Experimental Detection of Information Deficit in a Photonic Contextuality Scenario

Contextuality is an essential characteristic of quantum theory, and supplies the power for many quantum information processes. Previous tests of contextuality focus mainly on the probability distribution of measurement results. However, a test of contextuality can be formulated in terms of entropic inequalities whose violations imply information deficit in the studied system. This information deficit has not been observed on a single local system. Here we report the first experimental detection of information deficit in an entropic test of quantum contextuality based on photonic setup. The corresponding inequality is violated with more than 13 standard deviations.

Figure 1

(a) Single photons are distributed into three modes, which represent the basis states $|A_{i+1}⟩$, $|A_i\times A_{i+1}⟩$, and $|A_i⟩$. The clicks of detectors $D$ and $D^{\prime }$ assign the outcomes of the measurements $A_{i+1}$ and $A_i$ as 1, respectively. (b) A transformation $T_{i+1\to i-1}$ is applied to two upper modes, and the basis states are transformed into $|A_{i-1}⟩$ and $|A_{i-1}\times A_i⟩$. The lower mode is kept completely unchanged. (c) An example of realizing the projective measurements $\{A_1,A_2\}$. (d) Conceptual scheme for the measurements $\{A_5,A_1\}$. Vertical black (dark gray) line represents the blocker which blocks the photons in the certain mode corresponding to the outcome $a_5=0(1)$ of the projector $A_5$. Only the outcome of the projective measurement $A_1$ is monitored by the detector $D$ and provides the outcomes of the joint measurement $\{A_5,A_1\}$ as $[a_5=1(0),a_1]$.

Figure 2

Experimental setup. Heralded single photons are generated via SPDC. A polarization beam splitter (PBS) and two half-wave plates (HWPs) H0 and H1 are used to prepare the photonic three-level system in the basis states $|A_4⟩$, $|A_5⟩$, and $|A_4\times A_5⟩$. Different spatial modes are split and combined using calcite beam displacers (BDs). HWPs (H4, H5, and H8) are used to switch on or off the transformations between different bases. HWPs (H2, H3, H6, and H7) are used to compensate the different path lengths between two spatial modes and flip the polarization. Photons are detected by the single-photon avalanche photodiodes (APDs).