SLOCC transformations, tensor degeneration and Strassen's asymptotic rank conjecture

Joint seminar Department of Mathematics – BEC Bose-Einstein Condensation Trento 
 Q@TN Quantum Science and Technology in Trento - Centro Internazionale per la Ricerca Matematica

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Sala Seminari "-1"
Ore: 11:30

Relatore:

• Fulvio Gesmundo (QMATH University of Copenhagen)

Abstract:
SLOCC transformations of pure quantum states have a natural interpretation in the setting of projective geometry as tensor restriction under local operation. This problem has a long history in geometry, going back to at least the early 20th century, and finds several application in other fields, such as theoretical computer science and algebraic complexity theory. Following work by Bini and Schonage in the previous years, in the 80s Strassen developed a method (the so-called laser method) to study asymptotic tensor restriction which focuses on a geometric analog of the asymptotic SLOCC tranformation rate between quantum states; further, the laser method is responsible for the most recent upper bounds on the exponent of matrix multiplication. After explaining the method, I am going to present some recent work with Conner, Landsberg and Ventura, in which we investigate limits and generalizations of the laser method.

This seminar belongs to “Quantum Information, Geometry and Algebra Workgroup”
(https://me.unitn.it/alessandra-bernardi/research/quantum-information-alg...)

Referenti: Edoardo Ballico - Alessandra Bernardi - Iacopo Carusotto (BEC)