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It is important problem to clarify the class of implementable quantum measurements from both fundamental and applicable viewpoints. Positive-Operator-Valued Measure (POVM) measurements are implementable by the indirect measurement methods, and the class is the largest class determined by the mathematical structure of Hilbert space. However, if we assume probabilistic consistency in our operations instead of the structure of Hilbert space, we can deal with Non-Positive-Operator-Valued Measure (N-POVM) measurements in the framework of General Probabilistic Theories (GPTs). N-POVM measurements are not considered as implementable, but this paper gives a constructive way to implement N-POVM measurements by POVM measurements and post-selection in quantum theory when we restrict the domain of target states. Besides, we show that a post-selected POVM measurement is regarded as an N-POVM measurement in a restricted domain. These results provide a new relationship between N-POVM measurements in GPTs and post-selection., Comment: 12 pages, 1 figure

It is a key issue to characterize the model of standard quantum theory out of general models by an operational condition. The framework of General Probabilistic Theories (GPTs) is a new information theoretical approach to single out standard quantum theory. It is known that traditional properties, for example, Bell-CHSH inequality are not sufficient to single out standard quantum theory among possible models in GPTs. As a more precise property, we focus on the bound of the performance for an information task called state discrimination in general models. We give an equivalent condition for outperforming the minimum discrimination error probability under the standard quantum theory, which is given by the trace norm. Besides, by applying the equivalent condition, we characterize standard quantum theory out of general models in GPTs by the bound of the performance for state discrimination., Comment: 17 pages, 1 figure

With the recent development of quantum information theory, some attempts exist to construct information theory beyond quantum theory. Here we consider hypothesis testing relative entropy and one-shot classical capacity, that is, the optimal rate of classical information transmitted by using a single channel under a constraint of a certain error probability, in general physical theories where states and measurements are operationally defined. Then we obtain the upper bound of one-shot classical capacity by generalizing the method given by Wang and Renner [Phys. Rev. Lett. 108, 200501 (2012)]. Also, we derive the lower bound of the capacity by showing the existence of a good code that can transmit classical information with a certain error probability. Applying the above two bounds, we prove the asymptotic equivalence between classical capacity and hypothesis testing relative entropy even in any general physical theory., Comment: 7+6 pages, 1 figure. Accepted version for publication in PRA. We fixed typos, improved some explanations, and changed the structure of Chapters 5 and 6. The first sentence on page 5 is modified, adding the references

For a flat morphism $\pi \colon X \to T$ between smooth quasi-projective varieties and its fiber $X_0$, we prove that spherical objects on $D^b(X)$ pushed-forward from $D^b(X_0)$ induce autoequivalences of $D^b(X_0)$ itself. Our construction provides new derived symmetries for some singular varieties, which include singular fibers of elliptic surfaces (commonly referred to as Kodaira fibers) and type $III$ degenerations of K3 surfaces. In the case of Kodaira fibers of type $I_n$, we also show the induced autoequivalences of $D^b(X_0)$ correspond to the half twists on the $n$-punctured $2$-torus via homological mirror symmetry. As an application, we describe the autoequivalence groups of elliptic surfaces in terms of mapping class groups of punctured tori., Comment: 44 pages, 7 figures

This thesis deals with General Probabilistic Theories (GPTs) and Entanglement Structures (ESs). An ES is a possible structure of a quantum composite system in GPTs, which is not uniquely determined as the Standard Entanglement Structure (SES). It is an important problem to find reasonable postulates that determine various ESs as the SES. In order to solve this problem, this thesis explores the diversity of ESs. The topics of this thesis are roughly divided into two parts. First, this thesis considers state discrimination in ESs. As a main result, this thesis gives equivalent conditions for a given measurement in ESs to have a performance superior to standard quantum theory. Second, this thesis focuses on symmetry and self-duality. As a main result, this thesis gives derivations of the SES by symmetric conditions. On the other hand, this thesis clarifies that there are infinitely many self-dual ESs, even if they cannot be distinguished from the SES by a certain physical experiment with small errors., Comment: This is the author's Ph.D. thesis at Nagoya University. The equation (3.4) is modified from the original version due to an error. 94 pages, 7 figures

Device independent detections of quantum non-locality like Bell-CHSH inequality are important methods to detect quantum non-locality because the whole protocol can be implemented by uncertified local observables. However, this detection is not sufficient for the justification of standard quantum theory, because there are theoretically many types of beyond-quantum non-local states in General Probabilistic Theories. One important class is Entanglement Structures (ESs), which contain beyond-quantum non-local states even though their local systems are completely equivalent to standard quantum systems. This paper shows that any device independent detection cannot distinguish beyond-quantum non-local states from standard quantum states. To overcome this problem, this paper gives a device dependent detection based on local observables to distinguish any beyond-quantum non-local state from all standard quantum states. Especially, we give a way to detect any beyond-quantum non-local state in two-qubit ESs by observing only spin observables on local systems., Comment: 8 pages, 2 figure

