Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality

Abstract

Recent experiments have demonstrated ququart state-independent quantum contextuality and qutrit state-dependent quantum contextuality. So far, the most basic form of quantum contextuality pointed out by Kochen and Specker, and Bell, has eluded experimental confirmation. Here we present an experimentally feasible test to observe qutrit state-independent quantum contextuality using single photons in a three-path setup. In addition, we show that if the same measurements are performed on two entangled qutrits, rather than sequentially on the same qutrit, then the noncontextual inequality becomes a Bell inequality. We show that this connection also applies to other recently introduced noncontextual inequalities.

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

“…This is a significant simplification compared with the previous KS inequalities for single qutrits, and the number of variables cannot be further reduced as proven recently by Cabello [17]. Our experiment confirms quantum contextuality in a stateindependent fashion using the Yu-Oh version of the KS inequality for qutrits represented by three distinctive paths of single photons [18]. The maximum violation of this inequality by quantum mechanics is only 4% beyond the bound set by the noncontextual hidden variable theory, so we need to accurately control the paths of single photons in experiments to measure the 13 variables and their correlations for different types of input states.…”

Quantum nonlocality via local contextuality with qubit-qubit entanglement

“…These two are: nonlocal correlation between two distant parties, and contextual correlation in the sequential measurement of one's subsystem with correlation between distant parties admitting a local model. This equivalence is natural in the two scenarios studied in the literature, namely two-ququart [15] and twoqutrit [16] systems in maximally entangled states. Similarly, state-independent contextuality assisted by bipartite entanglement has been exploited to show fully nonlocal quantum correlations [18][19][20].…”

“…Then, we have shown that neither noise nor the lack of perfect entanglement impedes us to observe this effect. This makes this configuration valuable for observing quantum nonlocality via local contextuality in experiments, extending previous experiments without entanglement [21][22][23][24][25], since it is easier to perform sequential measurements on two qubits such that just one of them is entangled with a distant location than requiring both qubits to be entangled with a distant location [15] or requiring qutrit-qutrit entanglement [16].…”

Minimal true-implies-false and true-implies-true sets of propositions in noncontextual hidden-variable theories

“…From the perspective of NC inequalities, KS sets are a particular type of contextuality sets, defined as sets of observables for which outcome noncontextuality contradicts the quantum predictions. KS sets can be converted into NC inequalities whose violation reveals quantum state-independent contextuality [11,12], into Bell inequalities with quantum violation saturating the nonsignaling bound [13,14], and into proofs of nonlocality via local contextuality [15][16][17].…”