Fig. 3: Experimental setup. (a) d = 2 guessing game. (b) d = 3 guessing game.
From: Experimental study of quantum uncertainty from lack of information
The single-photon is prepared by detecting one of the photons from a photon-pair generated in the Type-II spontaneous parametric down-conversion process. The whole setup consists of three modules: the state preparation part (red region), the controlled Fourier gate (white region), and the measurement part (purple region). Firstly, Bob prepares the system B in state ρB and Alice prepares the register R in state ρR, and those two systems are uncorrelated at module 1. Then a controlled Fourier gate is applied to the systems to correlate them. At last, Alice measures the system B to obtain outcome X and Bob measures the system R in some optimal basis to help him guess X. In our experiment, the systems B and R are encoded in different degrees of freedom of a photon: the horizontally spatial modes marked as “0", “1" and “2" and the different path layers marked as upper layer “u" and lower layer “l”, respectively. Therefore, if the register R is in state \(\left|u\right\rangle\) (\(\left|l\right\rangle\)), then the photon passes through the upper (lower) layer and undergoes an identity (Fourier) transformation as shown by the red (purple) lines. In the end, Alice needs to perform a non-demolition measurement, which is very difficult to realize in practice33, before sending the system R to Bob. Here we perform both measurements simultaneously to ensure the efficiency. Abbreviations: IF interference filter, HWP half-wave plat, QWP quarter-wave plate, QP quartz plate, FC fiber coupler, PBS polarizing beam splitter, HB, horizontally placed beam displacer, VBD vertically placed beam displacer, BBO beta-barium-borate crystal.
