Optimal Quantum Cloning on a Beam Splitter

We demonstrate how a beam splitter in combination with different light sources can be used as an optimal universal $1\to 2$ quantum cloner and as an optimal universal quantum NOT machine for the polarization qubit of a single photon. For the cloning a source of single photons with maximally mixed polarization is required and for the NOT operation a source of maximally entangled photon pairs. We demonstrate both operations with near optimal fidelity. Our scheme can be generalized in a natural way to clone and NOT the spin state of electrons.

Figure 1

Apparatus used to demonstrate optimal universal quantum cloning and the optimal universal quantum NOT gate on a beam splitter. A central role is played by the beam splitter with input modes $a$ and $c$ and output modes $d$ and $e$. One photon of a polarization-entangled photon pair created by pulsed type-II parametric down-conversion inside a 2 mm thick $\beta$-BBO crystal enters the beam splitter in mode $a$. The photon to be cloned enters in mode $c$.

Figure 2

Experimental data demonstrating cloning on a beam splitter. $N_d(2,0)$ increases as the photon wave packets overlap, while $N_d(1,1)$ remains the same. The data on the left are fitted to a Gaussian and the fidelity, displayed in each plot, is deduced from the fit as described in the text.

Figure 3

Experimental data demonstrating the NOT operation of circularly polarized light. Similar results were obtained for all other polarizations attempted (linear $0°$, $90°$, $45°$, $-45°$).