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AIP conference proceedings

Geometrically controlled evolution of four-qubit states

Hoang Ngoc Duy, Hoshang Heydari, Andrei Yu. Khrennikov, Gregg S. Jaeger, M. Schlosshauer, Gregor Weihs

Published Jan 1, 2011• 0 citations
Publisher

Abstract

In this paper the evolution of some states of four qubits in [1] under global bipartite unitary operation and controlled by local unitary operation using four‐tangle [2] and the geometric invariants [3] is investigated. Particularly the entanglement distribution and properties of these four‐qubit states are studied.
DOI
10.1063/1.3578716

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The behavior of quantum states under local unitary transformations (LUTs) and stochastic local quantum operations and classical communication (SLOCC) has proven central to the understanding of entanglement in multipartite quantum systems. In particular, invariants under these operations have provided insight into quantum entanglement in multiple‐qubit states. Relationships between entanglement, mixedness and spin symmetry in multiple‐qubit quantum states can be found by exploiting these properties. For example, concurrence and n‐tangle are naturally expressed in terms of spin‐flip transformations. In the case of specialized entanglement measures and/or special families of states, complementarity relations involving these lengths and state transformations are derivable. Here, the role of geometry in such investigations is explored. Minkowskian geometry is seen to provide elegant representations of entanglement in multiple‐qubit systems, particularly the language of twistors.
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In this paper we will investigate the action of holonomic and topological quantum gates on different classes of four qubit states. In particular, we review the construction of holonomic quantum gate based on geometric phase and topological quantum gate based on braid group. Then, we investigate the entanglement properties of three different classes of four‐qubit states based on geometric invariants. The result shows that entanglement properties of the two most generic classes of four‐qubit states can be controlled by holonomic and topological quantum gate..