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arXiv · 1804.04204

A Subspace of Maximal Dimension with Bounded Schmidt Rank

Priyabrata Bag·Santanu Dey
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Abstract

We study Schmidt rank for a vector (i.e., a pure state) and Schmidt number for a mixed state which are entanglement measures. We show that if a subspace of a certain bipartite system contains no vector of Schmidt rank $\leqslant k$, then any state supported on that space has Schmidt number at least $k+1$. A construction of subspace of $\mathbb{C}^m \otimes \mathbb{C}^n$ of maximal dimension, which does not contain any vector of Schmidt rank less than $3$, is given here.

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Priyabrata Bag, Santanu Dey. 2018-04-11. A Subspace of Maximal Dimension with Bounded Schmidt Rank. https://arxiv.org/abs/1804.04204

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