Observer effect, quasi-probabilities and generalized Specker's boxes.

Quantum non-locality and contextuality can be simulated with quasi-probabilities, i.e. probabilities that take negative values. Here, we show that another quantum phenomenon, the observer effect, admits a quasi-probabilistic description too. We also investigate post-quantum observer effects based on the Specker's triangle scenario. This scenario comprises three observables, with the possibility of measuring two simultaneously. Represented as three boxes with a hidden ball, this scenario exhibits counterintuitive behaviour: regardless of the chosen pair of boxes, one box always contains the ball. Moreover, the scenario demonstrates a strong observer effect. When an observer selects and opens the first box, finding it empty, the ball is guaranteed to be in the second box, thereby allowing the observer to determine the ball's location among the remaining two boxes. We extend this scenario to include additional boxes and multiple balls. By employing negative probabilities, we demonstrate amplification of the observer effect. This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'.

Coherent chemical kinetics as quantum walks. I. Reaction operators for radical pairs.

Classical chemical kinetics uses rate-equation models to describe how a reaction proceeds in time. Such models are sufficient for describing state transitions in a reaction where coherences between different states do not arise, in other words, a reaction that contains only incoherent transitions. A prominent example of a reaction containing coherent transitions is the radical-pair model. The kinetics of such reactions is defined by the so-called reaction operator that determines the radical-pair state as a function of intermediate transition rates. We argue that the well-known concept of quantum walks from quantum information theory is a natural and apt framework for describing multisite chemical reactions. By composing Kraus maps that act only on two sites at a time, we show how the quantum-walk formalism can be applied to derive a reaction operator for the standard avian radical-pair reaction. Our reaction operator predicts the same recombination dephasing rate as the conventional Haberkorn model, which is consistent with recent experiments [K. Maeda et al., J. Chem. Phys. 139, 234309 (2013)], in contrast to previous work by Jones and Hore [J. A. Jones and P. J. Hore, Chem. Phys. Lett. 488, 90 (2010)]. The standard radical-pair reaction has conventionally been described by either a normalized density operator incorporating both the radical pair and reaction products or a trace-decreasing density operator that considers only the radical pair. We demonstrate a density operator that is both normalized and refers only to radical-pair states. Generalizations to include additional dephasing processes and an arbitrary number of sites are also discussed.

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

We apply the quantum-walk approach proposed in the preceding paper [A. Chia et al., preceding paper, Phys. Rev. E 93, 032407 (2016)] 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 exhibits 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 time scale of the reaction but not necessarily its population dynamics.

Entropic test of quantum contextuality.

We study the contextuality of a three-level quantum system using classical conditional entropy of measurement outcomes. First, we analytically construct the minimal configuration of measurements required to reveal contextuality. Next, an entropic contextual inequality is formulated, analogous to the entropic Bell inequalities derived by Braunstein and Caves [Phys. Rev. Lett. 61, 662 (1988)], that must be satisfied by all noncontextual theories. We find optimal measurements for violation of this inequality. The approach is easily extendable to higher dimensional quantum systems and more measurements. Our theoretical findings can be verified in the laboratory with current technology.

Local realism of macroscopic correlations.

We identify conditions under which correlations resulting from quantum measurements performed on macroscopic systems (systems composed of a number of particles of the order of the Avogadro number) can be described by local realism. We argue that the emergence of local realism at the macroscopic level is caused by an interplay between the monogamous nature of quantum correlations and the fact that macroscopic measurements do not reveal properties of individual particles.

Correlation complementarity yields bell monogamy relations.

We present a method to derive Bell monogamy relations by connecting the complementarity principle with quantum nonlocality. The resulting monogamy relations are stronger than those obtained from the no-signaling principle alone. In many cases, they yield tight quantum bounds on the amount of violation of single and multiple qubit correlation Bell inequalities. In contrast with the two-qubit case, a rich structure of possible violation patterns is shown to exist in the multipartite scenario.

Coincidence bell inequality for three three-dimensional systems.

We construct a Bell inequality for coincidence probabilities on a three three-dimensional (qutrit) system. We show that this inequality is violated when each observer measures two noncommuting observables, defined by the so-called unbiased six-port beam splitter, on a maximally entangled state of two qutrits. The strength of the violation agrees with the numerical results presented by Kaszlikowski et al, quant-ph/0202019. It is proven that the inequality defines facets of the polytope of local variable models.

Violations of local realism by two entangled N-dimensional systems are stronger than for two qubits

Tests of local realism versus quantum mechanics based on Bell's inequality employ two entangled qubits. We investigate the general case of two entangled quantum systems defined in N-dimensional Hilbert spaces, or " quNits." Via a numerical linear optimization method we show that violations of local realism are stronger for two maximally entangled quNits ( 3