Indian Statistical Institute, Delhi Centre

About: Indian Statistical Institute, Delhi Centre is a based out in . It is known for research contribution in the topics: Matrix (mathematics) & Fock space. The organization has 93 authors who have published 161 publications receiving 2362 citations. The organization is also known as: ISI Delhi.

On the maximal dimension of a completely entangled subspace for finite level quantum systems

Abstract: LetH ibe a finite dimensional complex Hilbert space of dimensiond i associated with a finite level quantum system Ai for i = 1, 2, ...,k. A subspaceS ⊂ $${\mathcal{H}} = {\mathcal{H}}_{A_1 A_2 ...A_k } = {\mathcal{H}}_1 \otimes {\mathcal{H}}_2 \otimes \cdots \otimes {\mathcal{H}}_k $$ is said to becompletely entangled if it has no non-zero product vector of the formu 1⊗u 2 ⊗ ... ⊗u k with ui inH i for each i. Using the methods of elementary linear algebra and the intersection theorem for projective varieties in basic algebraic geometry we prove that $$\mathop {max}\limits_{S \in \varepsilon } dim S = d_1 d_2 ...d_k - (d_1 + \cdots + d_k ) + k - 1$$ where e is the collection of all completely entangled subspaces. When $${\mathcal{H}} = {\mathcal{H}}_2 $$ andk = 2 an explicit orthonormal basis of a maximal completely entangled subspace of $${\mathcal{H}}_1 \otimes {\mathcal{H}}_2 $$ is given. We also introduce a more delicate notion of aperfectly entangled subspace for a multipartite quantum system, construct an example using the theory of stabilizer quantum codes and pose a problem.

Dynamic equilibria with unemployment due to undernourishment

Abstract: We provide characterization and stability results for the stationary equilibria of a competitive infinite-horizon model that incorporates the nutritional requirements of physical labor. We find that for many aggregate land stocks, there is a large continuum of stationary equilibrium unemployment rates. Since unemployment can be seen to stem from inequality in the initial distribution of land ownership, we suggest that certain land reforms can reduce unemployment.