MSGSS
Generalized Quantum Conditional Statements
The notion of a conditional statement is very important in theoretical computer science. From an operational point of view, a conditional statement allows for a program to adjust its behaviour to the input data it has been provided. From a more mathematical point of view, each conditional statement can be understood as a direct sum of operations, where the right summand is what happens when the condition is not true and the left summand is what happens when the condition is true. This generalization is useful when studying the categorical semantics of classical reversible programs.
Whereas classical conditional statements are well understood, quantum conditional statements are still an open area of research. In fact, there are many mathematical generalizations of the quantum conditional statement which are not equivalent to each other. This suggests that we still do not understand the mathematical aspects that characterize quantum conditional statements. In this talk, we will introduce several generalizations of the quantum conditional statement and discuss how they are related. We will argue that quantum conditional statements are characterized by how their analytic properties relate to their algebraic and logical properties. This is in contrast to existing generalizations, which focus on only one such property in isolation.