Entanglement Measures and Monogamy

TL;DR

This dissertation provides a comprehensive introduction to entanglement measures, focusing on their properties, propositions, and the concept of monogamy, including original insights into the monogamous nature of specific measures.

Contribution

It offers detailed proofs and comparisons of entanglement measures and introduces new observations on the monogamy properties of entanglement of formation.

Findings

Entanglement of formation is monogamous.

Regularised entropy of entanglement is monogamous.

Comparison of different monogamous entanglement measures.

Abstract

This dissertation will serve as an introduction to entanglement quantification, containing highly detailed proofs ensuring solid understanding of the subject. Specifically, we will review the properties of entanglement that should be satisfied by a "good" entanglement measure. Then we will have a look at some of the propositions of the entanglement measures that have been made over the years. We will review in greater detail the entanglement of formation. We will discuss the proposals of the mathematical representations of another property of entanglement, called monogamy. We will introduce some definitions of monogamous entanglement measures that were proposed and compare them. As an original observation of mine (page 28), I will also show that "Should Entanglement Measures be Monogamous or Faithful?" (arXiv:1604.02189) has already developed most of what is necessary to prove that the entanglement of formation and the regularised entropy of entanglement are monogamous entanglement measures in the sense of the definition that was given in "Monogamy of entanglement without inequalities" (arXiv:1710.03295).