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Lectures on Quantum Measurement Theory: IV

2026年6月30日(火) 15:30 - 17:00

小澤 正直 (名古屋大学 名誉教授)

Lecture IV: Instruments in classical mechanics, quantum field theory, and cognitive science In algebraic quantum field theory, measurements describable by interactions between the field and the measuring apparatus are characterized by the class of completely positive instruments that satisfy the condition called the normal extension property (NEP) (Okamura-Ozawa 2016). In classical mechanics, traditionally only non-invasive measurements—those with trivial interaction—were considered admissible, for the observability of the trajectory of motion. Here, however, the full class of measurements realizable by classical-mechanical interactions is characterized in terms of instruments with NEP for the basis of the study of invasive measurements of classical systems. Cognitive processes are also represented by completely positive instruments, along with the long-standing paradigm provided by von Helmholtz, who described a sensation-perception process as a sort of measuring interaction and referred to it as an unconscious inference. This framework is used to show the compatibility of the question order effect and the response replicability effect (Ozawa-Khrennikov 2019), which failed to be explained in an earlier approach using only projective measurement models. It is shown that there exists an instrument model, realizing both the question order effect and the response replicability effect, that is also capable of almost faithfully reproducing public-opinion survey data such as the well-known Clinton-Gore survey by Gallup in 1997 (Ozawa-Khrennikov 2021).

会場: セミナー室 (359号室) (メイン会場) / via Zoom

イベント公式言語: 英語

Lectures on Quantum Measurement Theory: III

2026年6月23日(火) 15:30 - 17:00

小澤 正直 (名古屋大学 名誉教授)

Lecture III: Measurement error, disturbance, the universally valid reformulation of Heisenberg’s uncertainty principle, and a quantitative generalization of the Wigner–Araki–Yanase theorem Definitions of measurement error and disturbance are introduced (Ozawa 2002, 2019) and it is shown that there exists a solvable model for a physically realizable measurement that serves as a counterexample both to Heisenberg’s uncertainty principle in the conventional formulation and to the SQL (Ozawa 1988, 1989, 2002). Thus, those limits are no more considered as universal limits. In fact, the above counter example to SQL was found in 1988 using the idea of contractive state measurements by Yuen (1983) and the LIGO was started in 1994 to succeed in the gravitational wave detection in 2015 as announced in 2016. New formulations are then proved for the uncertainty principle concerning the errors in the approximate simultaneous measurement of two physical quantities, called the "joint error relation" (Ozawa 2003b, 2004), and for the uncertainty principle concerning the error and disturbance associated with the measurement of a single physical quantity, called the "error-disturbance relation" (Ozawa 2003a). From the error-disturbance relation, a quantitative relation for measurement error under an additive conservation law is proved (Ozawa 2002a, 2003b), generalizing the "Wigner–Araki–Yanase theorem" (Wigner 1952, Araki-Yanase 1960), which states that a physical quantity not commuting with a conserved quantity cannot be measured accurately by a measurement interaction satisfying an additive conservation law. The above relation also derives limits for realizing quantum computing and operations under conservation laws (Ozawa 2002b), the results later developed as the resource theory of asymmetry.

会場: セミナー室 (359号室) (メイン会場) / via Zoom

イベント公式言語: 英語

Lectures on Quantum Measurement Theory: II

2026年6月16日(火) 15:30 - 17:00

小澤 正直 (名古屋大学 名誉教授)

Lecture II: Modern approach: Quantum instruments, POVMs, measuring processes, intersubjectivity, and value reproducibility The modern approach to quantum measurement theory is based on the "realizability theorem" stating that a measurement is physically realizable if and only if its statistical properties are represented by a completely positive instrument, and this is also equivalent to saying that the measurement can be described by an interaction with a measuring apparatus (Ozawa 1984, 2004). The conventional analysis of a measuring process determines the post-measurement object state by applying the "projection postulate" to the meter measurement in the post-measurement state that "entangles" the object and the apparatus, but the above result has been established without assuming the projection postulate altogether; rather we use only the classical Bayesian probability update rule (Ozawa 1984). We introduce the "intersubjectivity theorem" that states that, when multiple observers simultaneously and statistically correctly measure the same physical quantity, they obtain the same measurement value and the "value reproducibility theorem" that states that a statistically correct measurement correctly reproduces the value of the physical quantity immediately before the measurement (Ozawa 2025). The above three theorems essentially solves the so-called measurement problem, since we eliminate the collapse of the wave function and we establish the reality of the the pre-measurement value of the measured observable to be copied to the meter value and to be recorded by the observer.

