[quantum-info] Today's PIQuDos
Markus Mueller
markus14m at gmail.com
Wed Apr 4 09:07:12 EDT 2012
A reminder of Yi-Kai Liu's talk at 4pm in the Time room at PI.
Title: *Universal Low-rank Matrix Recovery from Pauli Measurements*
Speaker: Yi-Kai Liu (National Institute of Standards and Technology)
Abstract:
We study the problem of reconstructing an unknown matrix M, of rank r
and dimension d, using O(rd poly log d) Pauli measurements. This has
applications to compressed sensing methods for quantum state tomography.
We give a solution to this problem based on the restricted isometry
property (RIP), which improves on previous results using dual
certificates. In particular, we show that almost all sets of O(rd log^6
d) Pauli measurements satisfy the rank-r RIP. This implies that M can be
recovered from a fixed ("universal") set of Pauli measurements, using
nuclear-norm minimization (e.g., the matrix Lasso), with nearly-optimal
bounds on the error. Our proof uses Dudley's inequality for Gaussian
processes, together with bounds on covering numbers obtained via entropy
duality.
Date: April 04, 2012 - 4:00 pm
Series: Perimeter Institute Quantum Discussions
Location: Time Rm
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