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Experimental realization of the quantum universal NOT gate


In classical computation, a ‘bit’ of information can be flipped (that is, changed in value from zero to one and vice versa) using a logical NOT gate; but the quantum analogue of this process is much more complicated. A quantum bit (qubit) can exist simultaneously in a superposition of two logical states with complex amplitudes, and it is impossible1,2,3 to find a universal transformation that would flip the original superposed state into a perpendicular state for all values of the amplitudes. But although perfect flipping of a qubit prepared in an arbitrary state (a universal NOT operation) is prohibited by the rules of quantum mechanics, there exists an optimal approximation2 to this procedure. Here we report the experimental realization of a universal quantum machine4 that performs the best possible approximation to the universal NOT transformation. The system adopted was an optical parametric amplifier of entangled photon states, which also enabled us to investigate universal quantum cloning.

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Figure 1: The state space of a qubit is a Poincaré sphere.
Figure 2: Layout of the apparatus used for the experimental verification of the universality of the optical parametric amplifier (OPA).
Figure 3: Experimental verification of the universality of the OPA system for different field polarizations, either linear (Π), circular, or generally elliptical.
Figure 4: Experimental realization of the U-NOT gate. A single photon, N = 1, was injected with a definite π-state into the NL crystal of the OPA along the mode k1.
Figure 5: Experimental verification of the optimum conditions of the U-NOT gate.


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We thank M. Hillery, C. Simon, S. Popescu, M. D'Ariano for discussions, and V. Mussi, A. Mazzei, F. Bovino, S. Padua for early experimental collaboration. This work was supported by the FET European Networks ATESIT, EQUIP, QUBITS, MURST, and INFM.

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Correspondence to F. De Martini.

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De Martini, F., Bužek, V., Sciarrino, F. et al. Experimental realization of the quantum universal NOT gate. Nature 419, 815–818 (2002).

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