[quantum-info] PIQuDos Seminar next week: Gemma de las Cuevas
Markus Mueller
mmueller at perimeterinstitute.ca
Thu Feb 21 09:37:35 EST 2013
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
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