Institute for Mathematical Physics Universal State Inversion and Concurrence in Arbitrary Dimensions Universal State Inversion and Concurrence in Arbitrary Dimensions

Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the con-currence 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 × 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.