Related papers: Game Semantics for Higher-Order Unitary Quantum Co…
A working definition of the term \quantum game" is developed in an attempt to gain insights into aspects of quantum mechanics via game theory.
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…
We present a general method which expresses a unitary operator by the product of operators allowed by the Hamiltonian of spin-1/2 systems. In this method, the generator of an operator is found first, and then the generator is expanded by…
The characterization of second-order type isomorphisms is a purely syntactical problem that we propose to study under the enlightenment of game semantics. We study this question in the case of second-order λ$\mu$-calculus, which can be…
We continue the analysis of quantum-like description of markets and economics. The approach has roots in the recently developed quantum game theory and quantum computing. The present paper is devoted to quantum English auction which are a…
An interaction system has a finite set of agents that interact pairwise, depending on the current state of the system. Symmetric decomposition of the matrix of interaction coefficients yields the representation of states by self-adjoint…
In this paper, we establish structural analogies between core concepts in quantum mechanics and games. By constructing the Quantum Coin Toss on a quantum circuit, we preliminarily investigate the similarity between quantum system behavior…
This paper investigates first-order game logic and first-order modal mu-calculus, which extend their propositional modal logic counterparts with first-order modalities of interpreted effects such as variable assignments. Unlike in the…
The goal of this article is to emphasize the role of cubical sets in enriched categories theory and infinity-categories theory. We show in particular that categories enriched in cubical sets provide a convenient way to describe many…
Usually models for quantum computations deal with unitary gates on pure states. In this paper we generalize the usual model. We consider a model of quantum computations in which the state is an operator of density matrix and the gates are…
Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…
We provide a generalization of the idea of unitary designs to cover finite averaging over much more general operations on quantum states. Namely, we construct finite averaging sets for averaging quantum states over arbitrary reductive Lie…
This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also to physicists, computer scientists, and…
Game semantics has provided adequate models for a variety of programming languages, in which types are interpreted as two-player games and programs as strategies. Melli\`es (2018) suggested that such categories of games and strategies may…
We refine HO/N game semantics with an additional notion of pointer (mu-pointers) and extend it to first-order classical logic with completeness results. We use a Church style extension of Parigot's lambda-mu-calculus to represent proofs of…
We discuss how mathematical semantics has evolved, and suggest some new directions for future work. As an example, we discuss some recent work on encapsulating model comparison games as comonads, in the context of finite model theory.
Group representations play a central role in theoretical physics. In particular, in quantum mechanics unitary --- or, in general, projective unitary --- representations implement the action of an abstract symmetry group on physical states…
One of the open challenges in quantum computing simulations of problems of chemical interest is the proper enforcement of spin symmetry. Efficient quantum circuits implementing unitaries generated by spin-adapted operators remain elusive,…
A quantum game can be viewed as a state preparation in which the final output state results from the competing preferences of the players over the set of possible output states that can be produced. It is therefore possible to view state…
In this work we propose a quantum version of a generalized Monty Hall game, that is, one in which the parameters of the game are left free, and not fixed on its regular values. The developed quantum scheme is then used to study the expected…