There are two parts to this work: first, we study the error correction properties of the real-space renormalization group (RG). The long-distance operators are the (approximately) correctable operators encoded in the physical algebra of short-distance operators. This is closely related to modeling the holographic map as a quantum error correction code. As opposed to holography, the real-space RG of a many-body quantum system does not have the complementary recovery property. We discuss the role of large N and a large gap in the spectrum of operators in the emergence of complementary recovery.Second, we study the operator algebra exact quantum error correction for any von Neumann algebra. We show that similar to the finite dimensional case, for any error map in between von Neumann algebras the Petz dual of the error map is a recovery map if the inclusion of the correctable subalgebra of operators has finite index.

The entanglement theory in quantum systems with internal symmetries is rich due to the spontaneous creation of entangled pairs of charge/anti-charge particles at the entangling surface. We call these pair creation operators the bi-local intertwiners because of the role they play in the representation theory of the symmetry group. We define a generalized measure of entanglement entropy as a measure of information erased under restriction to a subspace of observables. We argue that the correct entanglement measure in the presence of charges is the sum of two terms; one measuring the entanglement of chargeneutral operators, and the other measuring the contribution of the bi-local intertwiners. Our expression is unambiguously defined in lattice models as well in quantum field theory (QFT). We use the Tomita-Takesaki modular theory to highlight the differences between QFT and lattice models, and discuss an extension of the algebra of QFT that leads to a factorization of the charged modes.

We report the result of our study on the dependency of the photon generation and storage to atomic geometry in an optical resonator. We show that the geometry of atoms in an ensemble can be engineered to control collective excitations in a way to achieve high degree of correlation between photons. Moreover, we discuss the role of geometry in such structures to efficiently store photons among a small number of atomic regions.

We use the Tomita-Takesaki modular theory and the Kubo-Ando operator mean to write down a large class of multi-state quantum f -divergences and prove that they satisfy the data processing inequality. For two states, this class includes the (α, z)-Rényi divergences, the f -divergences of Petz, and the measures in [1] as special cases. The method used is the interpolation theory of non-commutative L p ω spaces and the result applies to general von Neumann algebras including the local algebra of quantum field theory. We conjecture that these multi-state Rényi divergences have operational interpretations in terms of the optimal error probabilities in asymmetric multi-state quantum state discrimination.

Background. This study is aimed at verifying a hypothetical model of the structural relationship between the recovery process and difficulties in daily life mediated by occupational dysfunction in severe and persistent mental illness (SPMI). Methods. Community-dwelling participants with SPMI were enrolled in this multicenter cross-sectional study. The Recovery Assessment Scale (RAS), the World Health Organization Disability Assessment Schedule second edition (WHODAS 2.0), and the Classification and Assessment of Occupational Dysfunction (CAOD) were used for assessment. Confirmatory factor analysis, multiple regression analysis, and Bayesian structural equation modelling (BSEM) were determined to analyze the hypothesized model. If the mediation model was significant, the path coefficient from difficulty in daily life to recovery and the multiplication of the path coefficients mediated by occupational dysfunction were considered as each the direct effect and the indirect effect. The goodness of fit in the model was determined by the posterior predictive P value (PPP). Each path coefficient was validated with median and 95% confidence interval (CI). Results. The participants comprised 98 individuals with SPMI. The factor structures of RAS, WHODAS 2.0, and CAOD were confirmed by confirmatory factor analysis to be similar to those of their original studies. Multiple regression analysis showed that the independent variables of RAS were WHODAS 2.0 and CAOD, and that of CAOD was WHODAS 2.0. The goodness of fit of the model in the BSEM was satisfactory with a PPP = 0.27 . The standardized path coefficients were, respectively, significant at -0.372 from “difficulty in daily life” to “recovery” as the direct effect and at -0.322 (95% CI: -0.477, -0.171) mediated by “occupational dysfunction” as the indirect effect. Conclusions. An approach for reducing not only difficulty in daily life but also occupational dysfunction may be an additional strategy of person-centered, recovery-oriented practice in SPMI.