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SUMMARY:The NPA hierarchy does not always attain the commuting operator va
 lue
DTSTART:20260128T100000Z
DTEND:20260128T110000Z
DTSTAMP:20260508T030000Z
UID:indico-event-15734@indico.math.cnrs.fr
DESCRIPTION:Speakers: Denis Rochette (Inria Saclay)\n\nWe show that it is 
 undecidable to determine whether the commuting operator value of a nonloca
 l game is strictly greater than 1/2. As a corollary\, there is a boolean c
 onstraint system (BCS) nonlocal game for which the value of the Navascués
 \, Pironio\, and Acín (NPA) hierarchy does not attain the commuting opera
 tor value at any finite level. Our contribution involves establishing a co
 mputable mapping from Turing machines to BCS nonlocal games in which the h
 alting property of the machine is encoded as a decision problem for the co
 mmuting operator value of the game. Our techniques are algebraic and disti
 nct from those used to establish MIP*=RE. As a first step\, we construct a
  mapping from Turing machines to elements of the tensor product of free al
 gebras\, showing that deciding positivity of those elements is coRE-hard. 
 As a second step\, we extend this mapping to further realize these element
 s as game polynomials for BCS games.\n\nhttps://indico.math.cnrs.fr/event/
 15734/
LOCATION:salle de séminaire du 3eme (LPT)
URL:https://indico.math.cnrs.fr/event/15734/
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