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Title: On the Schmidt-rank-three bipartite and multipartite unitary operator

Unitary operations are physically implementable. We further the understanding of such operators by studying the possible forms of nonlocal unitary operators, which are bipartite or multipartite unitary operators that are not tensor product operators. They are of broad relevance in quantum information processing. We prove that any nonlocal unitary operator of Schmidt rank three on a d{sub A}×d{sub B} bipartite system is locally equivalent to a controlled unitary. This operator can be locally implemented assisted by a maximally entangled state of Schmidt rank min(d{sub A}{sup 2},d{sub B}) when d{sub A}≤d{sub B}. We further show that any multipartite unitary operator U of Schmidt rank three can be controlled by one system or collectively controlled by two systems, regardless of the number of systems of U. In the scenario of n-qubit, we construct non-controlled U for any odd n≥5, and prove that U is a controlled unitary for any even n≥4.
Authors:
;
Publication Date:
OSTI Identifier:
22403492
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 351; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; MATHEMATICAL OPERATORS; PROCESSING; QUANTUM ENTANGLEMENT; QUBITS; TENSORS; UNITARITY