Some upper and lower bounds on PSD-rank

Troy Lee; Zhaohui Wei; Ronald de Wolf

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arXiv · 1407.4308

Some upper and lower bounds on PSD-rank

Troy Lee·Zhaohui Wei·Ronald de Wolf

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Abstract

Positive semidefinite rank (PSD-rank) is a relatively new quantity with applications to combinatorial optimization and communication complexity. We first study several basic properties of PSD-rank, and then develop new techniques for showing lower bounds on the PSD-rank. All of these bounds are based on viewing a positive semidefinite factorization of a matrix $M$ as a quantum communication protocol. These lower bounds depend on the entries of the matrix and not only on its support (the zero/nonzero pattern), overcoming a limitation of some previous techniques. We compare these new lower bounds with known bounds, and give examples where the new ones are better. As an application we determine the PSD-rank of (approximations of) some common matrices.

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BibTeX RIS

Troy Lee, Zhaohui Wei, Ronald de Wolf. 2014-07-16. Some upper and lower bounds on PSD-rank. https://arxiv.org/abs/1407.4308

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