3D local qupit quantum code without string logical operator

Recently Haah introduced a new quantum error correcting code embedded on a cubic lattice. One of the defining properties of this code is the absence of string logical operator. We present new codes with similar properties by relaxing the condition on the local particle dimension. The resulting code is well-defined when the local Hilbert space dimension is prime. These codes can be divided into two different classes: the local stabilizer generators are either symmetric or antisymmetric with respect to the inversion operation. These is a nontrivial correspondence between these two classes. For any symmetric code without string logical operator, there exists a complementary antisymmetric code with the same property and vice versa. We derive a sufficient condition for the absence of string logical operator in terms of the algebraic constraints on the defining parameters of the code. Minimal number of local particle dimension which satisfies the condition is 5. These codes have logarithmic energy barrier for any logical error.Comment: 9 pages, 7 figure

Modulus of convexity for operator convex functions

Given an operator convex function $f(x)$, we obtain an operator-valued lower bound for $cf(x) + (1-c)f(y) - f(cx + (1-c)y)$, $c \in [0,1]$. The lower bound is expressed in terms of the matrix Bregman divergence. A similar inequality is shown to be false for functions that are convex but not operator convex.Comment: 5 pages, change of title. The new version shows that the main result of the original paper cannot be extended to convex functions that are not operator convex

Localization from superselection rules in translation invariant systems

We study a translation invariant spin model in a three-dimensional regular lattice, called the cubic code model, in the presence of arbitrary extensive perturbations. Below a critical perturbation strength, we show that most states with finite energy are localized; the overwhelming majority of such states have energy concentrated around a finite number of defects, and remain so for a time that is near-exponential in the distance between the defects. This phenomenon is due to an emergent superselection rule and does not require any disorder. An extensive number of local integrals of motion for these finite energy sectors are identified as well. Our analysis extends more generally to systems with immobile topological excitations.Comment: 7.5+1pages, 2 figure

Precursor problem and holographic mutual information

The recent proposal of Almheiri et al.http://arxiv.org/abs/1411.7041, together with the Ryu-Takayanagi formula, implies the entanglement wedge hypothesis for certain choices of boundary subregions. This fact is derived in the pure AdS space. A similar conclusion holds in the presence of quantum corrections, but in a more restricted domain of applicability. We also comment on http://arxiv.org/abs/1601.05416 and some similarities and differences with this workComment: 13 pages, 1 figur

Social Security, Demographic Trends, and Economic Growth: Theory and Evidence from the International Experience

The worldwide problem with pay-as-you-go (PAYG) social security systems isn't just financial. This study indicates that these systems may have exerted adverse effects on key demographic factors, private savings, and long-term growth rates. Through a comprehensive endogenous-growth model where human capital is the engine of growth, family choices affect human capital formation, and family formation itself is a choice variable, we show that social security taxes and benefits can create adverse incentive effects on family formation and subsequent household choices, and that these effects cannot be fully neutralized by counteracting intergenerational transfers within families. We implement the model using calibrated simulations as well as panel data from 57 countries over 32 years (1960-92). We find that PAYG tax measures account for a sizeable part of the downward trends in family formation and fertility worldwide, and for a slowdown in the rates of savings and economic growth, especially in OECD countries.

The Evolution of Income and Fertility Inequalities over the Course of Economic Development: A Human Capital Perspective

Using an endogenous-growth, overlapping-generations framework where human capital is the engine of growth, we trace the dynamic evolution of income and fertility distributions and their interdependencies over three endogenous phases of economic development. In our model, heterogeneous families determine fertility and children’s human capital, and generations are linked via parental altruism and social interactions. We derive and test discriminating propositions concerning the dynamic behavior of inequalities in fertility, educational attainments, and three endogenous income inequality measures -- family-income inequality, income-group inequality, and the Gini coefficient. In this context, we also reexamine the "Kuznets hypothesis" concerning the relation between income growth and inequality.