BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Entanglement of random quantum states: phase transitions - Stanisl
 aw Szarek\, Case Western Reserve University &amp\; Sorbonne Université
DTSTART:20250306T141500Z
DTEND:20250306T151500Z
UID:TALK229216@talks.cam.ac.uk
CONTACT:Laurens Lootens
DESCRIPTION:Consider a quantum system consisting of N identical particles 
 and assume that it is in a random pure state (i.e.\, uniformly distributed
  over the sphere of the corresponding Hilbert space) and two subsystems A 
 and B\, consisting of k particles each. Are A and B likely to share entang
 lement? For many natural properties\, of which "being entangled" is one ex
 ample\, there is a sharp "phase transition." In the current setting\, ther
 e is a threshold K (which is roughly N/5) such that A and B typically shar
 e entanglement if k > K\, and do not if k < K. We give precise statements 
 of results of the above type and hint on the arguments\, which involve ran
 dom matrices and various concepts/techniques from geometric functional ana
 lysis.
LOCATION:MR2
END:VEVENT
END:VCALENDAR