Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for by some realistic models with hidden variables. There are, however, two powerful theorems against the hidden-variable theories showing that certain quantum features cannot be reproduced based on two rationale premises of locality, Bell's theorem, and noncontextuality, due to Bell, Kochen and Specker (BKS). Noncontextuality is independent of nonlocality, and the contextuality manifests itself even in a single object. Here we report an experimental verification of quantum contextuality by a single spin-1 electron system at room temperature. Such a three-level system is indivisible and then we close the compatibility loophole which exists in the experiments performed on bipartite systems. Our results confirm the quantum contextuality to be the intrinsic property of single particles.
We investigate how unresolved quasistatic disorder in system bath coupling affects non-Markovian dynamics in spin environments. The coupling is fixed within each experimental shot but varies between shots, so repeated shot tomography reconstructs a disorder averaged dynamical map. For a single spin bath with pure dephasing Ising interaction, disorder can drive a transition to CP-divisible dynamics for fixed bath preparations, with a critical strength set by bath polarization along the interaction axis. However, when the bath state fluctuates physically between shots, the averaged dynamics remain CP indivisible at any finite disorder strength. We extend these results analytically to inhomogeneously coupled pure dephasing baths of any number
N of non-interacting spins. At any finite disorder strength, one unpolarized bath spin suffices to retain CP-indivisible dynamics, whereas a fully polarized bath yields Markovian (CP-divisible) dynamics. Dynamics with physically fluctuating bath states likewise remain non-Markovian (CP indivisible) at finite disorder for arbitrary
N in the pure dephasing case. For anisotropic Heisenberg interactions, any nonzero transverse exchange eliminates the disorder driven transition to CP divisibility in a single spin bath. Exact diagonalization of anisotropic models with inhomogeneous couplings up to
N=12 reveals persistent trace distance revivals for fixed bath preparations, sampled Haar random preparations, and physically fluctuating bath states, showing that this effect of transverse exchange extends beyond a single bath spin. Increasing disorder still suppresses experimentally accessible revivals and can make memory effects unresolvable at finite measurement resolution even as the dynamics remain CP indivisible. Thus, transverse exchange and physical bath state fluctuations preserve dynamical indivisibility against unresolved coupling disorder.