Related papers: Quantum geometry, logic and probability
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial…
A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of…
In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…
Quantum walks have been shown to have a wide range of applications, from artificial intelligence, to photosynthesis, and quantum transport. Quantum stochastic walks (QSWs) generalize this concept to additional non-unitary evolution. In this…
The building blocks of a quantum theory of general relativity are expected to be discrete structures. Loop quantum gravity is formulated using a basis of spin networks (wave functions over oriented graphs with coloured edges), thus…
Mott physics - the interplay between itinerancy and localization of electrons - is undergoing a paradigm shift from the binary "bandwidth - filling" tuning framework to an intertwining of geometric, topological, and fractionalized degrees…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…
Quantum walks are accepted as a generic model for quantum transport. The character of the transport crucially depends on the properties of the walk like its geometry and the driving coin. We demonstrate that increasing transport distance…
Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
Quantum mechanics is usually presented starting from a series of postulates about the mathematical framework. In this work we show that those same postulates can be derived by assuming that measurements are discrete interactions: that is,…
An outstanding challenge for models of non-perturbative quantum gravity is the consistent formulation and quantitative evaluation of physical phenomena in a regime where geometry and matter are strongly coupled. After developing appropriate…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
Categorical quantum mechanics exploits the dagger compact closed structure of finite dimensional Hilbert spaces, and uses the graphical calculus of string diagrams to facilitate reasoning about finite dimensional processes. A significant…
A new approach is suggested to quantum differential calculus on certain quantum varieties. It consists in replacing quantum de Rham complexes with differentials satisfying Leibniz rule by those which are in a sense close to Koszul complexes…
Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…
In the absence of a complete theory of quantum gravity, phenomenological models built upon minimal assumptions have been explored for the analysis of possible quantum effects in gravitational systems. Implications of a superposition of…
We present a quantum theory of distances along a curve, based on a linear line element that is equal to the operator square root of the quadratic metric of Riemannian geometry. Since the linear line element is an operator, we treat it…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
Recent studies have shown that the nonlinear optical response of crystalline systems is fundamentally a quantum geometric property. In this work, we propose two-dimensional coherent spectroscopy (2DCS), which measures the nonlinear…