Dear all,
please join us on Monday at 4pm for a quantum information seminar by
Gemma de las Cuevas.
Title: Bounding the purification rank of mixed states
Speaker: Gemma de las Cuevas (Max Planck Institute of
Quantum Optics, Garching)
Abstract:
A mixed state can be expressed as a sum of D tensor product
matrices, where D is its operator Schmidt rank, or as the result of
a purification with a purifying state of Schmidt rank D', where D'
is its purification rank. The question whether D' can be upper
bounded by D is important theoretically (to establish a description
of mixed states with tensor networks), as well as numerically (as
the first decomposition is more efficient, but the second one
guarantees positive-semidefiniteness after truncation). Here we show
that no upper bounds of the purification rank that depend only on
operator Schmidt rank exist, but provide upper bounds that also
depend on the number of eigenvalues. In addition, we formulate the
approximation problem as a Semidefinite Program.
Joint work with N. Schuch, D. Perez-Garcia, and J. I. Cirac.
Date: Monday, Feb 25, 2013 - 4:00 pm
Location: TBA (probably Time Room)
Best,
Markus