会場: セミナー室 (359号室) (メイン会場) / via Zoom

イベント公式言語: 英語

Noncritical Conformal Gravity and 4D Liouville Theory

2026年6月12日(金) 15:00 - 16:30

太田 信義 (大阪公立大学 南部陽一郎物理学研究所 客員教授)

We study the quantum aspects of the conformal gravity in four dimensions, specifically addressing a known discrepancy in beta functions between general quadratic curvature theories and conformal gravity, which corresponds to two scalar degrees of freedom. We demonstrate that this mismatch is resolved by carefully introducing gauge-fixing and ghost terms via the BRST symmetry, which effectively adds the two scalar modes. Drawing lessons from two-dimensional quantum gravity and Liouville theory, we proceed to integrate the four-dimensional trace anomaly to derive a consistent Liouville action, which is given by a free-field action for the conformal mode with a consistent conformal anomaly. We give the condition that the BRST transformation is anomaly free. Finally I would like to talk about some application of this theory.

会場: セミナー室 (359号室) 3階 359号室とZoomのハイブリッド開催

イベント公式言語: 英語

Quantum Improved Black Holes in Asymptotically Safe Gravity

2026年6月11日(木) 15:00 - 16:30

Chiang-Mei Chen (Professor, Department of Physics, National Central University, Taiwan)

In this talk, I will explore quantum-improved black hole solutions within the framework of asymptotic safety. In this approach, the Newton coupling becomes scale-dependent, necessitating a meaningful identification between the energy scale and a corresponding physical (length) scale to derive observable consequences for black hole spacetimes. I will argue that the requirement of consistency with the first law of black hole thermodynamics provides a physically motivated criterion for this scale-setting, particularly near the event horizon. Applying this principle, we propose a specific identification scheme that leads to a regularized geometry capable of resolving the ring singularity of Kerr black holes.

会場: セミナー室 (359号室) 3階 359号室とZoomのハイブリッド開催

イベント公式言語: 英語

Lectures on Quantum Measurement Theory: I

2026年6月2日(火) 15:30 - 17:00

小澤 正直 (名古屋大学 名誉教授)

Lecture I: Conventional approach: Repeatability, Heisenberg’s original uncertainty principle, and the SQL for gravitational-wave detection The conventional approach to quantum measurement theory taken by von Neumann (1932), Dirac (1958), and Schrödinger (1935) assumes the "repeatability hypothesis" stating that if a physical quantity is measured twice in succession, then the same value is obtained each time, which is often quantitatively generalized to the "approximately repeatable hypothesis" stating that after a measurement of a physical quantity with error ε, the post-measurement deviation around the measured value is no larger than ε; this is equivalent to saying that the state after obtaining a measurement result with error ε becomes an ε-approximate eigenstate corresponding to that measurement result. From the approximate repeatability hypothesis, one can derive "Heisenberg’s original formulation of the uncertainty principle," namely, that when position and momentum are approximately measured simultaneously, the product of their respective errors is at least ℏ/2 (Heisenberg 1927, Kennard 1927, Ozawa 2015), as well as the "standard quantum limit (SQL) for monitoring the free-mass position", which states that when the position of a free mass m is measured at a time interval τ, the result of the second measurement cannot be predicted with uncertainty smaller than (ℏτ/ m)^{1/2} (Caves 1985). The last result leads to a sensitivity limit for interferometric gravitational-wave detectors, and in the early 1980s it was therefore argued that gravitational waves of the expected strength could not be observed using interferometric detectors (Braginsky et al. 1980, Caves et al. 1980).

会場: セミナー室 (359号室) (メイン会場) / via Zoom

イベント公式言語: 英語

Introduction to categorification and link homology

2026年5月28日(木) 14:00 - 15:30

Mikhail Khovanov (Professor, Department of Mathematics, Johns Hopkins University, USA)

Quantum link invariants relate topology in 3 dimensions to mathematical physics and representation theory. They admit liftings to 4-dimensional structures, known as link homology. We will explain how the skein relations for quantum invariants turn into homological structures at this higher level and how semisimple representation theory turns into non-semisimple representations and homological algebra upon categorification.

会場: 大河内記念ホール (メイン会場) / via Zoom

イベント公式言語: 英語

The First RIKEN Quantum International Workshop on Frontiers of Quantum Computing Applications and Quantum-HPC Integration

2026年5月25日(月) - 26日(火)

This two-day workshop will bring together leading experts from academia, industry, and national laboratories to explore the rapidly evolving frontiers of quantum computing applications and their integration with high-performance computing (HPC) platforms. Hosted by RIKEN Quantum, the event will provide a forum for discussing recent advances, practical challenges, and future directions toward achieving utility-scale quantum computations and robust quantum–HPC hybrid workflows. The workshop is primarily an in-person event, but a special session on quantum computing in chemistry and life sciences will also be accessible via Zoom.

