Noisy Embezzlement of Entanglement and Applications to Entanglement Dilution

In this thesis we present the concept of embezzlement of entanglement, its properties, efficiency, possible generalizations and propose the linear programming characterization of this phenomenon. Then, we focus on the noisy setting of embezzlement of entanglement. We provide the detailed proof of the quantum correlated sampling lemma which can be considered a protocol for noisy embezzlement of entanglement. Next, we propose a classical synchronization scheme for two spatially separated parties which do not communicate and use shared randomness to synchronize their descriptions of a quantum state. The result, together with the canonical embezzlement of entanglement, improves the quantum correlated sampling lemma for small quantum states in terms of the probability of success and distance between desired and final states. Then, we discuss the role of entanglement spread in dilution of entanglement. We propose an explicit protocol for the task of dilution of entanglement without communication. The protocol uses EPR pairs and an embezzling state of a relatively small size for the task of diluting entangled quantum states up to small infidelity. We modify the protocol to work in a noisy setting where the classical synchronization scheme finds its application