Pranaw Rungta, V. Buzek, Carlton M. Caves, M. Hillery, G.J. Milburn
Universal State Inversion and Concurrence in Arbitrary Dimensions
The paper is published: Phys. Rev. A 64, 042315 (2001)

MSC:

81P05 General and philosophical

81P15 Quantum measurement theory

PACS: 03.67.Lx,03.65.Bz
Abstract: Wootters [Phys.\ Rev.\ Lett.\ {\bf 80}, 2245 (1998)] has given an
explicit formula for the entanglement of formation of two qubits
in terms of what he calls the {\it concurrence\/} of the joint
density operator. Wootters's concurrence is defined with the help
of the superoperator that flips the spin of a qubit. We
generalize the spin-flip superoperator to a ``universal
inverter,'' which acts on quantum systems of arbitrary dimension,
and we introduce the corresponding concurrence for joint pure
states of $D_1\times D_2$ bipartite quantum systems. The
universal inverter, which is a positive, but not completely
positive superoperator, is closely related to the completely
positive universal-NOT superoperator, the quantum analogue of a
classical NOT gate. We present a physical realization of the
universal-NOT superoperator.

Keywords: quantum information processing, quantum entanglement, CP maps