C08025 - Seeking SICs: A Workshop on Quantum Frames and Designs - 2008This workshop is organized with the hope of making significant progress to the question: the question of the existance of minimal symmetric informationally-complete (SIC) sets of pure quantum states.
http://pirsa.org/podcast/C08025
Science2020http://blogs.law.harvard.edu/tech/rssen-caThu, 13 Aug 2020 23:37:31 -0400Thu, 13 Aug 2020 23:37:31 -0400G180help@perimeterinstitute.capirsa.org<![CDATA[Why I care]]>Chris Fuchs
http://streamer2.perimeterinstitute.ca/mp3/08100067.mp3
Sciencehttp://streamer2.perimeterinstitute.ca/mp3/08100067.mp3Sun, 26 Oct 2008 10:30:00 -0400<![CDATA[SIC Triple Products]]>Marcus Appleby
http://streamer2.perimeterinstitute.ca/mp3/08100068.mp3
Sciencehttp://streamer2.perimeterinstitute.ca/mp3/08100068.mp3Sun, 26 Oct 2008 11:30:00 -0400<![CDATA[Seeking Symmetries of SIC-POVMs]]>Markus Grassl
http://streamer2.perimeterinstitute.ca/mp3/08100069.mp3
Sciencehttp://streamer2.perimeterinstitute.ca/mp3/08100069.mp3Sun, 26 Oct 2008 14:00:00 -0400<![CDATA[Quantum state tomography from yes/no measurements]]>Martin Roetteler
http://streamer2.perimeterinstitute.ca/mp3/08100070.mp3
Sciencehttp://streamer2.perimeterinstitute.ca/mp3/08100070.mp3Mon, 27 Oct 2008 10:30:00 -0400<![CDATA[Unitary design: bounds on their size]]>Andrew Scott
http://streamer2.perimeterinstitute.ca/mp3/08100071.mp3
Sciencehttp://streamer2.perimeterinstitute.ca/mp3/08100071.mp3Mon, 27 Oct 2008 11:30:00 -0400<![CDATA[Culs-de-sac and open ends]]> possesses some Clifford-symmetry, the same is already true for both its even and its odd parity components |Psi_e>, |Psi_o>. What is more, these components have potentially a larger symmetry group than their sum. Indeed, this effect can be verified when looking at the known numerical solutions in d=5 and d=7. A finding of remarkably little consequence! 2. In composite dimensions d=p_1^r_1 ... p_k^r_k, all elements of the Clifford group factor with respect to some tensor decomposition C^d=C^(p_1^r_1) x ... x C^(p_k^r_k) of the underlying Hilbert space. This structure may potentially be used to simplify the constraints on fiducial vectors. My optimism is vindicated by the following, ground-breaking result: In even dimensions 2d not divisible by four, the Hilbert space is of the form C^2 x C^d. So it makes sense to ask for the Schmidt-coefficients of a fiducial vector with respect to that tensor product structure. They can be computed to be 1/2(1 +/- sqrt{3/(d+1)}), removing one (!) parameter from the problem and establishing that, asymptotically, fiducial vectors are maximally entangled. 3. Becoming slightly more esoteric, I could move on to talk about discrete Wigner functions and show in what sense finding elements of a set of MUBs corresponds to imposing that a certain matrix be positive, while a similar argument for fiducial vectors requires a related matrix to be unitary. Now, positivity has 'local' consequences: it implies constraints on small sub-matrices. Unitarity, on the other hand, seems to be more 'global' in that all algebraic consequences of unitarity involve 'many' matrix elements at the same time. This point of view suggests that SICs are harder to find than MUBs (in case anybody wondered). If we solve the problem by Wednesday, I'll talk about quantum expanders. ]]>David Gross
http://streamer2.perimeterinstitute.ca/mp3/08100075.mp3
Sciencehttp://streamer2.perimeterinstitute.ca/mp3/08100075.mp3Mon, 27 Oct 2008 14:00:00 -0400<![CDATA[MUBs and SICs]]>Ingemar Bengtsson
http://streamer2.perimeterinstitute.ca/mp3/08100073.mp3
Sciencehttp://streamer2.perimeterinstitute.ca/mp3/08100073.mp3Tue, 28 Oct 2008 10:30:00 -0400<![CDATA[SICs, Convex Cones, and Algebraic Sets]]>Howard Barnum
http://streamer2.perimeterinstitute.ca/mp3/08100074.mp3
Sciencehttp://streamer2.perimeterinstitute.ca/mp3/08100074.mp3Wed, 29 Oct 2008 10:30:00 -0400<![CDATA[MUBS in infinite dimensions: the problematic analogy between L2(R) and C^d]]>Robin Blume-Kohout
http://streamer2.perimeterinstitute.ca/mp3/08100072.mp3
Sciencehttp://streamer2.perimeterinstitute.ca/mp3/08100072.mp3Thu, 30 Oct 2008 10:30:00 -0400