We experimentally observed state-independent violations of Kochen-Specker inequalities for the simplest indivisible quantum system manifesting quantum contextuality, a three-level (qutrit) system. We performed the experiment with a single trapped 171 Yb + ion, by mapping three ground states of the 171 Yb + ion to a qutrit system and carrying out quantum operatations by applying microwaves resonant to the qutrit transition frequencies. Our results are free from the detection loophole and cannot be explained by the non-contextual hidden variable models. 03.65.Ud, 37.10.Ty, 32.50.+d It is a long-standing problem whether the nature of physical system would be completely described by quantum mechanics. In classical views the measurement outcomes on physical properties are non-contextual, i.e., predetermined independently of their own and other simultaneous compatible measurements, while quantum mechanics is contextual. Kochen, Specker and Bell proved that quantum mechanics and any non-contextual classical theory are in conflict [1,2], deeply rooted in the essence of quantum mechanics regardless of states of the system. The original logical proof has been formulated to experimentally testable inequalities, called Kochen-Specker (KS) inequalities. The Bell's inequalities that hold for classical theories with local hidden variables can be considered as a special type of KS inequalities, where the contextuality is presented by non-locality. While Bell's inequalities can be violated by special entangled states in space-like separation, the violation of KS inequalities could be observed by any quantum state in a system with dimension d ≥ 3. For cases where d ≥ 4, KS inequalities were proposed [3][4][5] and demonstrated in both a state-dependent [6-8] and a state-independent manner [9][10][11]. For the smallest case d = 3, the state-dependent inequality was developed [12] and tested with a photon system [13]. Lately, the state-independent inequality was found [14,15] and the violations were informed with also a photon system [16]. However, these experimental demonstrations are open to the detection loophole. Here we report the experimental results of a single three-level atomic ion that are in conflict with non-contextual classical theories. The experimental violations of KS inequalities are observed independently of entanglement or superposition of the states and confirm the quantum contextuality at the most simple and fundamental level without the fair sampling assumption.In noncontextual classical models, values of an observable are determined by only a hidden variable independently of the measurement context, i.e., set of mutually compatible observables measured in a single experimental setting. The observables are compatible if their results are not dependent on the order of measurements. Kochen and Specker showed that any quantum state in larger than 2 dimensions would reveal conflict with the non-contextual theories. The demonstration of Table I. the conflict in a simplest three dimensional quantum system, a qut...

We theoretically study transport properties in one-dimensional interacting quasiperiodic systems at infinite temperature. We compare and contrast the dynamical transport properties across the many-body localization (MBL) transition in quasiperiodic and random models. Using exact diagonalization we compute the optical conductivity σ(ω) and the return probability R(τ ) and study their average low-frequency and long-time power-law behavior, respectively. We show that the low-energy transport dynamics is markedly distinct in both the thermal and MBL phases in quasiperiodic and random models and find that the diffusive and MBL regimes of the quasiperiodic model are more robust than those in the random system. Using the distribution of the DC conductivity, we quantify the contribution of sample-to-sample and state-to-state fluctuations of σ(ω) across the MBL transition. We find that the activated dynamical scaling ansatz works poorly in the quasiperiodic model but holds in the random model with an estimated activation exponent ψ ≈ 0.9. We argue that near the MBL transition in quasiperiodic systems, critical eigenstates give rise to a subdiffusive crossover regime on finite-size systems.arXiv:1707.02984v2 [cond-mat.dis-nn]

The class of d-setting, d-outcome Bell inequalities proposed by Ji and collaborators [Phys. Rev. A 78, 052103] are reexamined. For every positive integer d > 2, we show that the corresponding non-trivial Bell inequality for probabilities provides the maximum classical winning probability of the Clauser-Horne-Shimony-Holt-like game with d inputs and d outputs. We also demonstrate that the general classical upper bounds given by Ji et al. are underestimated, which invalidates many of the corresponding correlation inequalities presented thereof. We remedy this problem, partially, by providing the actual classical upper bound for d less than or equal to 13 (including non-prime values of d). We further determine that for prime value d in this range, most of these probability and correlation inequalities are tight, i.e., facet-inducing for the respective classical correlation polytope. Stronger lower and upper bounds on the quantum violation of these inequalities are obtained. In particular, we prove that once the probability inequalities are given, their correlation counterparts given by Ji and co-workers are no longer relevant in terms of detecting the entanglement of a quantum state.Comment: v3: Published version (minor rewordings, typos corrected, upper bounds in Table III improved/corrected); v2: 7 pages, 1 figure, 4 tables (substantially revised with new results on the tightness of the correlation inequalities included); v1: 7.5 pages, 1 figure, 4 tables (Comments are welcome