Advisor(s)

Christopher King

Contributor(s)

Armen Stepanyants, Jonathan Weitsman, Ginestra Bianconi

Date of Award

2011

Date Accepted

12-2011

Degree Grantor

Northeastern University

Degree Level

Ph.D.

Degree Name

Doctor of Philosophy

Department or Academic Unit

College of Science, Departments of Physics and Mathematics

Keywords

quantum physics, additivity, average, energy, entropy, kinetic network, transfer

Subject Categories

Entropy, Force and energy

Disciplines

Mathematics | Physics

Abstract

Quantum channels are functions that map density matrices to density matrices. They can be used to describe a vast array of system environment interactions for quantum mechanical systems. The focus in quantum information theory lies on the study of the information content -- the quantum entropy -- of input and output system. The property of how much information a channel can convey is called capacity. When two quantum channels are combined they act on a bigger, possibly entangled state in parallel. The effects of entanglement on the capacity of a pair of channels have been widely studied. Still, recent work showed unexpected behavior. Hastings found that the capacities of two channels to transmit classical information does not simply add, but can exceed the sum of the individual quantum capacities, a property called superadditivity. We study Hastings' work and find estimates for how large the dimensions of such channels would have to be. The question of capacity relates to the behavior of quantum channels in extremal cases, when the output entropy is minimized. It is natural to wonder about the "standard" behavior of quantum channels and consider their average output entropy. We have studied this behavior in particular in cases where many relatively simple quantum channels act in parallel. When combining quantum channels in parallel, the parts of the system evolve independently of each other -- up to entanglement -- and only interact with the environment. Expanding on this idea one can think of a system where the parts not only interact with the environment but also directly with each other, a quantum channel network. Interesting cases of such systems arise naturally in the study of large biological molecules. In this case, information is often transmitted via energy pulses. Thus, the study of entropy and the study of energy overlap. Of particular interest to us are antennas in photo-active systems, they absorb light energy and transports it to a chemical reaction site. Recently, it has been discovered in the FMO molecule that this process evolves coherently, i.e. shows quantum oscillatory behavior. We study such quantum channel networks and how they can be approximated by kinetic networks. When considering the transport efficiency, this helps separating possible coherent effects from incoherent hopping.

Document Type

Dissertation

Rights Information

copyright 2011

Rights Holder

David K. Moser


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