Related papers: Quantum version of the Euler's problem: a geometri…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
Provided a complete set of putative $k$-body reductions of a multipartite quantum state, can one determine if a joint state exists? We derive necessary conditions for this to be true. In contrast to what is known as the quantum marginal…
In this note we present preliminary study on the relation between the quantum entanglement of boundary states and the quantum geometry in the bulk in the framework of spin networks. We conjecture that the emergence of space with non-zero…
This paper presents the quantum Moebius-Escher-Penrose hypergraph, drawing inspiration from paradoxical constructs such as the Moebius strip and Penrose's `impossible objects'. The hypergraph is constructed using faithful orthogonal…
In the Newtonian 3-body problem, for any choice of the three masses, there are exactly three Euler configurations (also known as the three Euler points). In Helmholtz' problem of 3 point vortices in the plane, there are at most three…
Quantum computing promises to solve difficult optimization problems in chemistry, physics and mathematics more efficiently than classical computers, but requires fault-tolerant quantum computers with millions of qubits. To overcome errors…
Quantum states are represented by positive semidefinite Hermitian operators with unit trace, known as density matrices. An important subset of quantum states is that of separable states, the complement of which is the subset of…
Despite rapid recent progress towards the development of quantum computers capable of providing computational advantages over classical computers, it seems likely that such computers will, initially at least, be required to run in a hybrid…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
A perfect Euler cuboid is a rectangular parallelepiped with integer edges and integer face diagonals whose space diagonal is also integer. Such cuboids are not yet discovered and their non-existence is also not proved. Perfect Euler cuboids…
Classical surfaces in phase space correspond to quantum states in Hilbert space. Subsystems specify factor spaces of the Hilbert space. An entangled state corresponds semiclassically to a surface that cannot be decomposed into a product of…
Using master equations we present an analytical solution of the time evolution of an entangled electron spin pair which can occupy 36 different quantum states in a double quantum dot nanostructure. This solution is exact given a few…
Modern quantum annealers can find high-quality solutions to combinatorial optimisation objectives given as quadratic unconstrained binary optimisation (QUBO) problems. Unfortunately, obtaining suitable QUBO forms in computer vision remains…
A perfect Euler cuboid is a rectangular parallelepiped with integer edges, with integer face diagonals, and with integer space diagonal as well. Finding such parallelepipeds or proving their non-existence is an old unsolved mathematical…
In gravitational theories with boundaries, diffeomorphisms can become physical and acquire a non-vanishing Noether charge. Using the covariant phase space formalism, on shell of the gravitational constraints, the latter localizes on…
The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a…
The mathematical structure of quantum entanglement is studied and classified from the point of view of quantum compound states. We show that t he classical-quantum correspondences such as encodings can be treated as dia gonal (d-)…
We consider multiple collisions of quantum wave packets in one dimension. The system under investigation consists of an impenetrable wall and of two hard-core particles with very different masses. The lighter particle bounces between the…
Machine learning techniques have achieved impressive results in recent years and the possibility of harnessing the power of quantum physics opens new promising avenues to speed up classical learning methods. Rather than viewing classical…
Two quantum Macro-states and their Macroscopic Quantum Superpositions (MQS) localized in two far apart, space - like separated sites can be non-locally correlated by any entangled couple of single-particles having interacted in the past.…