Max-Planck-Institut für Informatik
max planck institut
informatik
mpii logo Minerva of the Max Planck Society
 

MPI-INF or MPI-SWS or Local Campus Event Calendar

New for: D1
<< Previous Entry Next Entry >> New Event Entry Edit this Entry Login to DB (to update, delete)
What and Who
Title:On the tensor rank of graph tensors
Speaker:Jeroen Zuiddam
coming from:Centrum voor Wiskunde en Informatica, Amsterdam
Speakers Bio:
Event Type:AG1 Mittagsseminar (own work)
Visibility:D1
We use this to send out email in the morning.
Level:AG Audience
Language:English
Date, Time and Location
Date:Tuesday, 18 October 2016
Time:13:00
Duration:30 Minutes
Location:Saarbrücken
Building:E1 4
Room:024
Abstract
We prove upper bounds on the tensor rank of graph tensors. We present two methods. First, we introduce a surgery-like procedure to transform a good decomposition of a well-chosen tensor into a good decomposition of a tensor of interest. We illustrate the method with surgery on the cycle graph and obtain the first nontrivial rank results for large odd cycles and optimal asymptotic rank results for all cycles. Second, we generalize Strassen's laser method to higher-order tensors in order to show a nontrivial upper bound on the asymptotic rank for the complete graph. "Per edge" this improves on the best upper bound on the matrix multiplication exponent of Le Gall, for four or more vertices. In entanglement theory, our results amount to protocols for creating a network of entangled pairs from Greenberger-Horne-Zeilinger (GHZ) states by stochastic local operations and classical communication (SLOCC). In communication complexity theory, our results imply new bounds on the nondeterministic quantum communication complexity of equality games. Our work is inspired and tightly connected with the vast body of research on matrix multiplication.

This is joint work with Matthias Christandl (Copenhagen) and Péter Vrana (Budapest).

Contact
Name(s):Christian Ikenmeyer
Video Broadcast
Video Broadcast:NoTo Location:
Tags, Category, Keywords and additional notes
Note:
Attachments, File(s):

Created by:Christian Ikenmeyer, 10/17/2016 01:11 AMLast modified by:Uwe Brahm/MPII/DE, 11/24/2016 04:13 PM
  • Christian Ikenmeyer, 11/02/2016 03:30 PM
  • Christian Ikenmeyer, 10/17/2016 01:12 AM
  • Christian Ikenmeyer, 10/17/2016 01:11 AM -- Created document.