A Functorial Construction of Quantum Subtheories

Abstract

We apply the geometric quantization procedure via symplectic groupoids to the setting of epistemically-restricted toy theories formalized by Spekkens (Spekkens, 2016). In the continuous degrees of freedom, this produces the algebraic structure of quadrature quantum subtheories. In the odd-prime finite degrees of freedom, we obtain a functor from the Frobenius algebra of the toy theories to the Frobenius algebra of stabilizer quantum mechanics.

Keywords

• categorical quantum mechanics
• geometric quantization
• epistemically-restricted theories
• Frobenius algebras