Optical implementation of the encoding of two qubits to a single qutrit

We have devised an optical scheme for the recently proposed protocol for encoding two qubits into one qutrit. In this protocol, Alice encodes an arbitrary pure product state of two qubits into a state of one qutrit. Bob can then restore either of the two encoded qubit states error-free but not both of them simultaneously. We have successfully realized this scheme experimentally using spatial-mode encoding. Each qubit (qutrit) was represented by a single photon that could propagate through two (three) separate fibers. We theoretically propose two generalizations of the original protocol. We have found a probabilistic operation that enables us to retrieve both qubits simultaneously with average fidelity above 90% and we have proposed an extension of the original encoding transformation to encode $N$ qubits into one $(N+1)$-dimensional system.

Figure 1

Setup of the experiment. NLC denotes a nonlinear crystal, A an attenuator, FC a fiber coupler, PM a phase modulator, AG an adjustable air gap, VRC a variable-ratio coupler, and D1–D3 denote detectors.

Figure 2

Hong-Ou-Mandel dip for the splitting ratio 25:75. The full line shows a Gaussian fit.

Figure 3

Observed fidelities of reconstructed qubit states for various input states.