An experimental verification of the maximally entangled state ensures that the constructed state is close to the maximally entangled state, but it does not guarantee that the state is exactly the same as the maximally entangled state. Further, the entanglement structure is not uniquely determined in general probabilistic theories even if we impose that the local subsystems are fully equal to quantum systems. Therefore, the existence of the maximally entangled state depends on whether the standard entanglement structure is valid. To examine this issue, we introduce pseudo standard entanglement structure as a structure of quantum composite system under natural assumptions based on the existence of projective measurements and the existence of approximations of all maximally entangled standard states. Surprisingly, there exist infinitely many pseudo standard entanglement structures different from the standard entanglement structure. In our setting, any maximally entangled state can be arbitrarily approximated by an entangled state that belongs to our obtained pseudo standard entanglement structure. That is, experimental verification does not exclude the possibility of our obtained pseudo standard entanglement structure that is different from the standard entanglement structure. On the other hand, such pseudo structures never possess global unitary symmetry, i.e., global unitary symmetry is essential condition for the standard entanglement structure., Comment: The previous version contains two wrong statements (Theorem3 and existence of G-symmetric self-dual models in the previous version). In order to replace them with correct statements, we revise mainly the following three points from the previous version. 1. Definition of pseudo standard entanglement structure. 2. Construction of our examples. 3. Statements and proofs for discrimination

Von Neumann obtained the formula for the entropy of a quantum state by assuming the validity of the second law of thermodynamics in a thought experiment involving semipermeable membranes and an ideal gas of quantum-labeled particles. Despite being operational in the most part, von Neumann's argument crucially departs from an operational narrative in its use of the spectral theorem. In this work we show that the role of the spectral theorem in von Neumann's argument can be taken over by the operational assumptions of repeatability and reversibility, and using these we are able to explore the consequences of the second law also in theories that do not possess a unique spectral decomposition. As a byproduct, we obtain the Groenewold--Ozawa information gain as a natural monotone for a suitable ordering of instruments, providing it with an operational interpretation valid in quantum theory and beyond., Comment: 10 pages, 4 figures. [v2]: Accepted version for the publication on PRR

We study the entanglement structure, i.e., the structure of quantum composite system from operational aspects. The structure is not uniquely determined in General Probabilistic Theories (GPTs) even if we impose reasonable postulate about local systems. In this paper, we investigate the possibility that the standard entanglement structure can be determined uniquely by repeatability of measurement processing and its saturated situation called self-duality. Surprisingly, self-duality cannot determine the standard entanglement structure even if we additionally impose local unitary symmetry assumption. In this paper, we show the existence of infinite structures of quantum composite system such that it is self-dual with local unitary symmetry. Besides, we also show the existence of a structure of quantum composite system such that non-orthogonal states in the structure are perfectly distinguishable. In addition, as a byproduct, we derive an sufficient condition to achieve the detection of the entanglement property with a finite number of parameterized minimizations., Comment: We found out some mathematical mistakes in the proofs of statements in Section V. Therefore we withdraw this paper

To build a robust and practical content-based image retrieval (CBIR) system that is applicable to a clinical brain MRI database, we propose a new framework -- Disease-oriented image embedding with pseudo-scanner standardization (DI-PSS) -- that consists of two core techniques, data harmonization and a dimension reduction algorithm. Our DI-PSS uses skull stripping and CycleGAN-based image transformations that map to a standard brain followed by transformation into a brain image taken with a given reference scanner. Then, our 3D convolutioinal autoencoders (3D-CAE) with deep metric learning acquires a low-dimensional embedding that better reflects the characteristics of the disease. The effectiveness of our proposed framework was tested on the T1-weighted MRIs selected from the Alzheimer's Disease Neuroimaging Initiative and the Parkinson's Progression Markers Initiative. We confirmed that our PSS greatly reduced the variability of low-dimensional embeddings caused by different scanner and datasets. Compared with the baseline condition, our PSS reduced the variability in the distance from Alzheimer's disease (AD) to clinically normal (CN) and Parkinson disease (PD) cases by 15.8-22.6% and 18.0-29.9%, respectively. These properties allow DI-PSS to generate lower dimensional representations that are more amenable to disease classification. In AD and CN classification experiments based on spectral clustering, PSS improved the average accuracy and macro-F1 by 6.2% and 10.7%, respectively. Given the potential of the DI-PSS for harmonizing images scanned by MRI scanners that were not used to scan the training data, we expect that the DI-PSS is suitable for application to a large number of legacy MRIs scanned in heterogeneous environments., Comment: 13 pages, 7 figures

