Related papers: Quantum polymorphism characterisation of commutati…
We carry out a generalization of quantum group co-representations in order to encode in this structure those cases where non-commutativity between endomorphism matrix entries and quantum space coordinates happens.
We prove a number of results concerning monomorphisms, epimorphisms, dominions and codominions in categories of coalgebras. Examples include: (a) representation-theoretic characterizations of monomorphisms in all of these categories that…
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…
Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of…
We introduce a multiparametric quantum superspace with $m$ even generators and $n$ odd generators whose commutation relations are in the sense of Manin such that the corresponding algebra has a Hopf superalgebra. By using its Hopf…
This thesis explores foundational aspects of quantum information theory and quantum cryptography. First, we investigate quantum correlations in interactive settings, including the CHSH and graph isomorphism games. We aim to distinguish…
Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here we study the compatibility of these two…
There are not many tools to quantitatively monitor the emergence of classical geometric features from a quantum spacetime, whose microscopic structure may be a highly quantum-fluctuating "spacetime foam". To improve this situation, we…
The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups…
We propose a scheme for scalable and robust quantum computing on two-dimensional arrays of qubits with fixed longitudinal coupling. This opens the possibility for bypassing the device complexity associated with tunable couplers required in…
Quantum theory departs from classical probabilistic theories in foundational ways. These departures--termed quantumness here--power quantum information and computation. This thesis charts the role of discrete structures in assessing…
Quantum computing offers fundamentally more expressive mechanisms for generative modeling, yet current approaches remain constrained by classical neural components that bottleneck quantum capability and hardware efficiency. We propose the…
Quantum groups and quantum homogeneous spaces - developed by several authors since the 80's - provide a large class of examples of algebras which for many reasons we interpret as `coordinate algebras' over noncommutative spaces. This…
This paper presents an elementary introduction to Consistent Quantum Theory (CQT), as developed by Griffiths and others over the past 25 years. The theory is a version of orthodox(Copenhagen) quantum mechanics, based on the notion that the…
The equivalence postulate approach to quantum mechanics entails a derivation of quantum mechanics from a fundamental geometrical principle. Underlying the formalism there exists a basic cocycle condition, which is invariant under…
For classical gravitational systems the lapse function and the shift vector are usually determined by imposing appropriate gauge fixing conditions and then demanding their preservation with respect to the dynamics generated by a canonical…
This paper develops the tools of formal algebraic geometry in the setting of noncommutative manifolds, roughly ringed spaces locally modeled on the free associative algebra. We define a notion of noncommutative coordinate system, which is a…
Classical-quantum computational complexity separations are an important motivation for the long-term development of digital quantum computers, but classical-quantum complexity equivalences are just as important in our present era of noisy…
A fully relational quantum theory necessarily requires an account of changes of quantum reference frames, where quantum reference frames are quantum systems relative to which other systems are described. By introducing a relational…
We analyze the effects of noncommutativity in conformal quantum mechanics (CQM) using the $\kappa$-deformed space-time as a prototype. Upto the first order in the deformation parameter, the symmetry structure of the CQM algebra is preserved…