Abstract
dc:description.abstractBell's theory of nonlocality in quantum mechanics allows for interesting correlations between separated parties. In this scenario, both parties share a quantum state and measure it to obtain a classical value. Through entanglement, the results of the measurement from one party can affect the results of the other party's measurement. Quantum correlations reflect this idea as a probability distribution p(ab|xy) based on the measurements used (x for Alice and y for Bob) and the respective results obtained (a and b). In this thesis, we introduce an expression that limits what quantum states could be used to generate a given quantum correlation. This, in turn, yields a lower bound on the dimension needed for this quantum state. For a quantum correlation p(ab|xy), the dimension of the quantum state acts as a resource needed to generate it. Thus, having a bound on the dimension helps one to quantify the resources needed to generate a given correlation. In addition to quantum correlations, we adjust the bound to work with classical correlations as well, which are correlations generated using a shared probability distribution instead of a quantum state. We apply our quantum and classical bounds to well-studied correlations to test them based on known results and also generate randomly generated correlations to better understand their behavior. Finally, we report on our numerical findings.
Degree
thesis:*- Name thesis:degree_name
- Master of Science
- Level thesis:degree_level
- masters
- Discipline thesis:degree_discipline
- Computer Science and Applications
- Department dc:contributor.department
- Computer Science
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 2022
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Koenig, Jonathan A.
- Chair dc:contributor.committeechair
-
- Sikora, Jamie
- Committee members dc:contributor.committeemember
-
- Heath, Lenwood S.
- Barnes, Edwin Fleming
Subjects
dc:subject × 3Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
- Language dc:language.iso
- en
Identifiers
dc:identifier.*- Dc Identifier Other
- vt_gsexam:34610
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/110149