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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 derive standard quantum theory out of classes of general models under a condition., 8 pages, 1 figure

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., 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., 8 pages, 2 figure

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

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., 7 pages, 7 figures