State-Independent Experimental Test of Quantum Contextuality in an Indivisible System

We report the first state-independent experimental test of quantum contextuality on a single photonic qutrit (three-dimensional system), based on a recent theoretical proposal [Phys. Rev. Lett. 108, 030402 (2012)]. Our experiment spotlights quantum contextuality in its most basic form, in a way that is independent of either the state or the tensor product structure of the system.

Figure 1

Illustration of the 13 unit vectors that describe the superposition coefficients of 13 corresponding qutrit states. The KS inequality proposed in Ref. 6 requires one to detect projection operators onto these 13 states and their correlations.

Figure 2

The measured expectation values $⟨A_i⟩$ and the correlations $⟨A_i{A}_j⟩$ for all the compatible pairs under a particular input state $|s⟩=(|0⟩+|1⟩+|2⟩)/\sqrt{3}$. For the experimental values, the numbers in the bracket represent the statistical error associated with the photon detection under the assumption of a Poissonian distribution for the photon counts, for instance, $⟨A_{z_1}⟩=0.328(18)\equiv 0.328\pm 0.018$. Both of the inequalities (2, 3) are significantly violated by the experimental data.

Figure 3

Illustration of the experimental setup to detect the KS inequalities. The setup in box (a) is for state preparation of a single photonic qutrit. Ultrafast laser pulses (with a repetition rate of 76 MHz) at the wavelength of 400 nm from a frequency doubled Ti:sapphire laser pump two joint beta-barium-borate crystals, each of 0.6 mm depth with a perpendicular optical axis, to generate correlated (entangled) photon pairs at the wavelength of 800 nm. With registration of a photon count at the detector D0, we get a heralded single-photon source in the other output mode. This photon is split by two PBSs into three optical paths, representing a single photonic qutrit. By adjusting the angle of the half wave plates (HWP1 and HWP2), we can control the superposition coefficients of this qutrit state. The setup in box (b) is for measurement of the qutrit state along compatible projections to three orthogonal states. By tuning the wave plates (HWP5 and HWP6), we choose these projection operators to be along the directions specified by the $A_i$ operators to measure the correlations of the compatible $A_i$. The wave plates HWP3 and HWP4 are used to balance the Mach-Zehnder interferometers and can be tilted for fine-tuning of the relative phase.

Figure 4

The measurement results for the two inequalities (2) (shown by the blue label) and (3) (shown by the red label) under different types of input states. The left-side dashed line specifies the upper bounds imposed by any noncontextual hidden variable models, while the right-side dashed line corresponds to the quantum mechanical prediction under the ideal input states. The error bars account for the statistical error associated with the photon detection.