LIRa summer session: Joshua Sack

NOTE: This is a one-time event. No other LIRa summer sessions are planned.

Speaker: Joshua Sack (California State University Long Beach)

Date and Time: Thursday, July 13th 2023, 16:30-18:00

Venue: ILLC seminar room F1.15 in Science Park 107 and online

Title: Relating algebraic quantum logic structures

Abstract. Different quantum structures emphasize different aspects of a quantum system, making it easier for us to reason about those emphasized aspects. The original quantum logics are defined on orthomodular lattices, which generalize the orthocomplemented lattice structure of closed linear subspaces of a Hilbert space. These subspaces represent the testable properties of a quantum system and emphasize static properties of a quantum system. Quantales offer a dynamic perspective of a quantum system, and a quantale-module illustrates the effects of quantum actions and may serve as an algebraic semantics for dynamic quantum logics. A complemented quantale augments a quantale with an orthocomplementation-inducing unary operator. This talk discusses two complemented quantales that are each equivalent to complete orthomodular lattices and account for two basic classes of functions of quantum computation: projectors and unitary operators.