Ferro, Leonardo
(2014)
Observables and States, Reduction, Quantumness and Classicality.
[Tesi di dottorato]
| Tipologia del documento: |
Tesi di dottorato
|
| Lingua: |
English |
| Titolo: |
Observables and States, Reduction, Quantumness and Classicality. |
| Autori: |
| Autore | Email |
|---|
| Ferro, Leonardo | lferro@na.infn.it |
|
| Data: |
30 Marzo 2014 |
| Numero di pagine: |
112 |
| Istituzione: |
Università degli Studi di Napoli Federico II |
| Dipartimento: |
Fisica |
| Scuola di dottorato: |
Scienze fisiche |
| Dottorato: |
Fisica fondamentale ed applicata |
| Ciclo di dottorato: |
26 |
| Coordinatore del Corso di dottorato: |
| nome | email |
|---|
| Velotta, Raffaele | rvelotta@unina.it |
|
| Tutor: |
| nome | email |
|---|
| Marmo, Giuseppe | [non definito] |
|
| Data: |
30 Marzo 2014 |
| Numero di pagine: |
112 |
| Parole chiave: |
Reduction Quantumness Classicality |
| Settori scientifico-disciplinari del MIUR: |
Area 02 - Scienze fisiche > FIS/02 - Fisica teorica, modelli e metodi matematici |
[error in script]
[error in script]
| Depositato il: |
08 Apr 2014 10:14 |
| Ultima modifica: |
27 Gen 2015 13:30 |
| URI: |
http://www.fedoa.unina.it/id/eprint/9834 |
Abstract
The main objective of this dissertation is the study of the theory of Lie-Jordan Banach algebras, their role in the framework of classical and quantum mechanics, and their applications to different aspects of quantum systems.
One of the main results of this thesis is the novel proof of a theorem which characterizes the Jordan (-Banach) algebras that are in a unique correspondence with C*-algebras. The novelty lies in the introduction of a Lie structure on the algebra, which is required to be compatible with the Jordan one. The physical interpretation of this connection with the Lie structure reflects the dual role played by the observables: they are measurable quantities but also the generators of motions of the state space.
Whenever constraints are imposed on a quantum system or symmetries are present, both dynamical or gauge, some reduction on the state space must be considered either because not all states are physical and/or because families of states are equivalent. We address this problem in algebraic terms and obtain a reduction procedure which is free from the problems of gauge anomalies which is often encountered in a heuristic approach to the quantization of constraints.
Then we study the composition of physical systems and we prove, from algebraic considerations only, the uniqueness of the Planck's constant. This is a strong result, since he existence of multiple Planck's constants would lead to violations of basic space-time conservation laws, which are not observed experimentally.
Finally we address the problem of characterizing classical and quantum states, which has become particularly relevant for the field of quantum information and quantum computation, since a number of tasks in computation and communication can be performed only if quantum resources are available. By using the Jordan product we are able to provide a general definition of classical states and the associated quantumness witness which is suitable to infinite-dimensional systems. Then we propose a measure of nonclassicality based on the incompatibility of states relative to each other, rather than on correlations. Surprisingly, this new measure turns out to be experimentally suitable to a direct estimation by using a
quantun circuit based on an interference experiment. We finally describe this experiment which is realizable with current technology.
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