Experimental creation of superposition of unknown photonic quantum states

As one of the most intriguing intrinsic properties of the quantum world, quantum superposition provokes great interest in its own generation. Though a universal quantum machine that creates superposition of two arbitrary unknown states has been shown to be physically impossible, a probabilistic protocol exists given that two input states have nonzero overlaps with the referential state. Here we report a probabilistic quantum machine realizing superposition of two arbitrary unknown photonic qubits as long as they have nonzero overlaps with the horizontal polarization state $|H\rangle$. A total of 11 different qubit pairs are chosen to test this protocol and we obtain the average fidelity as high as 0.99, which shows the excellent reliability of our realization. This realization may have significant applications in quantum information and quantum computation, e.g., generating nonclassical states and realizing information compression in a quantum computation.

Figure 1

Schematic of the quantum adder. A quantum adder outputs a superposed state $|\mathrm{\Psi }\rangle =h|\psi \rangle +f|\varphi \rangle$ for two arbitrary input states $|\psi \rangle$ and $|\varphi \rangle$ probabilistically with the requirement that $\langle \chi |\psi \rangle \ne 0,\langle \chi |\varphi \rangle \ne 0$ are known.

Figure 2

Experimental setup for realizing the quantum adder. A pair of photons in state $|H\rangle \otimes |H\rangle$ is generated via spontaneous parametric down-conversion (SPDC) process by pumping a type-I cut $\beta$-BBO crystal with an ultraviolet (UV) laser at 404 nm. By using half-wave plates (HWP1, HWP2) and quarter-wave plates (QWP1, QWP2) placed before beam displacers (BD1, BD2), two arbitrary photons' state $\left(a\right|H\rangle +b|V\rangle )\otimes \left(c\right|H\rangle +d|V\rangle )$ can be produced. BD1, BD2, HWP3, HWP4 (HWPs are fixed at $22.5^{\circ }$), and a polarizing beam splitter (PBS1) together with the detection of coincident events realize the control-swap operation. BD1, BD2, HWP3, and HWP4 are used to transform polarization qubits into path qubits. PBS1 placed at the center of the setup combined with selection of coincidence realizes the swap operation between different path qubits with control state ${|H\rangle }_1{|H\rangle }_2+{|V\rangle }_1{|V\rangle }_2$. Path qubits are transformed back into polarization qubits through HWP7, HWP8, HWP9, HWP10, BD3, and BD4, in which HWP7 and HWP9 are fixed at ${45}^{\circ }$ while HWP8 and HWP10 are fixed at $0^{\circ }$ for optical path compensation. The $P_1$ section stands for the projection operation of the control qubit by setting HWP5 and HWP6 at $22.5^{\circ }$, and only allowing photons in horizontal polarization state $|H\rangle$ to pass through PBS2 and PBS3. HWP11 and PBS4 in section $P_2$ realize the projection operation of photon 2. QWP3 and HWP12 combined with PBS5 are used for state tomography of the output state. The coincident events imply the success of superposing two input qubits.