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The geometric phase can be used as a fruitful venue of investigation to infer features of the quantum systems. Its application can reach new theoretical frontiers and imply innovative and challenging experimental proposals. Herein, we take…
Geometric phases arise in a number of physical situations and often lead to systematic shifts in frequencies or phases measured in precision experiments. We describe, by working through some simple examples, a method to calculate geometric…
We consider the generic problem of suddenly changing the geometry of an integrable, one-dimensional many-body quantum system. We show how the physics of an initial quantum state released into a bigger system can be completely described…
Matchgates are a group of two-qubit gates associated with free fermions. They are classically simulatable if restricted to act between nearest neighbors on a one-dimensional chain, but become universal for quantum computation with…
The issue of whether some manifestations of gravitation in the quantum domain, are indicative or not of a non-geometrical aspect in gravitation is discussed. We examine some examples that have been considered in this context, providing a…
We propose a new class of unconventional geometric gates involving nonzero dynamic phases, and elucidate that geometric quantum computation can be implemented by using these gates. Comparing with the conventional geometric gate operation,…
The concept of quantum superposition is reconsidered and discussed from the viewpoint of Bohmian mechanics, the hydrodynamic formulation of quantum mechanics, in order to elucidate some physical consequences that go beyond the simple…
This thesis explores the application of differential geometric and general relativistic techniques to deepen our understanding of quantum mechanical systems. We focus on three systems, employing these mathematical frameworks to uncover…
Aspects of quantum mechanics on a ring are studied. Either one or two impenetrable barriers are inserted at nodal and non-nodal points to turn the ring into either one or two infinite square wells. In the process, the wave function of a…
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…
It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually studied in the context of Bell…
Superpositions of black holes can be described geometrically using a combined canonical formulation for space-time and quantum states. A previously introduced black-hole model that includes quantum fluctuations of metric components is shown…
Geometric and holonomic quantum computation utilizes intrinsic geometric properties of quantum-mechanical state spaces to realize quantum logic gates. Since both geometric phases and quantum holonomies are global quantities depending only…
We study the properties of the Newtonian gravitational potential in a spherical Universe for different topologies. For this, we use the non-Euclidean Newtonian theory developed in Vigneron [2022, Class. & Quantum Gravity, 39, 155006]…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…
The purpose of this article is to exploit the geometric structure of Quantum Mechanics and of statistical manifolds to study the qualitative effect that the quantum properties have in the statistical description of a system. We show that…
As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…