Glockenpolytope mit nichttrivialen Symmetrien

Question

Glockenpolytope mit nichttrivialen Symmetrien

Physik
Quanteninformation
Glocken-ungleichung

Marcin Kotowski

Nehmen $N$ $N$ $N.$ Parteien, von denen jede eine Eingabe erhält $s_{i} \in 1, \dots, m_{i}$ $s_{i} \in 1, \dots, m_{i}$ $s_{i} \in 1, \dots, m_{i}$ $s_{i} \in 1, \dots, m_{i}$ $s_{i} \in 1, \dots, m_{i}$ $s_{i} \in 1, \dots, m_{i}$ $s_{i} \in 1, \dots, m_{i}$ $s_{i} \in 1, \dots, m_{i}$ $s_{ich} \in 1, \dots, m_{ich}$ und erzeugt eine Ausgabe $r_{i} \in 1, \dots, v_{i}$ $r_{i} \in 1, \dots, v_{i}$ $r_{i} \in 1, \dots, v_{i}$ $r_{i} \in 1, \dots, v_{i}$ $r_{i} \in 1, \dots, v_{i}$ $r_{i} \in 1, \dots, v_{i}$ $r_{i} \in 1, \dots, v_{i}$ $r_{i} \in 1, \dots, v_{i}$ $r_{ich} \in 1, \dots, v_{ich}$ möglicherweise auf nicht deterministische Weise. Wir sind an gemeinsamen bedingten Wahrscheinlichkeiten der Form interessiert $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N})$ $p (r_{1} r_{2} \dots r_{N.} | s_{1} s_{2} \dots s_{N.})$ . Das Glockenpolytop ist das Polytop, das von den Wahrscheinlichkeitsverteilungen der Form überspannt wird $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N} | s_{1} s_{2} \dots s_{N}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N}, r_{N, s_{N}}}$ $p (r_{1} r_{2} \dots r_{N.} | s_{1} s_{2} \dots s_{N.}) = δ_{r_{1}, r_{1, s_{1}}} \dots δ_{r_{N.}, r_{N., s_{N.}}}$ für alle möglichen Zahlenwahlen $r_{i, s_{i}}$ $r_{i, s_{i}}$ $r_{i, s_{i}}$ $r_{i, s_{i}}$ $r_{i, s_{i}}$ $r_{i, s_{i}}$ $r_{ich, s_{ich}}$ (Mit anderen Worten, jede Eingabe $s_{i}$ $s_{i}$ $s_{i}$ $s_{i}$ $s_{ich}$ erzeugt ein Ergebnis $r_{i, s_{i}}$ $r_{i, s_{i}}$ $r_{i, s_{i}}$ $r_{i, s_{i}}$ $r_{i, s_{i}}$ $r_{i, s_{i}}$ $r_{ich, s_{ich}}$ entweder mit einer Wahrscheinlichkeit von 0 oder 1, unabhängig von den Eingaben anderer Spieler). Polytope dieser Art sind in der Quanteninformationstheorie von Interesse.

Jedes Bell-Polytop weist eine bestimmte Anzahl trivialer Symmetrien auf, z. B. die Permutation von Parteien oder die Neukennzeichnung von Ein- oder Ausgängen. Ist es möglich, ein explizites Bell-Polytop mit nichttrivialen Symmetrien zu geben? (zB Transformationen des Polytops in sich selbst, die Gesichter zu Gesichtern nehmen und im obigen Sinne nicht trivial sind) Mit anderen Worten, ich bin interessiert, ob ein bestimmtes Bell-Szenario irgendwelche "versteckten" Symmetrien besitzen kann

Bell-Polytope in der Literatur sind normalerweise durch ihre Gesichter gekennzeichnet, die durch Mengen von Ungleichungen (Bell-Ungleichungen) gegeben sind, die jedoch normalerweise keine offensichtliche Symmetriegruppe aufweisen.

Frédéric Grosshans

Nur um zu sagen, dass die Frage seitdem auf der theoretischen Physik SE gestellt und beantwortet wurde: theoretische Physik.stackexchange.com/q/65/37

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Glockenpolytope mit nichttrivialen Symmetrien

Nur um zu sagen, dass die Frage seitdem auf der theoretischen Physik SE gestellt und beantwortet wurde: theoretische Physik.stackexchange.com/q/65/37

Glockenpolytope mit nichttrivialen Symmetrien

Marcin Kotowski

Frédéric Grosshans

Antworten (0)

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