Related papers: Geometry from quantum temporal correlations
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…
We give a survey of our joint ongoing work with Ali Chamseddine, Slava Mukhanov and Walter van Suijlekom. We show how a problem purely motivated by "how geometry emerges from the quantum formalism" gives rise to a slightly noncommutative…
Interactions govern the flow of information and the formation of correlations in quantum systems, dictating the phases of matter found in nature and the forms of entanglement generated in the laboratory. Typical interactions decay with…
Assuming that Quantum Mechanics is universal and that it can be applied over all scales, then the Universe is allowed to be in a quantum superposition of states, where each of them can correspond to a different space-time geometry. How can…
Correlations between spacelike separated measurements on entangled quantum systems are stronger than any classical correlations and are at the heart of numerous quantum technologies. In practice, however, spacelike separation is often not…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
In non-relativistic physics, the concepts of geometry and topology are usually applied to characterize spatial structures or structures in momentum space. We introduce the concept of temporal geometry, which encompasses the geometric and…
The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However,…
Can the state-space of $d$-dimensional quantum theory be derived from studying the behavior of a single "reference" measuring device? The answer is yes, if the measuring device corresponds to a complex-projective 3-design. In this…
Weyl famously argued that if space were discrete, then Euclidean geometry could not hold even approximately. Since then, many philosophers have responded to this argument by advancing alternative accounts of discrete geometry that recover…
The absolute/relative debate on the nature of space and time is ongoing for thousands of years. Here we attempt to investigate space and time from the information theoretic point of view to understand spatial and temporal correlations under…
Geometric quantization is a natural way to construct quantum models starting from classical data. In this work, we start from a symplectic vector space with an inner product and -- using techniques of geometric quantization -- construct the…
Andreka and her colleagues have described various geometrically inspired first-order theories of special and general relativity, while Szekely's PhD dissertation focuses on an intermediate logic of accelerated observers. In this paper we…
Influence network of events is a view of the universe based on events that may be related to one another via influence. The network of events form a partially-ordered set which, when quantified consistently via a technique called chain…
The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by labelled compact two-dimensional…
This paper proposes a method of unifying quantum mechanics and gravity based on quantum computation. In this theory, fundamental processes are described in terms of pairwise interactions between quantum degrees of freedom. The geometry of…
The Weyl geometry promises potential applications in gravity and quantum mechanics. We study the relationships between the Weyl geometry, quantum entropy and quantum entanglement based on the Weyl geometry endowing the Euclidean metric. We…
With toy modelling of conceptual aspects of quantum cosmology and the problem of time in quantum gravity in mind, I study the classical and quantum dynamics of the pure-shape (i.e. scale-free) triangle formed by 3 particles in 2-d. I do so…
Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…
We show how the quantization of two-dimensional gravity leads to an (Euclidean) quantum space-time where the average geometry is that of constant negative curvature and where the Hartle-Hawking boundary condition arises naturally.