Effect of decoherence on the contextual and nonlocal properties of a biphoton

Quantum contextuality is a nonintuitive property of quantum mechanics that distinguishes it from any classical theory. A complementary quantum property is quantum nonlocality, which is an essential resource for many quantum information tasks. Here we experimentally study the contextual and nonlocal properties of polarization biphotons. First, we investigate the ability of the biphotons to exhibit contextuality by testing the violation of the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) inequality. In order to do so, we used the original protocol suggested in the KCBS paper and adjusted it to the real scenario, where some of the biphotons are distinguishable. Second, we transmitted the biphotons through different unital channels with a controlled amount of noise. We measured the decohered output states and demonstrated that the ability to exhibit quantum contextuality using the KCBS inequality is more fragile to noise than the ability to exhibit nonlocality.

Figure 1

The experimental setup. (a) Biphoton generation and characterization units: photon pairs are generated in the BBO crystals, which are located after a lens (L1) and a half-wave plate (HWP, $\lambda /2$) whose angle is $\delta$. The down-converted photon pairs pass through a dichroic mirror (DM), a birefringent-compensating crystal ($\phi$), a single-mode fiber (SM), an interference band-pass filter (IF), and another HWP ($\alpha$). In the state characterization unit, the biphotons are split probabilistically by a beam splitter (BS) into two ports. In each port, the photons pass a sequence of a quarter-wave plate (QWP, $\lambda /4$, labeled a), a HWP, another QWP (labeled b) and a polarizing beam splitter (PBS) before being coupled into single-photon detectors. The decoherence channels ($\mathcal{E}$) are plugged in only when the noise effects on the biphotons are studied. (b) The one-field (dephasing) channel, composed of two translatable quartz wedges. (c) The two-field channel, composed of two perpendicularly oriented identical 2-mm-thick calcite crystals. (d) The three-field (isotropic) channel. This channel is composed of four crystals and two fixed HWPs. The thickness of the two outer (inner) crystals is 1 mm (2 m). The fields' strengths for both the two- and the three-field channels is set by rotating the middle HWP.

Figure 2

The polarization states used for the direct projection protocol. The five $|s_k\rangle$ states, along with their antipodes, $|t_k\rangle$ states are presented in the Stokes representation. $S_1,S_2\text{and}{S}_3$ represent the degree of linear, diagonal and circular polarizations, respectively. All ten states have the same distance from the black solid line that connects the horizontal and the vertical polarizations, located at the poles of the Poincaré sphere.

Figure 3

The KCBS and the CHSH values in the presence of unital noise. The maximal possible expectation values for the KCBS (blue stars) and CHSH (red squares) operators of the output biphoton states are presented as a function of the noise probability. Data are presented for the three principal unital channels: (a) dephasing, (b) two-field, and (c) isotropic channels. Solid lines represent the theoretical predictions. Dashed lines represent the value 2: the upper bound allowed by any classical theory for the expectation values of both operators.