Sponsor
S.C. was supported in part by the National Science Foundation through Grant No. PHY-1205931. L. Yu was supported by the National Research Foundation and Ministry of Education in Singapore. en_US dc.format.extent 5 pages
Published In
Physical Review A: Atomic, Molecular & Optical Physics
Document Type
Article
Publication Date
2-1-2013
Subjects
Linear algebra, Schmidt coefficients, Schmidt rank
Abstract
We prove that every unitary acting on any multipartite system and having operator Schmidt rank equal to 2 can be diagonalized by local unitaries. This then implies that every such multipartite unitary is locally equivalent to a controlled unitary with every party but one controlling a set of unitaries on the last party. We also prove that any bipartite unitary of Schmidt rank 2 is locally equivalent to a controlled unitary where either party can be chosen as the control, and at least one party can control with two terms, which implies that each such unitary can be implemented using local operations and classical communication (LOCC) and a maximally entangled state on two qubits. These results hold regardless of the dimensions of the systems on which the unitary acts.
DOI
10.1103/PhysRevA.87.022329
Persistent Identifier
http://archives.pdx.edu/ds/psu/9276
Citation Details
Cohen, S. M., & Li, Y. (2013). All unitaries having operator Schmidt rank 2 are controlled unitaries. Physical Review A: Atomic, Molecular & Optical Physics, 87(2-A), 022329-1-022329-6.
Description
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