July 17, 2024

Thematic Program on Mathematics in Quantum Information
July-August, 2009

July 27-31, 2009
Workshop on Quantum Marginals and Density Matrices

Organizing Committee:
Matthias Christandl (LMU Munich)
Robert Erdahl (Queen's University)
Patrick Hayden (McGill University)
Mary Beth Ruskai (Tufts University)

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In order to have a workshop format with ample time for discussions, all talks will be invited, but suggestions for speakers are welcome. It is neither necessary nor desirable that all participants give a formal talk. All participants can submit a poster and every presenter of a poster will have an opportunity to give a 5 minute presentation to let people know who they are and what they are working on. These will take place early in the workshop before the reception or breaks.A few poster submissions may be selected, at the option of the organizers for 20 minute talks on recent developments.
Abstract Submission for Contributed Talk/Poster (closed- deadline to submit was June 28)


Reduced density matrices (RDM) of states of multi-partite systems play a fundamental role in both quantum chemistry and quantum information theory. The quantum marginal problem asks when a set of RDM's is consistent with the existence of a multi-partite state with certain properties. The special case in which the N-particle state is required to have permutational symmetry was extensively studied by quantum chemists in the 1960's and is known as N-representability.

In the last decade, new methods have been developed which use the two-electron RDM to study N-electron systems while circumventing the N-representability problem. More recently, two striking results were obtained on this long-standing question, the solution of the pure state problem for the one-particle RDM and a proof of the existence of computationally intractable model Hamiltonians (even with a quantum computer) for the two-particle RDM.

Quantum information theory has led to developments in different directions. There are some surprising connections with representations of the symmetric group and with spin coherent states. A different type of approximation for symmetric density matrices is treated by the so-called quantum di Finetti theorems. Recent developments involving density matrix renormalization methods for treating strongly correlated systems in spin chains will be treated, with emphasis on the practical implications.

Because Schubert calculus plays a key role some recent developments, Allen Knutson will give a "crash course" on this topic during the first two days. By bringing together quantum chemists, mathematicians and quantum information scientists, we hope to identify the new mathematical challenges in this area and the practical uses of recent theoretical developments.

Workshop Program:

Monday July 27
8:45 - 9:00 a.m. Welcome and Introduction
Fields Director Ed Bierstone and Workshop Organizers
9:00-10:00 a.m. Allen Knutson (University of California, San Diego)
Schubert Calculus short course
10:00-10:30 a.m. Coffee Break
10:30-11:15 a.m. Robert Erdahl (Queen's University)
Reduced density matrices, the lower bound method and the contracted Schroedinger equation
11:15-12:00 a.m. Paul W. Ayers (McMaster University)
Variational Reduced Density Matrix Theory: Successes and Failures
12:00-2:00 p.m. Lunch Break
2:00-3:00 p.m. Allen Knutson (University of California, San Diego)
Schubert Calc. short course
3:00-3:30 p.m. Tea Break
3:30-4:15 p.m. Stefano Pironio (University of Geneva)
Non-commutative polynomial optimization and the varianional RDM method
4:15-5:00 p.m. very short talks
5:00 - 6:00 p.m. Reception --Fields Institute
Tuesday July 28
9:00-10:00 a.m. Allen Knutson (University of California, San Diego)
Schubert Calc. short course
10:00-10:30 a.m. Coffee Break
10:30-11:15 a.m. Garnet Kin-Lic Chan (Cornell University)
The DMRG and Correlator Product States
11:15-12:00 noon Frank Verstraete (University of Vienna)
Density matrices in real-space renormalization group methods
12:00-2:00 p.m. Lunch Break
2:00-3:00 p.m. Allen Knutson (University of California, San Diego)
Schubert Calc. short course
3:00-3:30 p.m. Tea Break
3:30-4:30 p.m. Robert Koenig (Caltech) and Graeme Mitchison (University of Cambridge)
de Finetti theorems for quantum states
4:30-5:00 p.m. First Wrap Up
Wednesday July 29
9:00-9:40 a.m. Mary Beth Ruskai (Tufts University)
transition remarks
9:40-10:30 a.m. Renato Renner (ETH Zurich)
De Finetti and entropies
10:30-11:00 a.m. Coffee Break
11:00-12:00 noon Alexander Klyachko (Bilkent University)
Quantum marginal problem
  Free Afternoon
Thursday July 30
9:00-9:45 a.m. Matthias Christandl (Ludwig-Maximilians-Universität München)
Estimating the spectrum of an operator - a technique for the analysis of spectral relations via representation theory
9:45-10:30 a.m. Michael M. Wolf (Niels Bohr Institute)
Bell inequalities and joint measurability - relating classical and quantum marginal problems
10:30-11:00 a.m. Coffee Break
11:00-12:00 p.m. Alexander Klyachko (Bilkent University)
The Pauli exclusion principle and beyond
12:00-2:00 p.m. Lunch Break
2:00-2:45 p.m. Bastiaan Braams (Emory University)
The reduced density matrix method and some complexity issues
2:45 - 3:30 pm Yi-Kai Liu (California Institute of Technology)
N-representability is QMA-complete
3:30 - 4:00 p.m. Tea Break
4:00 - 4:25 Tzu-Chieh Wei (University of Waterloo)
Bosonic N-representability problem is also QMA-complete
4:25-4:50 p.m. Peter Love (Haverford College)
QMA-complete problems for stoquastic Hamiltonians and Markov matrices
4:50 - 5:15 p.m. discussion
Friday July 31
9:30 - 10:15 a.m. Aspuru-Guzik (Harvard University)
Quantum computer simulation for chemical dynamics and molecular electronic structure
10:15 - 11:00 a.m. Coffee Break
11:00 - 11: 45 a.m. Andreas Winter (University of Bristol)
A new inequality for the von Neumann entropy
11:45 - 12:15 wrap-up discussion
  Coleman dinner in Kingston


