Related papers: Stabilizer notation for Spekkens' toy theory
A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…
We establish a link between stabilizer states, stabilizer rank, and higher-order Fourier analysis -- a still-developing area of mathematics that grew out of Gowers's celebrated Fourier-analytic proof of Szemer\'edi's theorem…
We show that the operational definition of contextuality introduced by Spekkens is, in general, not Lorentz invariant. Specifically, we consider an explicit example with particle states consisting of both spin and momentum, we apply a…
This work is concerned with multi-party stabilizer states in the sense of quantum information theory. We investigate the homological invariants for states of which each party holds a large equal number N of quantum bits. We show that in…
I describe a toy model of quantum measurement in which wave function collapse is described as a stochastic entropically-driven event guided by interactions between a measured two-state particle and an Ising-like measurement device. The…
A theory of quantum measurement was introduced some time ago that was based on the notion of the so-called separation status. This separation status had a spatial, local character, so that the theory worked only in special cases.…
We present a toy model approach to the canonical non-perturbative quantization of the spatially-flat Robertson-Walker Universes with cosmological constant, based on the fact that such models are exactly solvable within the framework of a…
We study a two-state quantum system with a non linearity intended to describe interactions with a complex environment, arising through a non local coupling term. We study the stability of particular solutions, obtained as constrained…
The Kochen-Specker theorem asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on all operators, and which…
These lecture notes attempt a mathematical treatment of game theory akin to mathematical physics. A game instance is defined as a sequence of states of an underlying system. This viewpoint unifies classical mathematical models for 2-person…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…
Feedback asymptotic stabilization of control systems is an important topic of control theory and applications. Broadly speaking, if the system $\dot{x} = f(x,u)$ is locally asymptotically stabilizable, then there exists a feedback control…
Theory of quantum measurements is often classified as decision theory. An event in decision theory corresponds to the measurement of an observable. This analogy looks clear for operationally testable simple events. However, the situation is…
A popular three-dimensional reduction of the Bethe-Salpeter formalism for the description of bound states in quantum field theory is the Salpeter equation, derived by assuming both instantaneous interactions and free propagation of all…
A simple and general formulation of the quantum game theory is presented, accommodating all possible strategies in the Hilbert space for the first time. The theory is solvable for the two strategy quantum game, which is shown to be…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…
Contextuality, a generalization of non-locality, has been proposed as the resource that provides the computational speed-up for quantum computation. For universal quantum computation using qudits, of odd-prime dimension, contextuality has…
This article presents the basis of a theory of entanglement. We begin with a classical theory of entangled discrete measures in Section~1. Section~2 treats quantum mechanics and discusses the statistics of bounded operators on a Hilbert…
We introduce a new notion of "regularity structure" that provides an algebraic framework allowing to describe functions and / or distributions via a kind of "jet" or local Taylor expansion around each point. The main novel idea is to…
Another stabilizer term is used in the classical Hamiltonian of the Skyrme Model that permits in a much simple way the generalization of the higher-order terms in the pion derivative field. Improved numerical results are obtained.