電気通信大学 講堂, http://www.nict.go.jp/advanced_ict/quantum/NICT-UEC-2013.html, Domestic conference
06 Nov. 2013 - Quantum error correction with orbital angular momentum of single photons
Jun Suzuki
Oral presentation, Japanese, 量子情報技術時限研究専門委員会,第28回量子情報技術研究会
May 2013 - A numerical study on a noisy order of quantum channels and information quantuties
Taishi Okazawa; Jun Suzuki; Tomohiro Ogawa
Oral presentation, Japanese, Information and communication engineers
Mar. 2013 - On the Landau's critical velocity
Jun Suzuki
Others, Japanese, 電気通信大学・東京農工大学合同シンポジウム委員会,電気通信大学・東京農工大学第９回合同シンポジウム予稿集
Dec. 2012 - Symmetric coupling of four spin-1/2 systems
Jun Suzuki; Berthold-Georg Englert
Others, Japanese, 第２７回量子情報技術研究会, 量子情報技術時限研究専門委員会
Nov. 2012 - 単一光子軌道角運動量を用いた量子ビット構成法
鈴木 淳
Others, Japanese, 電気通信大学・東京農工大学合同シンポジウム委員会
Dec. 2011 - Long-lived qubit from three spin-1/2 atoms
Rui Han; Niels Lorch; Jun Suzuki; Berthold-Georg Englert
Oral presentation, Japanese, 量子情報技術時限研究専門委員会,第25回量子情報技術研究会
Nov. 2011 - Radiation from accelerated impurities in a Bose-Einstein condensate
鈴木 淳
Oral presentation, Japanese, 量子情報技術時限研究専門委員会,第24回量子情報技術研究会
May 2011 - 単一光子起動角運動量を用いた多量子ビット演算法
鈴木 淳
Others, Japanese, 日本学術会議総合工学委員会ICO分科会,第２回先端フォトニクスシンポジウム
Apr. 2011 - Robust construction of many qubits in infinite dimensional Hilbert spaces
鈴木淳; 根本香絵
Oral presentation, Japanese, 量子情報技術時限研究専門委員会,第２３回量子情報技術研究会
Nov. 2010 - Entanglement detection from interference fringes in atom-photon systems
Jun Suzuki; Christian Miniatura; Kae Nemoto
Oral presentation, English, 2010 International Workshop on Quantum Information Science
Mar. 2010 - Relations between entanglement and interference visibility from atom-photon interaction
鈴木淳; 根本香絵
Oral presentation, Japanese, 量子情報技術時限研究専門委員会,第21回 量子情報技術研究会
Nov. 2009 - Properties of decoherence-free qubits under non-collective noises
鈴木 淳
Oral presentation, Japanese, 量子情報技術時限研究専門委員会,第19回 量子情報技術研究会
Nov. 2008 - Critical Velocities for Energy Dissipation from Periodic Motions of Impurity in Bose-Einstein Condensates
Jun Suzuki
Oral presentation, English, 3th Central European Workshop on Quantum Optics, Vienna, Austria, 2006
May 2006
Courses
- インターンシップ（海外）（Ⅱ類）
The University of Electro-Communications - インターンシップ（海外）（Ⅱ類）
電気通信大学 - 大学院インターンシップ（海外・長期）
The University of Electro-Communications - 大学院インターンシップ（海外・長期）
電気通信大学 - 大学院インターンシップ（長期）
The University of Electro-Communications - 大学院インターンシップ（長期）
電気通信大学 - 大学院インターンシップ（海外）
The University of Electro-Communications - 大学院インターンシップ（海外）
電気通信大学 - 数理統計（Ｉエリア）
The University of Electro-Communications - 数理統計（Ｉエリア）
電気通信大学 - インターンシップ（Ⅱ類）
The University of Electro-Communications - インターンシップ（Ⅱ類）
電気通信大学 - 大学院インターンシップ
The University of Electro-Communications - 大学院インターンシップ
電気通信大学 - 大学院技術英語
The University of Electro-Communications - 大学院技術英語
電気通信大学 - 情報幾何学特論（夜間開講）
The University of Electro-Communications - 情報幾何学特論（夜間開講）
電気通信大学 - Current Topics in Emerging Multi-interdisciplinary Engineering A
The University of Electro-Communications - Current Topics in Emerging Multi-interdisciplinary Engineering A
The University of Electro-Communications - K課程卒研輪講
The University of Electro-Communications - K課程卒研輪講
電気通信大学 - 基礎演習A
The University of Electro-Communications - 基礎演習A
電気通信大学 - 基礎電磁気学
The University of Electro-Communications - 基礎電磁気学
電気通信大学 - 基礎演習B
The University of Electro-Communications - 応用数学B
The University of Electro-Communications - ネットワーク基礎論１
The University of Electro-Communications - 基礎演習B
The University of Electro-Communications - 基礎演習B
電気通信大学 - 応用数学B
The University of Electro-Communications - 応用数学B
電気通信大学 - 情報幾何学特論
The University of Electro-Communications - 基礎科学実験A
The University of Electro-Communications - 基礎科学実験A
The University of Electro-Communications - 基礎科学実験A
電気通信大学 - 情報幾何学特論
The University of Electro-Communications - 情報幾何学特論
電気通信大学 - ネットワーク基礎論１
The University of Electro-Communications - ネットワーク基礎論１
電気通信大学 - 情報理論演習
東京農工大学 - 情報理論演習
東京農工大学 - 情報理論演習
東京農工大学 - 情報ネットワーク学基礎１
The University of Electro-Communications - 情報ネットワーク学基礎１
The University of Electro-Communications - 情報ネットワーク学基礎１
電気通信大学
Research Themes
- 量子ベイズ統計モデリング法と量子確率的コンプレキシティの開拓
鈴木 淳
日本学術振興会, 科学研究費助成事業, 電気通信大学, 基盤研究(C), Principal investigator, 24K14816
Apr. 2024 - Mar. 2027 - 量子情報幾何学に基づく非線形最適実験計画法における最適なデザインの探究
