Universal state inversion and concurrence in arbitrary dimensions

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Authors	RUNGTA P. BŮŽEK Vladimír CAVES C.M. HILLERY M. MILBURN G.J.
Year of publication	2001
Type	Article in Periodical
Magazine / Source	Physical Review A
MU Faculty or unit	Faculty of Informatics
Citation
Field	Informatics
Keywords	QUANTUM ERROR-CORRECTION ENTANGLEMENT OPERATIONS QUBITS GATE
Description	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 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 generalized concurrence for joint pure states of D-1 X D-2 bipartite quantum systems. We call this generalized concurrence the I concurrence to emphasize its relation to the universal inverter. 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.
Related projects:	Informatics as the third methodology Non-sequential Models of Computing -- Quantum and Concurrent Distributed Models of Computing