Universal state inversion and concurrence in arbitrary dimensions - art. no. 042315

Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula f or the entanglement of formation of two qubits in terms of what he calls th e concurrence of the joint density operator. Wootters's concurrence is defi ned with the help of the superoperator that flips the spin of a qubit. We g eneralize the spin-flip superoperator to a "universal inverter," which acts on quantum systems of arbitrary dimension, and we introduce the correspond ing generalized concurrence for joint pure states of D-1 X D-2 bipartite qu antum systems. We call this generalized concurrence the I concurrence to em phasize its relation to the universal inverter. The universal inverter, whi ch is a positive, but not completely positive superoperator, is closely rel ated to the completely positive universal-NOT superoperator, the quantum an alogue of a classical NOT gate. We present a physical realization of the un iversal-NOT Superoperator.