Related papers: Discretised Hilbert Space and Superdeterminism

Bell's theorem is often said to imply that quantum mechanics violates local causality, and that local causality cannot be restored with a hidden-variables theory. This however is only correct if the hidden-variables theory fulfils an…

The engineering and control of devices at the quantum-mechanical level--such as those consisting of small numbers of atoms and photons--is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests…

We develop a synthesis of Turing's paradigm of computation and von Neumann's quantum logic to serve as a model for quantum computation with recursion, such that potentially non-terminating computation can take place, as in a quantum Turing…

I explore the possibility that a quantum system S may be described completely by the combination of its standard quantum state $|\psi\rangle$ and a (hidden) quantum state $|\phi\rangle$ (that lives in the same Hilbert space), such that the…

The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…

Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…

Why does quantum theory need the complex numbers? With a view toward answering this question, this paper argues that the usual Hilbert-space formalism is a special case of the general method of Markovian embeddings. This paper then…

We show how combining a discrete symmetry with topological Hilbert space fragmentation can give rise to exponentially many topologically stable qubits protected by a single discrete symmetry. We illustrate this explicitly with the example…

In recent work, Benjamin Schumacher and Michael~D. Westmoreland investigate a version of quantum mechanics which they call "modal quantum theory" but which we prefer to call "discrete quantum theory". This theory is obtained by…

We constructed a Hilbert space representation of a contextual Kolmogorov model. This representation is based on two fundamental observables -- in the standard quantum model these are position and momentum observables. This representation…

We study algorithmic applications of a natural discretization for the hard-sphere model and the Widom-Rowlinson model in a region $\mathbb{V}\subset\mathbb{R}^d$. These models are used in statistical physics to describe mixtures of one or…

It has become common practice to model large spin ensembles as an effective pseudospin with total angular momentum J = N x j, where j is the spin per particle. Such approaches (at least implicitly) restrict the quantum state of the ensemble…

A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…

Franson showed that Aspect's experiment to test Bell's inequality did not rule out local realistic theories with delayed determinism. A class of local, deterministic discrete mathematical models with delayed determinism is described that…

Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…

It is widely accepted that the states of any quantum system are vectors in a Hilbert space. Not everyone agrees, however. The recent paper ``The unphysicality of Hilbert spaces'' by Carcassi, Calder\'on and Aidala is a thoughtful dissection…

The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR…

We propose a definition of determinism for a physical system that includes, besides the measurement device, the surrounding environment. This enlarged system is assumed to follow a predefined trajectory starting from some (unknown) initial…

An extension of the Born rule, the {\it quantum typicality rule}, has recently been proposed [B. Galvan: Found. Phys. 37, 1540-1562 (2007)]. Roughly speaking, this rule states that if the wave function of a particle is split into…

This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…