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Open Systems & Information Dynamics

Quantum Gate Entangler and Entangling Capacity of a General Multipartite Quantum System

Hoshang Heydari

Published Sep 1, 2008• 3 citations
Publisher

Abstract

We construct quantum gate entangler for general multipartite states based on the construction of complex projective varieties. We also discuss in detail the construction of quantum gate entangler for higher dimensional bipartite and multipartite quantum systems. Moreover, we construct and discuss entangling capacity of general multipartite quantum systems.

DOI
10.1142/s1230161208000171

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We construct quantum gate entangler for general multipartite states based on the construction of complex projective varieties. We also discuss in detail the construction of quantum gate entangler for higher dimensional bipartite and multipartite quantum systems. Moreover, we construct and discuss entangling capacity of general multipartite quantum systems.
In this paper, I will discuss the geometrical structures of multipartite quantum systems based on complex projective schemes. In particular, I will explicitly construct multi‐qubit states in terms of these schemes and also discuss separability and entanglement of bipartite and multipartite quantum states. These results give some geometrical insight to the fascinating quantum mechanical phenomena of entanglement which is fundamentally important and has many applications in the field of quantum computing.
In this paper, I will discuss the geometrical structures of multipartite quantum systems based on complex projective schemes. In particular, I will explicitly construct multi‐qubit states in terms of these schemes and also discuss separability and entanglement of bipartite and multipartite quantum states. These results give some geometrical insight to the fascinating quantum mechanical phenomena of entanglement which is fundamentally important and has many applications in the field of quantum computing.
Multipartite entanglement determines the strength and range of interactions in many-body quantum systems. Yet, it is hard to evaluate it, due to the complex structures of quantum states. Here, we introduce a generic method to quantify the k <= N-partite entanglement of an N-particle system, by maximizing an arbitrary bipartite entanglement measure within subsystems of size up to k. The resulting classification of multipartite states captures their experimental cost: creating a k-partite entangled state requires at least k-1 two-particle entangling gates. Further, we analytically calculate the newly defined k-partite entanglement of formation, which generalizes an important bipartite entanglement measure, in several classes of states, including the W states of any dimension.