Experimental Demonstration of Quantum Pseudotelepathy

Quantum pseudotelepathy is a strong form of nonlocality. Different from the conventional nonlocal games where quantum strategies win statistically, e.g., the Clauser-Horne-Shimony-Holt game, quantum pseudotelepathy in principle allows quantum players to with probability 1. In this Letter, we report a faithful experimental demonstration of quantum pseudotelepathy via playing the nonlocal version of Mermin-Peres magic square game, where Alice and Bob cooperatively fill in a $3\times 3$ magic square. We adopt the hyperentanglement scheme and prepare photon pairs entangled in both the polarization and the orbital angular momentum degrees of freedom, such that the experiment is carried out in a resource-efficient manner. Under the locality and fair-sampling assumption, our results show that quantum players can simultaneously win all the queries over any classical strategy.

Figure 1

The Mermin-Peres magic square game. The referee randomly sends $x$ and $y$ to Alice and Bob, respectively. Alice and Bob reply with three numbers, either $+1$ or $-1$, in a row and in a column, respectively. They win the game if the overlapped entry is the same.

Figure 2

Experimental setup to play quantum magic square game. (a) The generation of two-photon Polarization- and OAM hyperentangled state. (b) Polarization interferometric prism (PIP). Implement a Polarization-OAM Controlled-NOT (CNOT) gate for single photons with the polarization acting as the control qubit and the OAM as the target qubit. The HWP with a WiFi sign represents HWP that changes angle according to QRN (quantum random number). (c) Polarization measurement (d) Dual-channel OAM readout by coherently convert OAM to the polarization by a swap gate (inset). (e) Quantum random number sends 0, 1 and 2 to Alice and Bob, where 0, 1 and 2 denote the first, second and third row or column in the game, respectively.

Figure 3

Summary of results. The winning probability for each query pair $(x,y)$ is calculated from experimental data. The standard deviation is less than 0.01%, which is negligible in the histogram. The dotted blue line represents the unbiased classical bound $8/9$.