Geometry of Simulability: Λ-Polytopes, CNC Phase Spaces, and Quasiprobability Methods
Sanchit Srivastava
Classical simulation of quantum circuits is often formulated in terms of quasiprobability representations, where negativity signals genuinely nonclassical behavior. Recent work on closed noncontextual (CNC) phase spaces extends this perspective by enlarging the set of observables over which noncontextual value assignments are defined, yielding simulation frameworks that go beyond standard discrete Wigner positivity.
In this talk, I will present a geometric viewpoint on these developments based on Λ-polytopes: convex sets of trace-one Hermitian operators that assign nonnegative Born probabilities to all pure stabilizer-state projectors. I will discuss how CNC phase-space constructions can be understood as selecting structured regions within Λ-polytopes, and how quasiprobability simulation corresponds geometrically to staying within these regions. This perspective highlights a unifying picture: classical simulability is characterized by containment in specific noncontextual polytopes, while quantum resources emerge when operational statistics leave them.
Location
QNC 1201