Elliptic Curve Cryptography and Quantum Computing
... transformed into today. While it was fascinating to look at all the various cryptosystems that have been created throughout time, one cryptosystem caught my eye in particular—Elliptic Curve Cryptography, commonly referred to as ECC. I had heard of a few cryptosystems but never the ECC. As such, my i ...
... transformed into today. While it was fascinating to look at all the various cryptosystems that have been created throughout time, one cryptosystem caught my eye in particular—Elliptic Curve Cryptography, commonly referred to as ECC. I had heard of a few cryptosystems but never the ECC. As such, my i ...
From quantum foundations to quantum information protocols and back PhD thesis
... (Classical) information theory In 1948 Claude Shannon published “A mathematical theory of communication’ [Sha48] founding information theory. Few articles can claim to be so influential and to have such big relevance in shaping our modern world. Boosted by the invention of the transistor, informatio ...
... (Classical) information theory In 1948 Claude Shannon published “A mathematical theory of communication’ [Sha48] founding information theory. Few articles can claim to be so influential and to have such big relevance in shaping our modern world. Boosted by the invention of the transistor, informatio ...
Abstract Experiments demonstrating entanglement swapping have
... summarizing our information about the system. While ascribing such a quantum state allows us to predict non-local correlations, this view stops short of recognizing a physical entanglement relation between the particles themselves (if there are such things). Second, consider a Bohmian who takes the ...
... summarizing our information about the system. While ascribing such a quantum state allows us to predict non-local correlations, this view stops short of recognizing a physical entanglement relation between the particles themselves (if there are such things). Second, consider a Bohmian who takes the ...
higher dimensional defects in cosmology tufts university
... gravity with quantum field theory. Our best candidate of quantum gravity, superstring theory, requires ten-dimensional space-time for mathematical consistency. However, since our world appears four-dimensional there must be a mechanism that “hides” extra dimensions so that we do not experience them ...
... gravity with quantum field theory. Our best candidate of quantum gravity, superstring theory, requires ten-dimensional space-time for mathematical consistency. However, since our world appears four-dimensional there must be a mechanism that “hides” extra dimensions so that we do not experience them ...
Renormalization
In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities.Renormalization specifies relationships between parameters in the theory when the parameters describing large distance scales differ from the parameters describing small distances. Physically, the pileup of contributions from an infinity of scales involved in a problem may then result in infinities. When describing space and time as a continuum, certain statistical and quantum mechanical constructions are ill defined. To define them, this continuum limit, the removal of the ""construction scaffolding"" of lattices at various scales, has to be taken carefully, as detailed below.Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory. Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics. Today, the point of view has shifted: on the basis of the breakthrough renormalization group insights of Kenneth Wilson, the focus is on variation of physical quantities across contiguous scales, while distant scales are related to each other through ""effective"" descriptions. All scales are linked in a broadly systematic way, and the actual physics pertinent to each is extracted with the suitable specific computational techniques appropriate for each.