9 papers
Proof Identity and Categorical Models of BV
Matteo Acclavio, Lutz StraÃburger, Vladimir Zamdzhiev
BV-categories are a recent development that aims to give categorical semantics to proofs in the logic BV. However, due to the absence of a coherence theorem on one side and a well-…
On the Centre of Strong Graded Monads
Flavien Breuvart, Quan Long, Vladimir Zamdzhiev
We introduce the notion of 'centre' for pomonoid-graded strong monads which generalizes some previous work that describes the centre of (not graded) strong monads. We show that, wh…
Quantum Coherence Spaces Revisited: A von Neumann (Co)Algebraic Approach
Thea Li, Vladimir Zamdzhiev
We describe a categorical model of MALL (Multiplicative Additive Linear Logic) inspired by the Heisenberg-Schrödinger duality of finite-dimensional quantum theory. Proofs of formu…
A programming language combining quantum and classical control
Kinnari Dave, Louis Lemonnier, Romain Péchoux +1
The two main notions of control in quantum programming languages are often referred to as "quantum" control and "classical" control. With the latter, the control flow is based on c…
Central Submonads and Notions of Computation: Soundness, Completeness and Internal Languages
TItouan Carette, Louis Lemonnier, Vladimir Zamdzhiev
Monads in category theory are algebraic structures that can be used to model computational effects in programming languages. We show how the notion of "centre", and more generally…
IMALL with a Mixed-State Modality: A Logical Approach to Quantum Computation
Kinnari Dave, Alejandro DÃaz-Caro, Vladimir Zamdzhiev
We introduce a proof language for Intuitionistic Multiplicative Additive Linear Logic (IMALL), extended with a modality B to capture mixed-state quantum computation. The language s…