Coherent chemical kinetics as quantum walks II: Radical-pair reactions in Arabidopsis thaliana

We apply the quantum-walk approach recently proposed in arXiv:quant-ph-1506.04213 to a radical-pair reaction where realistic estimates for the intermediate transition rates are available. The well-known average hitting time from quantum walks can be adopted as a measure of how quickly the reaction occurs and we calculate this for varying degrees of dephasing in the radical pair. The time for the radical pair to react to a product is found to be independent of the amount of dephasing introduced, even in the limit of no dephasing where the transient population dynamics exhibit strong coherent oscillations. This can be seen to arise from the existence of a rate-limiting step in the reaction and we argue that in such examples, a purely classical model based on rate equations can be used for estimating the timescale of the reaction but not necessarily its population dynamics

Using Explainability for Constrained Matrix Factorization

Explainable Model Black Box (opaque) predictors such as Deep learning and Matrix Factorization are accurate, ... but lack interpretability and ability to give explanations. White Box models such as rules and decision trees are interpretable (explainable), ... but lack accuracy

Logical independence and quantum randomness

We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements are capable of revealing whether or not a given proposition is logically dependent on the axiomatic system. Whenever a mathematical proposition is logically independent of the axioms encoded in the measured state, the measurement associated with the proposition gives random outcomes. This allows for an experimental test of logical independence. Conversely, it also allows for an explanation of the probabilities of random outcomes observed in Pauli group measurements from logical independence without invoking quantum theory. The axiomatic systems we study can be completed and are therefore not subject to Goedel's incompleteness theorem.Comment: 9 pages, 4 figures, published version plus additional experimental appendi

Bell inequality with an arbitrary number of settings and its applications

Based on a geometrical argument introduced by Zukowski, a new multisetting Bell inequality is derived, for the scenario in which many parties make measurements on two-level systems. This generalizes and unifies some previous results. Moreover, a necessary and sufficient condition for the violation of this inequality is presented. It turns out that the class of non-separable states which do not admit local realistic description is extended when compared to the two-setting inequalities. However, supporting the conjecture of Peres, quantum states with positive partial transposes with respect to all subsystems do not violate the inequality. Additionally, we follow a general link between Bell inequalities and communication complexity problems, and present a quantum protocol linked with the inequality, which outperforms the best classical protocol.Comment: 8 pages, To appear in Phys. Rev.

Nonclassical trajectories in head-on collisions

Rutherford scattering is usually described by treating the projectile either classically or as quantum mechanical plane waves. Here we treat them as wave packets and study their head-on collisions with the stationary target nuclei. We simulate the quantum dynamics of this one-dimensional system and study deviations of the average quantum solution from the classical one. These deviations are traced back to the convexity properties of Coulomb potential. Finally, we sketch how these theoretical findings could be tested in experiments looking for the onset of nuclear reactions.Comment: 16 pages, 8 figure

Information complementarity in quantum physics

We demonstrate that the concept of information offers a more complete description of complementarity than the traditional approach based on observables. We present the first experimental test of information complementarity for two-qubit pure states, achieving close agreement with theory; We also explore the distribution of information in a comprehensive range of mixed states. Our results highlight the strange and subtle properties of even the simplest quantum systems: for example, entanglement can be increased by reducing correlations between two subsystems.Comment: 6 pages, 7 figures (including supplementary material

Local Realism of Macroscopic Correlations

We show that for macroscopic measurements which cannot reveal full information about microscopic states of the system, the monogamy of Bell inequality violations present in quantum mechanics implies that practically all correlations between macroscopic measurements can be described by local realistic models. Our results hold for sharp measurement and arbitrary closed quantum systems.Comment: 9 pages incl. one Appendix, 2 figure

Correlation tensor criteria for genuine multiqubit entanglement

We present a development of a geometric approach to entanglement indicators. The method is applied to detect genuine multiqubit entanglement. The criteria are given in form of non-linear conditions imposed on correlation tensors. Thus they involve directly observable quantities, and in some cases require only few specific measurements to find multiqubit entanglement. The non-linearity of each of the criteria allows detection of entanglement in wide classes of states. In contrast to entanglement witnesses, which in the space of Hermitian operators define a hyperplane, the new conditions define a geometric figure encapsulating the non-fully entangled states within it.Comment: 8 pages, 1 figure, journal versio

Experimental test of nonlocal realistic theories without the rotational symmetry assumption

We analyze the class of nonlocal realistic theories that was originally considered by Leggett [Found. Phys. 33, 1469 (2003)] and tested by us in a recent experiment [Nature (London) 446, 871 (2007)]. We derive an incompatibility theorem that works for finite numbers of polarizer settings and that does not require the previously assumed rotational symmetry of the two-particle correlation functions. The experimentally measured case involves seven different measurement settings. Using polarization-entangled photon pairs, we exclude this broader class of nonlocal realistic models by experimentally violating a new Leggett-type inequality by 80 standard deviations.Comment: Published versio