Confirmed Participants as of August 4, 2009

Full Name University/Affiliation
Acin, Antonio ICFO
Anderson, James McMaster University
Andrews, Rob (no affiliation)
Aspuru-Guzik, Alán Harvard University
Ayers, Paul McMaster University
Belinschi, Serban University of Saskatchewan
Beny, Cedric National University of Singapore
Berta, Mario Ludwig-Maximilians-Universität München
Boche, Holger Technical University Berlin
Braams, Bastiaan J. Emory University
Brooke, James University of Saskatchewan
Chan, Garnet Cornell University
Changlani, Hitesh Cornell University
Choi, Man-Duen University of Toronto
Christandl, Matthias Ludwig-Maximilians-Universität München
Collins, Benoît University of Ottawa
Cubitt, Toby University of Bristol
Cuevas-Saavedra, Rogelio McMaster University
Cui, Wei University of Toronto
Curty, Marcos University of Vigo
De Baerdemacker, Stijn University of Toronto
Dupuis, Frédéric University of Montreal
Erdahl, Robert Queen's University
Fan, Guangzhe University of Waterloo
Garcia-Saez, Artur ICFO - The Institute of Photonic Sciences
Gottlieb, Alexander Wolfgang Pauli Institute
Guenda, Kenza University of Algiers
Halevy, Itamar  
Hayden, Patrick McGill University
Helwig, Wolfram University of Toronto
Janssen, Gisbert Technische Universitaet Berlin
Ji, Zhengfeng Perimeter Institute
Johnson, Paul McMaster University
Klyachko, Alexander Bilkent University
Knutson, Allen University of California, San Diego
Koenig, Robert California Institute of Technology
Kulikov, Pavel McMaster University
Lim, Jacques Bunrith IRMAR
Liu, Yi-Kai California Institute of Technology
Love, Peter J. Haverford College
Lyons, David Lebanon Valley College
Matthews, William University of Waterloo
Menicucci, Nicolas Perimeter Institute for Theoretical Physics
Mitchison, Graeme Centre for Mathematical Sciences
Mosonyi, Milan Centre for Quantum Technologies, NUS
Movassagh, Ramis Massachusetts Institute of Technology
Myhr, Geir Ove University of Waterloo
Nakata, Maho RIKEN
Nechita, Ion Institut Camille Jordan, Université Claude Bernard Lyon 1
Noetzel, Janis Technische Universität Berlin
Orser, Brenda B.I.O. Letha Information Systems, Inc.
Piani, Marco University of Waterloo
Pironio, Stefano University of Geneva
Ralph, Claire Cornell University
Renner, Renato ETH Zürich
Rosgen, Bill University of Waterloo
Ruskai, Mary Beth Tufts University
Schuch, Norbert Max-Planck-Institute for Quantum Optics
van Aggelen, Helen Ghent University
Van Neck, Dimitri Ghent University
Verstraete, Frank University of Vienna
Walck, Scott Lebanon Valley College
Walgate, Jonathan Perimeter Institute
Wei, Tzu-Chieh University of Waterloo
Winter, Andreas University of Bristol
Wolf, Michael Copenhagen University
Zeier, Robert Technische Universitaet Muenchen


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