[quantum-info] Today's PIQuDos

[Markus Mueller]

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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