Quantum correlations in composite systems under global unitary operations

TL;DR

This thesis investigates how quantum states exhibit non-classical properties and how these properties behave under global unitary operations, focusing on the distinction between absolute and non-absolute possession of such properties.

Contribution

It introduces the concept of absolute versus non-absolute properties of quantum states under unitary transformations and analyzes conditions for their preservation.

Findings

Properties can be possessed both in absolute and non-absolute ways.

Necessary and sufficient conditions for absolute possession of properties are identified.

Relations between different quantum properties under unitary operations are analyzed.

Abstract

The subject of this thesis are various properties of quantum states that make them "non-classical" and their behaviour under unitary operations. In chapter 2 some basic concepts of quantum mechanics and quantum information are reviewed. In chapter 3 properties of quantum states analysed in the literature are identified. I chapter 4 relations between them are analysed: whether possessing of one property by a given state implies possessing another property by the same state. In chapter 5 the central notion of the thesis is introduced, namely possessing a given property in absolute vs. non-absolute way. A property is possessed by a given state in an absolute way if it is preserved under arbitrary unitary operation on this state. This will be applied notion to all properties listed in chapter 3. Two main questions asked here are as follows: Can a given property be possessed both in an absolute way and in a non-absolute way (by different classes of states)? If yes, what are necessary and sufficient conditions for a state possessing a given property in an absolute way?