D-functions and immanants of unitary matrices and submatrices

Motivated by recent results in multiphoton interferometry, we expand a result of Kostant on immanants of an arbitrary $m\times m$ unitary matrix $T\in$ su$(m)$ to the submatrices of $T$. Specifically, we show that immanants of principal submatrices of a unitary matrix $T$ are a sum $\sum_{t} D^{(\lambda)}_{tt}(\Omega)$ of the diagonal $D$-functions of group element $\Omega$, with $t$ determined {by} the choice of submatrix, and the irrep $(\lambda)$ determined by the immanant under consideration. We also provide evidence that this result extends to some submatrices that are not principal diagonal, and we discuss how this result can be extended to cases where $T$ carries an su$(m)$ representation that is different from the defining representation.Comment: 13 pages. Updated to published version. Comments welcom

The Politics and the Dharma of Conversion: Reflections from the Mahabharata

This reflection is in the context of trends of the last decade in India, in which some Hindu nationalists have resisted the proselytizing activities of Christian missionaries with tactics of intimidation and terror

Proposal for Quantum Simulation via All-Optically Generated Tensor Network States

We devise an all-optical scheme for the generation of entangled multimode photonic states encoded in temporal modes of light. The scheme employs a nonlinear down-conversion process in an optical loop to generate one- and higher-dimensional tensor network states of light. We illustrate the principle with the generation of two different classes of entangled tensor network states and report on a variational algorithm to simulate the ground-state physics of many-body systems. We demonstrate that state-of-the-art optical devices are capable of determining the ground-state properties of the spin-1/2 Heisenberg model. Finally, implementations of the scheme are demonstrated to be robust against realistic losses and mode mismatch.Comment: 6 pages main text plus 6 pages Supplementary Material and many figures. Updated to published version. Comments welcom