Experimental contextuality in classical light

Abstract

The Klyachko, Can, Binicioglu, and Shumovsky (KCBS) inequality is an important contextuality inequality in three-level system, which has been demonstrated experimentally by using quantum states. Using the path and polarization degrees of freedom of classical optics fields, we have constructed the classical trit (cetrit), tested the KCBS inequality and its geometrical form (Wright’s inequality) in this work. The projection measurement has been implemented, the clear violations of the KCBS inequality and its geometrical form have been observed. This means that the contextuality inequality, which is commonly used in test of the conflict between quantum theory and noncontextual realism, may be used as a quantitative tool in classical optical coherence to describe correlation characteristics of the classical fields.

Hypergraph Contextuality

“…Recently, quantum contextuality found applications in quantum communication [ 1 , 2 ], quantum computation [ 3 , 4 ], quantum nonlocality [ 5 ] and lattice theory [ 6 , 7 ]. This has prompted experimental implementation with photons [ 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ], classical light [ 20 , 21 , 22 , 23 ], neutrons [ 24 , 25 , 26 ], trapped ions [ 27 ], solid state molecular nuclear spins [ 28 ] and superconducting quantum systems [ 29 ].…”

“…The smallest MMPH non-binary set we obtain is a pentagon with five vectors (vertices) cyclically connected with 5 pairs of orthogonality (edges). It corresponds to the pentagram from Reference [ 53 ], implemented in [ 15 , 20 , 23 ]. The difference is that the pentagram inequality is state dependent, while the MMPH pentagon inequality is state independent.…”

State-independent contextuality in classical light

“…When the input state projects onto the eigenstates at the three output ports, namely the input base vectors are mapped to the polarization mode at the three output ports, we measure the optical intensities at these output ports. Then the optical intensities are normalized, namely, the optical intensity at each output port is divided by the total optical intensities, the probabilities of these eigenvalues can be obtained 47 . The probabilities at output port PD1, PD2 and PD3 are expressed as , and , respectively.…”

“…On the other hand, recent investigations have also shown that many quantum phenomena, which are considered as the unique properties of quantum system, can also be simulated in classical systems, such as the violations of Clauser-Horne-Shimony-Holt (CHSH) Bell inequality in classical wave systems 33–43 , the Hardy’s thought experiment in classical light 44 , violating the Leggett-Garg inequality in classical optical systems 45 , the violation of Mermin’s inequality in classical nonseparability systems 46 , and so on. Recently, the state-dependent contextuality involving 5 variables has been studied in classical optical systems, and violations of the Klyachko-Can-Binicioglu-Shumovski (KCBS) inequality and its geometrical form (Wright’s inequality) have been demonstrated experimentally 47 . The two-bit state-independent contextuality has also been explored in classical microwave systems 48 .…”

Experimental Test of Contextuality in Quantum and Classical Systems

“…In particular, there have been debates on whether classical fields, i.e. coherent or stochastic light beams, can reproduce the correlations to violate NC inequalities [19,20] or not [21], and whether such correlations may enhance the performance of certain applications [22][23][24].…”