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

Journal Article · Mon Dec 15 04:00:00 EST 2014 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2014.09.026· OSTI ID:22403492

Chen, Lin; Yu, Li

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.

• OSTI ID: 22403492
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Vol. 351; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MATHEMATICAL OPERATORS
PROCESSING
QUANTUM ENTANGLEMENT
QUBITS
TENSORS
UNITARITY