[quantum-info] Today's PIQuDos

Markus Mueller mmueller at perimeterinstitute.ca
Mon Feb 25 09:39:44 EST 2013


Hi all,

this is a reminder of Gemma de las Cuevas' talk today at 4 pm in the 
Time Room.


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: Time Room (294)


Best,
Markus

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