Universal low-rank matrix recovery from Pauli measurements

@inproceedings{Liu2011UniversalLM,
  title={Universal low-rank matrix recovery from Pauli measurements},
  author={Yi-Kai Liu},
  booktitle={NIPS},
  year={2011}
}
We study the problem of reconstructing an unknown matrix M of rank r and dimension d using O(rdpoly log d) Pauli measurements. This has applications in quantum state tomography, and is a non-commutative analogue of a well-known problem in compressed sensing: recovering a sparse vector from a few of its Fourier coefficients. We show that almost all sets of O(rd log d) Pauli measurements satisfy the rankr restricted isometry property (RIP). This implies that M can be recovered from a fixed… CONTINUE READING
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Universal low-rank matrix recovery from Pauli measurements

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