Quantum entanglement - monogamy relations and applications. - Tran, Minh Cong. (2013)
Quantum entanglement is arguably at the heart of quantum information and quantum computation. Although the problem of identification of entanglement in pure states has been resolved, alternative criteria for the existence of entanglement are still interesting problems. In this project, such criteria are investigated using monogamy relations. First, a complete set of monogamy relations based on the positive-semidefiniteness of density operators is developed. Next, new monogamy relations as results of correlation complementarity are introduced. A criterion for the existence of entanglement in pure states that involves correlations between all the parties is conjectured. The proofs for systems of two and three qubits are also presented. Finally, implication of monogamy relations on the fidelity of Remote State Preparation is discussed.