caa a22 4500 445886595 CHVBK 20180317145601.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s11128-010-0207-9 doi (NATIONALLICENCE)springer-10.1007/s11128-010-0207-9 Operator-Schmidt decomposition and the geometrical edges of two-qubit gates [Elektronische Daten] [S. Balakrishnan, R. Sankaranarayanan] Nonlocal two-qubit quantum gates are represented by canonical decomposition or equivalently by operator-Schmidt decomposition. The former decomposition results in geometrical representation such that all the two-qubit gates form tetrahedron within which perfect entanglers form a polyhedron. On the other hand, it is known from the later decomposition that Schmidt number of nonlocal gates can be either 2 or 4. In this work, some aspects of later decomposition are investigated. It is shown that two gates differing by local operations possess same set of Schmidt coefficients. Employing geometrical method, it is established that Schmidt number 2 corresponds to controlled unitary gates. Further, all the edges of tetrahedron and polyhedron are characterized using Schmidt strength, a measure of operator entanglement. It is found that one edge of the tetrahedron possesses the maximum Schmidt strength, implying that all the gates in the edge are maximally entangled. Springer Science+Business Media, LLC, 2010 Two-qubit gates nationallicence Canonical decomposition nationallicence Operator Schmidt decomposition nationallicence Schmidt number nationallicence Schmidt strength nationallicence Balakrishnan S. Department of Physics, National Institute of Technology, 620015, Tiruchirappalli, India aut Sankaranarayanan R. Department of Physics, National Institute of Technology, 620015, Tiruchirappalli, India aut Quantum Information Processing Springer US; http://www.springer-ny.com 10/4(2011-08-01), 449-461 1570-0755 10:4<449 2011 10 11128 https://doi.org/10.1007/s11128-010-0207-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11128-010-0207-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Balakrishnan S. Department of Physics, National Institute of Technology, 620015, Tiruchirappalli, India aut NATIONALLICENCE 700 1- Sankaranarayanan R. Department of Physics, National Institute of Technology, 620015, Tiruchirappalli, India aut NATIONALLICENCE 773 0- Quantum Information Processing Springer US; http://www.springer-ny.com 10/4(2011-08-01), 449-461 1570-0755 10:4<449 2011 10 11128 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer