The life of quanta : entanglement wormholes and the second law
Name
898337263-MIT.pdf
Description
Full printable version
Size
9.08 MB
Format
Adobe PDF
Checksum (MD5)
d7d3790894b621dce7e15181a80ed6b7
Author(s)
Gharibyan, Hrant
Advisor(s)
Max Tegmark.
Date Issued
2014
Publisher
Massachusetts Institute of Technology
Abstract
This thesis explores two different topics in physics. The first is related to the study of the ER = EPR conjecture that relates the entanglement entropy of a collection of black holes to the cross sectional area of Einstein-Rosen (ER) bridges (or wormholes) connecting them. We show that the geometrical entropy of classical ER bridges satisfies the subadditivity, triangle, strong subadditivity, and CLW inequalities. These are nontrivial properties of entanglement entropy, so this is evidence for ER = EPR. We further show that the entanglement entropy associated to classical ER bridges has nonpositive tripartite information. This is not a property of entanglement entropy, in general. For example, the entangled four qubit pure state IGHZ4) = (I0000) + (I1111))/[square root]2 has positive tripartite information, so this state cannot be described by a classical ER bridge. Large black holes with massive amounts of entanglement between them can fail to have a classical ER bridge if they are built out of IGHZ4) states. States with nonpositive tripartite information are called monogamous. We conclude that classical ER bridges require monogamous EPR correlations. The second is a generalization of the second law of thermodynamics. We prove a generalization of the classic Groenewold-Lindblad entropy inequality, combining decoherence and the quantum Bayes theorem into a simple unified picture where decoherence increases entropy while observation decreases it. This provides a rigorous quantum-mechanical version of the second law of thermodynamics, governing how the entropy of a system evolves under general decoherence and observation. The powerful tool of spectral majorization enables both simple alternative proofs of the classic Lindblad and Holevo inequalities without using strong subadditivity, and also novel inequalities for decoherence and observation that hold not only for von Neumann entropy, but also for arbitrary concave entropies.
Description
Thesis: S.B., Massachusetts Institute of Technology, Department of Physics, 2014.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 105-111).
Subjects
Physics.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.
Persistent DSpace Link
