Entanglement, Matrix Multiplication and Group Representations

Matthias Christandl - Institute for Theoretical Physics, ETH Z├╝rich

Feb. 22, 2013, 1 p.m. - Feb. 22, 2013, 2 p.m.


In quantum information theory, strong correlations between quantum particles, known as entanglement, are responsible for the security of quantum cryptography and the speed-up in quantum computation. But how can we find out whether a state of two particles is entangled? Answering this question has kept the field of quantum information theory busy since its beginning. After an introduction to the subject, I will present the currently fastest algorithm for solving this question (Brandao, Christandl & Yard, STOC'11). I will then explain the surprising connection between the matrix multiplication problem and entanglement. This connection motivated us to employ quantum information tools (based on group representations) in algebraic complexity theory and led to a contribution to Mulmuley and Sohoni's effort in solving Valiant's P vs NP problem (Christandl, Doran & Walter, FOCS'12). Matthias Christandl is assistant professor at the Institute for Theoretical Physics at the ETH Zurich. He is an expert on quantum information theory and known for his contributions to entanglement theory and quantum cryptography. Matthias received his diploma in physics from the ETH Zurich in 2002. In 2006 he completed his PhD, which was supervised by Artur Ekert at the University of Cambridge. He then took up the post as Thomas Nevile Research Fellow at Magdalene College, Cambridge. In 2008, he became Juniorprofessor at the LMU Munich, before returning to the ETH Zurich in 2010 in his current position. Matthias has been awarded the Cambridge University Hamilton prize and a prize of the German Physical Society. Serving the need of the growing community of quantum cryptographers, he co-founded QCRYPT, a series of conferences on this topic and presided over its first edition in Zurich in 2011.