|Ph.D Student||Kalev Amir|
|Subject||Local Hidden Variables Underpinning of Entanglement and|
|Department||Department of Physics||Supervisors||Professor Ady Mann|
|Professor Emeritus Michael Revzen|
|Full Thesis text|
In this dissertation we study various problems in quantum information theory and foundations of quantum mechanics. We are concerned mainly with the question: how crucial is the quantum reasoning in accounting for non trivial quantum effects such as teleportation.
We begin with investigating if and under what conditions may teleportation of continuous variables be accounted for via a local-hidden-variables theory. Our study allows us to expose the role of various quantum requirements. These are, e.g., the uncertainty relation among non-commuting operators, and the no-cloning theorem which forces the complete elimination of the teleported state at its initial port.
Next, we address the question: to what extent is the quantum-mechanical nature of the process relevant for
teleportation of a spin-1/2 state. When we try to describe the teleportation process following two
different mathematical routes, we find two different hidden-variables densities, which thus end up having a doubtful physical significance within the ``reality" that a hidden-variables model tries to restore.
We consider this result as indicating a conflict between quantum teleportation and local-hidden-variables models. We also show that this kind of conflict arises when considering successive measurements (one of which is selective projective) for a single spin-1/2 particle.
We continue by addressing another hallmark of quantum mechanics -- that quantum information cannot be cloned. We present a general proof for nonclonability of quantum information which applies to arbitrary density matrices. The proof relies on entropic considerations, and as such can also be linked directly to its classical counterpart, which applies to probabilistic distributions of statistical ensembles.
In the last part of the dissertation we derive equations of motion for the normal-order, the symmetric-order and the antinormal-order quantum characteristic functions, applicable for general Hamiltonian systems. We do this by utilizing the `characteristic form' of both quantum states and Hamiltonians.
The equations of motion we derive here are rather simple in form and in essence, and as such have a number of attractive features. As we shall see, our approach enables the descriptions of quantum and classical time evolutions in one unified language. It allows for a direct comparison between quantum and classical dynamics, providing insight into the relations between quantum and classical behavior,
while also revealing a smooth transition between quantum and classical time evolutions. In particular, the h—> 0 limit of the quantum equations of motion instantly recovers their classical counterpart.