Related papers: Logical aspects of quantum structures
Quantum logic gates provide fundamental examples of conditional quantum dynamics. They could form the building blocks of general quantum information processing systems which have recently been shown to have many interesting non--classical…
We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different…
The phenomenon of quantum entanglement is thoroughly investigated, focussing especially on geometrical aspects and on bipartite systems. After introducing the formalism and discussing general aspects, some of the most important separability…
We explore a wider theoretical framework that has quantum field theory built-in, taking the fact that quantum mechanics is reconstructed from quantum field theory as a hint. We formulate a quantum theory with an embedded structure by…
We propose a categorical and algebraic study of quantale modules. The results and constructions presented are also applied to abstract algebraic logic and to image processing tasks.
Some notes about quantum physics, an interpretation if one wishes, are put forward, insisting on `closely following the mathematics/formalism, the `nuts and bolts of what quantum physics says'. These, basically well-known, issues seem to…
In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic…
We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…
Although quantum circuits have been ubiquitous for decades in quantum computing, the first complete equational theory for quantum circuits has only recently been introduced. Completeness guarantees that any true equation on quantum circuits…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider…
The complexity of a quantum gate, defined as the minimal number of elementary gates to build it, is an important concept in quantum information and computation. It is shown recently that the complexity of quantum gates built from random…
Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate…
Conceptual consequences of recent results in loop quantum gravity are collected and discussed here in view of their implications for a modern philosophy of science which is mainly understood as one that totalizes scientific insight so as to…
Difficulties around the idea of spontaneous breaking of time translation symmetry in a closed quantum mechanical system are identified, and then overcome in a simple model. The possibility of ordering in imaginary time is also discussed.
In quantum mechanics and quantum information, to establish the orthogonal bases is a useful means. The existence of unextendible product bases impels us to study the `entanglement bases' problems. In this paper, the concepts of entanglement…
We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…
The extravagances of quantum mechanics never fail to enrich daily the debate around natural philosophy. Entanglement, non-locality, collapse, many worlds, many minds, and subjectivism have challenged generations of thinkers. Its approach…
Quantum computing is changing the way we think about computing. Significant strides in research and development for managing and harnessing the power of quantum systems has been made in recent years, demonstrating the potential for…
We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers.…
Recently a stochastic underpinning for space time has been considered, what may be called Quantized Fractal Space Time. This leads us to a number of very interesting consequences which are testable, and also provides a rationale for several…