[quantum-info] Next week's PIQuDos
Markus Mueller
markus14m at gmail.com
Fri Mar 30 09:27:33 EDT 2012
Hi all,
next week, we have a talk by Yi-Kai Liu on Wednesday at 4pm in the Time
Room.
Best wishes,
Markus
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 4, 2012 - 4:00 pm
Series: Perimeter Institute Quantum Discussions
Location: Time Rm
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