Related papers: Intuitionistic quantum logic of an n-level system

We provide ways to turn ancillas into phase gates (chapter 1), leading to irrational phase gates (chapter 2). We realize all the 2-qubit permutation gates (chapter 3).

Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…

A quantum circuit is a computational unit that transforms an input quantum state to an output one. A natural way to reason about its behavior is to compute explicitly the unitary matrix implemented by it. However, when the number of qubits…

Nonreflexive quantum mechanics is a formulation of quantum theory based on a non-classical logic termed \ita{nonreflexive logic} (a.k.a. `non-reflexive'). In these logics, the standard notion of identity, as encapsulated in classical logic…

A thought experiment is formulated to unify quantum mechanics and general relativity in a topological manner. An analysis of the interactions in Nature is then presented. The universal ground state of the constructed theory derives from the…

We propose a semantic foundation for logics for reasoning in settings that possess a distinction between equality of variables, a coarser equivalence of variables, and a notion of conditional independence between variables. We show that…

We introduce a logic modelling some aspects of the behaviour of the measurement process, in such a way that no direct mention of quantum states is made, thus avoiding the problems associated to this rather evasive notion. We then study some…

A collective system of atoms in a high quality cavity can be described by a nonlinear interaction which arises due to the Lamb shift of the energy levels due to the cavity vacuum [Agarwal et al., Phys. Rev. A 56, 2249 (1997)]. We show how…

This paper follows recent steps towards a nonassociative quantum theory and points out the mathematical structure behind the proposed modifications to conventional quantum theory. An N=1 supersymmetry model and a strong force glueball…

Contextuality is a key signature of quantum non-classicality, which has been shown to play a central role in enabling quantum advantage for a wide range of information-processing and computational tasks. We study the logic of contextuality…

This survey article is concerned with the modeling of the kinematical structure of quantum systems in an algebraic framework which eliminates certain conceptual and computational difficulties of the conventional approaches. Relying on the…

We construct a class of quantum field theories depending on the data of a holomorphic Poisson structure on a piece of the underlying spacetime. The main technical tool relies on a characterization of deformations and anomalies of such…

We propose a novel machine learning architecture that departs from conventional neural network paradigms by leveraging quantum spectral methods, specifically Pade approximants and the Lanczos algorithm, for interpretable signal analysis and…

In this paper, we deal with quantum theories on presheaves and sheaves on context categories consisting of commutative von Neumann algebras of bounded operators on a Hilbert space, from two viewpoints. One is to reduce presheaf-based topos…

Quantum mechanics challenges classical intuitions of space, time, and causality via the superposition principle, which allows systems to exist in multiple states simultaneously. Niels Bohr addressed these paradoxes through his…

We provide a systematic approach to quantum mechanics from an information-theoretic perspective using the language of tensor networks. Our formulation needs only a single kind of object, so-called positive *-tensors. Physical models…

The novel concept of quantum logical entropy is presented and analyzed. We prove several basic properties of this entropy with regard to density matrices. We hereby motivate a different approach for the assignment of quantum entropy to…

In a previous paper, we have proposed assigning as the value of a physical quantity in quantum theory, a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a…

Quantum mechanics emerged as the result of a successful resolution of stringent empirical and profound conceptual conflicts within the development of atomic physics at the beginning of the last century. At first glance, it seems to be…

Various topological concepts are often involved in the research of mathematical logic, and almost all of these concepts can be regarded as developing from the Stone representation theorem. In the Stone representation theorem, a Boolean…