会場: 理化学研究所和光キャンパス 本部棟2階大会議室

イベント公式言語: 英語

Positivity constraints for the gravitational path integral

2026年5月21日(木) 10:00 - 11:50

ガブリエル・ディウバルド (理化学研究所 数理創造研究センター (iTHEMS) 国内外連携・人材育成部門 理研バークレーセンター 特別研究員)

For a quantum theory of gravity to have a well-defined Hilbert space, the inner product between different states of open and closed universes must be positive semi-definite. Positivity however is not manifest in the low-energy effective theory and in fact imposes nontrivial constraints on the theory. Working in the Gravitational Path Integral (GPI) approach, we derive the general set of positivity constraints on the closed and open universe Hilbert spaces. In the case of AdS gravity, open universe positivity in principle follows from CFT unitarity, however the holographic description of closed universes remains unclear. Strikingly, we exhibit positivity of closed universes across many theories and prove that open positivity implies closed positivity, showing that the CFT 'knows' about the closed universe hilbert space. We then analyze positivity constraints on gravitational theories coupled to axions. We present a method to compute off-shell axion wormholes in AdS and flat space which we use to show that positivity is violated if the axion shift symmetry is exact. In low-energy EFTs where these wormholes are perturbatively stable, to restore positivity the wormhole must have a non-perturbative instability due to instantons that breaks the shift symmetry. Positivity then leads to a proof of a sharp version of the Axion Weak Gravity Conjecture A-WGC, including precise numerical constants. For the QCD axion this provides a bound on the axion decay constant which has phenomenological and experimental consequences for axion searches. In string theory, positivity gives a bound on the coupling between the axion and the dilaton in the low energy effective action.

会場: via Zoom

イベント公式言語: 英語

Realizing two-dimensional discrete time crystals on a digital quantum computer

2026年5月19日(火) 15:00 - 16:30

新城 一矢 (理化学研究所 創発物性科学研究センター (CEMS) 計算物性物理研究室 研究員)

This work was featured in a RIKEN press release. For details, please see the related link.

会場: セミナー室 (359号室) (メイン会場) / via Zoom

イベント公式言語: 英語

Introduction to quantum resource theories (3)

2026年5月15日(金) 9:00 - 17:00

高木 隆司 (東京大学 大学院総合文化研究科 准教授)

[Registration Closed] Due to high demand and venue capacity limits, registration for this course is now closed as of April 25. If you wish to be placed on a waiting list in case of cancellations, please contact us via the inquiry form at the bottom of this page. One of the central goals of quantum information theory is to quantitatively clarify the relationship between the performance of quantum information processing and the valuable quantum features that underlie it. In this lecture, we will discuss quantum resource theories, a framework that provides a useful approach to this question. By presenting concrete examples—starting with entanglement theory, the most representative resource theory—as well as recent research results, we will see how perspectives and tools from information theory enable the quantification of quantum resources and the characterization of their convertibility. Beyond entanglement theory, we plan to discuss other key settings such as quantum thermodynamics, resource theory of asymmetry, and quantum magic—relevant resource in fault-tolerant quantum compuation. The overall aim of this lecture is to provide new analytical viewpoints that can be applied to a wide range of systems and quantum information processing tasks. While we do not plan to change the overall start and end times for each day, the detailed lecture schedule is subject to change. The intensive course will be held over three days. Please register for the course using the form. The registration deadline is May 7 (Thu). Please note that the registration form is the same for all three days, so you only need to register once. The 3rd day: May 15 (Fri) 9:00–10:30 Lecture 7 10:30–11:00 Coffee break 11:00–12:30 Lecture 8 12:30-13:30 Lunch time 13:30-15:00 Lecture 9 15:00-15:30 Coffee break 15:30-17:00 Seminar (or Lecture 10) This event is in-person only.

会場: 研究本館 4階 435-437号室

イベント公式言語: 英語

Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation

2026年5月14日(木) 14:30 - 15:30

ジアン・シュウ (理化学研究所 数理創造研究センター (iTHEMS) 数理展開部門 量子数理科学チーム 特別研究員)

In quantum machine learning (QML), classical data are often encoded as quantum pure states and processed directly as quantum representations, motivating \emph{representation-level generative modeling} that samples new quantum states from an underlying pure-state ensemble rather than re-preparing them from perturbed classical inputs. However, extending \emph{score-based} diffusion models with well-defined reverse-time samplers to quantum pure-state ensembles remains challenging, due to the non-Euclidean geometry of the complex projective space $\mathbb{CP}^{d-1}$ and the intractability of transition densities. We propose \emph{Stochastic Schr\"odinger Diffusion Models} (SSDMs), an intrinsic score-based generative framework on $\mathbb{CP}^{d-1}$ endowed with the Fubini--Study (FS) metric. SSDMs formulate a forward Riemannian diffusion with a stochastic Schr\"odinger equation (SSE) realization, and derive reverse-time dynamics driven by the Riemannian score $\nabla_{\mathrm{FS}} \log p_t$. To enable training without analytic transition densities, we introduce a local-time objective based on a local Euclidean Ornstein--Uhlenbeck approximation in FS normal coordinates, yielding an analytic teacher score mapped back to the manifold. Experiments show that SSDMs faithfully capture target pure-state ensemble statistics, including observable moments, overlap-kernel MMD, and entanglement measures, and that SSDM-generated quantum representations improve downstream QML generalization via representation-level data augmentation.

会場: セミナー室 (359号室) 3階 359号室 (メイン会場) / via Zoom

イベント公式言語: 英語