Schmidt Strength of the Geometrical Edges of Two-Qubit Gates
S. Balakrishnan, R. Sankaranarayanan, Dipankar Home, Guruprasad Kar, Archan S. Majumda · AIP conference proceedings · 2011
Nonlocal two‐qubit 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, all the edges of tetrahedron are characterized using Schmidt strength, a measure of operator entanglement. It is found that one edge of the tetrahedron, which includes SWAP and Double‐CNOT, possesses the maximum Schmidt strength. It implies that all the gates in the edge are maximally entangled.