R. de Wolf
- Some upper and lower bounds on PSD-rank
- Mathematical programming
- Volume | Issue number
- 162 | 1-2
- Pages (from-to)
- Document type
- Interfacultary Research Institutes
- Institute for Logic, Language and Computation (ILLC)
Positive semidefinite rank (PSD-rank) is a relatively new complexity measure on matrices, 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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