Date: Tuesday 21 November 2023, from 10am
Venue: Nagoya University, 文系総合館7階カンファレンスホール
Coordinates: 35.153838053176955, 136.96406005462265 (copy and paste these in your favourite map application)
Organizer: Francesco Buscemi (Graduate School of Informatics, Nagoya University)
slots are 45 min long (ideally, 40 min for the talk itself and 5 min for discussions)
| time | speaker | title |
|---|---|---|
| 10:00~10:45 | Jenčová | On some characterizations of sufficient quantum channels |
| 10:45~11:30 | Fujiwara | A theory of quantum local asymptotic normality, Part I: Quantum contiguity |
| 11:30~12:15 | Yamagata | A theory of quantum local asymptotic normality, Part II: Asymptotic representation theorem |
| 12:15~13:00 | Wakakuwa | Exact Exponent for Atypicality of Random Quantum States |
| 13:00~14:30 | lunch break | |
| 14:30~15:15 | Dall'Arno | Tight conic approximation of testing regions for quantum statistical models and measurements |
| 15:15~16:00 | Kimura | Norm inequalies and their application to quantum physics |
| 16:00~16:45 | Kuramochi | Compact convex structure and simulability of measurements |
| 16:45~17:30 | Kato | Exact and Local Compression of Quantum Bipartite States |
Speaker: Anna Jenčová (Slovak Academy of Science)
Title: On some characterizations of sufficient quantum channels
Abstract: We say that a quantum channel is sufficient with respect to a set of states if all states in the set can be recovered by another channel. This property was studied and characterized by Petz, who proved a number of equivalent conditions. Such conditions can be given in terms of some structural properties of the channel and the states, or by preservation of some information-theoretic quantities such as the relative entropy.
In this talk, we give a review of some of these conditions. We first note that characterizations of sufficient channels can be obtained from the mean ergodic theorem. We then focus on the conditions given by preservation of sandwiched Rényi relative entropies and quantities related to hypothesis testing.
Slides: PDF
Speaker: Akio Fujiwara (Osaka University)
Title: A theory of quantum local asymptotic normality, Part I: Quantum contiguity
Abstract: We develop a theory of contiguity in the quantum domain based on 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, Ann. Statist. 41 (2013) 2197– 2217], yielding substantial enlargement of the scope of quantum statistics.
Reference: A. Fujiwara and K. Yamagata, Bernoulli 26 (2020) 2105-2141.
Slides: PDF
Speaker: Koichi Yamagata (Kanazawa University)
Title: A theory of quantum local asymptotic normality, Part II: Asymptotic representation theorem
Abstract: We 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.
Reference: A. Fujiwara and K. Yamagata, Annals of Statistics, 51 (2023) 1159-1182.
Slides: PDF
Speaker: Eyuri Wakakuwa (Nagoya University)
Title: Exact Exponent for Atypicality of Random Quantum States
Abstract: We study properties of the random quantum states induced from the uniformly random pure states on a bipartite quantum system by taking the partial trace over the larger subsystem. Most of the previous approaches have focused on the behavior of the states close to the average, as known under the name of measure concentration. In contrast, we investigate the large deviation regime, where the states may be far from the average.
We prove the following results: First, the probability that the induced random state is within a given set obeys the large deviation principle, i.e., it decreases no slower or faster than exponential in the dimension of the system traced out. Second, the exponent is equal to the quantum relative entropy of the maximally mixed state and the given set, multiplied by the dimension of the remaining system. Third, the total probability of a given set strongly concentrates around the element closest to the maximally mixed state, a property that we call conditional concentration. Along the same line, we also investigate an asymptotic behavior of coherence of random pure states in a single system with large dimension.
Speaker: Michele Dall'Arno (Toyohashi University of Technology)
Title: Tight conic approximation of testing regions for quantum statistical models and measurements
Abstract: Quantum statistical models (i.e., families of normalized density matrices) and quantum measurements (i.e., positive operator-valued measures) can be regarded as linear maps: the former, mapping the space of effects to the space of probability distributions; the latter, mapping the space of states to the space of probability distributions. The images of such linear maps are called the testing regions of the corresponding model or measurement. Testing regions are notoriously impractical to treat analytically in the quantum case. Our first result is to provide an implicit outer approximation of the testing region of any given quantum statistical model or measurement in any finite dimension: namely, a region in probability space that contains the desired image, but is defined implicitly, using a formula that depends only on the given model or measurement. The outer approximation that we construct is minimal among all such outer approximations, and close, in the sense that it becomes the maximal inner approximation up to a constant scaling factor. Finally, we apply our approximation formulas to characterize, in a semi-device independent way, the ability to transform one quantum statistical model or measurement into another.
Slides: PDF
Speaker: Gen Kimura (Shibaura Institute of Technology)
Title: Norm inequalies and their application to quantum physics
Abstract: We propose several norm inequalities that either generalize or are associated with the Böttcher-Wenzel inequality and apply them to quantum physics. The first application pertains to open quantum dynamics, investigating a universal relation concerning relaxation times. The second application relates to the uncertainty relations.
Speaker: Yui Kuramochi (Kyushu University)
Title: Compact convex structure and simulability of measurements
Abstract: In this talk, we introduce basic properties of the measurement space, which is the set of post-processing equivalence classes of continuous-outcome measurements (effect-valued measures) on a possibly infinite-dimensional general probabilistic theory (GPT). We particularly consider convex structure and weak topology of measurement space. The weak topology is defined as the weakest topology in which the state discrimination probability functionals are continuous and this topology is shown to be compact. Based on this general structure of measurements, we also discuss the simulability of measurements and generalize some known results known in finite-dimensional quantum measurements.
Slides: PDF
Speaker: Kohtaro Kato (Nagoya University)
Title: Exact and Local Compression of Quantum Bipartite States
Abstract: Quantum data compression is one of the most fundamental quantum information processing. We study an exact local compression of a quantum bipartite state; that is, exact and noiseless one-shot quantum data compression of general mixed state sources without side information or entanglement assistance. We provide a formula for computing the minimal achievable compression dimensions, provided as a minimization of the Schmidt rank of a particular pure state constructed from that state. We will then discuss a possible application to tensor-network states.