鈴木淳
01 Apr. 2021 - 31 Mar. 2023 - 量子干渉と推定法を用いた光の波動関数を測定する方法に関する研究
張贇
01 Apr. 2021 - 31 Mar. 2023 - 不確定な環境系と相互作用している量子系に対する最適な量子状態推定法の開拓
Suzuki Jun
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, The University of Electro-Communications, Grant-in-Aid for Scientific Research (C), In this project, we developed the general framework to analyze the parameter estimation problem when a quantum system of interest interacts with unknown environment. As the main result, we established the quantum estimation theory for quantum statistical models containing nuisance parameters. We extended the theory of optimal design of experiments to the more general setting such as quantum state and channel estimation problem. The proposed method were applied to find an optimal estimation strategy for quantum estimation problems in the presence of nuisance parameters. We characterized quantum statistical models based on the properties of tangent spaces. Our method aimed at unifying different choices of operator monotone metrics on the quantum state manifold in quantum information geometry. We applied our proposal to several examples in physical systems to illustrate effectiveness of our approach., 17K05571
01 Apr. 2017 - 31 Mar. 2020
Social Contribution Activities
- 電気通信大学 出張講義
Lecturer, 千葉県立長生高等学校, Visiting lecture
09 Nov. 2023 - 09 Nov. 2023 - 電気通信大学 出張講義
Appearance, 東京都立立川国際中等教育学校, ボーア・アインシュタイン論争で見る量子力学の世界, 東京都立立川国際中等教育学校, Visiting lecture, 普通科 中等５年生
28 Oct. 2022 - オープントラカレ講座
Appearance, 言語交流研究所, 多量子の相関の不思議さ：２と３以上では何が違うのか？, Lecture
08 May 2022 - オープントラカレ講座
Appearance, 言語交流研究所, 量子と情報：量子の世界でのコミュニケーション, Lecture
29 Apr. 2021 - オープントラカレ講座
Appearance, 言語交流研究所, 量子力学における相補性, Lecture
04 Dec. 2016 - オープントラカレ講座
Appearance, 言語交流研究所, 不確定性関係と量子力学, Lecture
24 Mar. 2015 - オープントラカレ講座
Appearance, 言語交流研究所, 確率と量子力学, Lecture
29 Jul. 2014 - オープントラカレ講座
Appearance, 言語交流研究所, Lecture
27 Mar. 2013 - オープントラカレ講座
Appearance, 言語交流研究所, 情報と量子 -量子もつれで広がる新しいコミュニケーション-, Lecture
02 Aug. 2012
Academic Contribution Activities
- Quantum
Peer review etc, Peer review, Jul. 2024 - Present - Physical Review Research
Peer review, Apr. 2023 - Present - Physical Review B
Peer review etc, Peer review, Feb. 2022 - Present - Photonics
Peer review, Aug. 2021 - Present - Atoms
Peer review, Mar. 2021 - Present - Physical Review Letters
Peer review, Jan. 2021 - Present - New Journal of Physics
Peer review, Jan. 2021 - Present - Quantum Reports
Peer review, Nov. 2020 - Present - Physical Review A
Peer review, Oct. 2020 - Present - Physical Review X: Quantum
Peer review, Aug. 2020 - Present - Applied Sciences
Peer review, Nov. 2019 - Present - Communications in Mathematical Physics
Peer review, Jun. 2018 - Present - Entropy
Peer review, Jan. 2018 - Present - 電子情報通信学会和文論文誌A
Peer review, Nov. 2017 - Present - Journal of Physics A
Peer review, Sep. 2017 - Present - International Journal of Adaptive Control and Signal Processing
Peer review, Apr. 2017 - Present - IEEE Transactions on Information Theory
Peer review, Feb. 2016 - Present - Europhysics Letters
Peer review, Aug. 2013 - Present - International Journal of Geometric Methods in Modern Physics
Peer review, Jun. 2013 - Present - International Journal of Modern Physics A
Peer review, Feb. 2012 - Present - International Journal of Modern Physics B
Peer review, Oct. 2009 - Present - Physica A
Peer review, Sep. 2006 - Present - International Journal of Quantum Information
Peer review etc, Peer review, Jan. 2006 - Present - The International Symposium on Information Theory and Its Applications (ISITA) TPC
Competition etc, Review, Jan. 2024 - Nov. 2024 - 24th Asian Quantum Information Science Conference (AQIS) TPC
Competition etc, Review, May 2024 - Aug. 2024 - Physics Letters A
Peer review etc, Peer review, Mar. 2024 - Quantum Science and Technology
Peer review etc, Peer review, Feb. 2024 - Physica Scripta
Peer review etc, Peer review, Nov. 2023 - 第45回情報理論とその応用シンポジウム（SITA2022）
Competition etc, Planning etc, Apr. 2022 - 29 Nov. 2022 - 2022 International Symposium on Information Theory (ISITA)
Competition etc, Others, Nov. 2022 - 教務および実験・実習・実技等に関する実務・設備の管理運営
Others, Others, Oct. 2022, 2022年度 安全保障輸出管理セミナー 安全保障輸出管理に関するセミナー - 電子情報通信学会英文論文雑誌A SITA特集号
Academic society etc, Others, Feb. 2022
