Bell'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. / Master of Science / In quantum theory, the state of a quantum object, the simplest known as a qubit, can be manipulated from two or more different physical locations, even when they are not connected through any type of network. This is known as Bell's theory, and it allows for interesting behavior involving two or more separated locations that would not be possible otherwise. However, the minimum amount of resources needed for certain behaviors may be unknown. In this thesis, we present a lower bound on the quantum resources needed in such a scenario. We also apply it to the classical case and test our bounds on well-studied and randomized examples and report on our findings.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/110149 |
| Date | 23 May 2022 |
| Creators | Koenig, Jonathan A. |
| Contributors | Computer Science, Sikora, Jamie, Heath, Lenwood S., Barnes, Edwin Fleming |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
Page generated in 0.0018 seconds