As a modern approach for the foundation of quantum theory, existing studies of General Probabilistic Theories gave various models of states and measurements that are quite different from quantum theory. In this paper, to seek a more realistic situation, we investigate models approximately close to quantum theory. We define larger measurement classes that are smoothly connected with the class of POVMs via a parameter, and investigate the performance of perfect discrimination. As a result, we give a sufficient condition of perfect discrimination, which shows a significant improvement beyond the class of POVMs., Comment: 14 pages, 2 figures

Increasing numbers of MRI brain scans, improvements in image resolution, and advancements in MRI acquisition technology are causing significant increases in the demand for and burden on radiologists' efforts in terms of reading and interpreting brain MRIs. Content-based image retrieval (CBIR) is an emerging technology for reducing this burden by supporting the reading of medical images. High dimensionality is a major challenge in developing a CBIR system that is applicable for 3D brain MRIs. In this study, we propose a system called disease-oriented data concentration with metric learning (DDCML). In DDCML, we introduce deep metric learning to a 3D convolutional autoencoder (CAE). Our proposed DDCML scheme achieves a high dimensional compression rate (4096:1) while preserving the disease-related anatomical features that are important for medical image classification. The low-dimensional representation obtained by DDCML improved the clustering performance by 29.1\% compared to plain 3D-CAE in terms of discriminating Alzheimer's disease patients from healthy subjects, and successfully reproduced the relationships of the severity of disease categories that were not included in the training., Comment: To appear in the IEEE BigData 2019 Workshop on Advances in High Dimensional (AdHD) Big Data

We address perfect discrimination of two separable states. When available states are restricted to separable states, we can theoretically consider a larger class of measurements than the class of measurements allowed in quantum theory. The framework composed of the class of separable states and the above extended class of measurements is a typical example of general probabilistic theories. In this framework, we give a necessary and sufficient condition to discriminate two separable pure states perfectly. In particular, we derive measurements explicitly to discriminate two separable pure states perfectly, and find that some non-orthogonal states are perfectly distinguishable. However, the above framework does not improve the capacity, namely, the maximum number of states that are simultaneously and perfectly distinguishable., Comment: 18 pages

Property by design is one appealing idea in material synthesis but hard to achieve in practice. A recent successful example is the demonstration of van der Waals (vdW) heterostructures,1-3 in which atomic layers are stacked on each other and different ingredients can be combined beyond symmetry and lattice matching. This concept, usually described as a nanoscale Lego blocks, allows to build sophisticated structures layer by layer. However, this concept has been so far limited in two dimensional (2D) materials. Here we show a class of new material where different layers are coaxially (instead of planarly) stacked. As the structure is in one dimensional (1D) form, we name it "1D vdW heterostructures". We demonstrate a 5 nm diameter nanotube consisting of three different materials: an inner conductive carbon nanotube (CNT), a middle insulating hexagonal boron nitride nanotube (BNNT) and an outside semiconducting MoS2 nanotube. As the technique is highly applicable to other materials in the current 2D libraries,4-6 we anticipate our strategy to be a starting point for discovering a class of new semiconducting nanotube materials. A plethora of function-designable 1D heterostructures will appear after the combination of CNTs, BNNTs and semiconducting nanotubes.

Magnetoresistance in single crystals of black phosphorus is studied at ambient and hydrostatic pressures. In the semiconducting states at pressures below 0.71 GPa, the magnetoresistance shows periodic oscillations, which can be ascribed to the magneto-phonon resonance that is characteristic of high mobility semiconductors. In the metallic state above 1.64 GPa, the both transverse and longitudinal magnetoresistance show titanic increase with exhibiting superposed Shubnikov-de Haas oscillations. The observed small Fermi surfaces, high mobilities and light effective masses of carriers in semimetallic black phosphorus are comparable to those in the representative elemental semimetals of bismuth and graphite., Comment: 11 pages, 5 figures, to be published in J. Phys. Soc. Jpn

Motivated by recent experiments on isovalent-doped 1111 iron-based superconductors LaFeAs$_{1-{x}}$P$_{x}$O$_{1-{y}}$F$_{y}$ and the theoretical study that followed, we investigate, within the five orbital model, the correlation between the spin fluctuation and the superconducting transition temperature, which exhibits a double dome feature upon varying the Fe-As-Fe bond angle. Around the first dome with higher $T_c$, the low energy spin fluctuation and $T_c$ are not tightly correlated because the finite energy spin fluctuation also contributes to superconductivity. On the other hand, the strength of the low-energy spin fluctuation originating from the $d_{xz/yz}$ orbital is correlated with $T_c$ in the second dome with lower $T_c$. These calculation results are consistent with recent NMR study, and hence strongly suggest that the pairing in the iron-based superconductors is predominantly caused by the multi-orbital spin fluctuation., Comment: 7 pages, 7 figures