No Arabic abstract
Bell inequalities or Bell-like experiments are supposed to test hidden variable theories based on three intuitive assumptions: determinism, locality and measurement independence. If one of the assumptions of Bell inequality is properly relaxed, the probability distribution of the singlet state, for example, can be reproduced by a hidden variable model. Models that deal with the relaxation of some condition above, with more than one hidden variable, have been studied in the literature nowadays. In this work the relation between the number of hidden variables and the degree of relaxation necessary to reproduce the singlet correlations is investigated. For the examples studied, it is shown that the increase of the number of hidden variables does not allow for more efficiency in the reproduction of quantum correlations.
The recent progress of the Majorana experiments paves a way for the future tests of non-abelian braiding statistics and topologically-protected quantum information processing. However, a deficient design in those tests could be very dangerous and reach false-positive conclusions. A careful theoretical analysis is necessary in order to develop loophole-free tests. We introduce a series of classical hidden variable models to capture certain key properties of Majorana system: non-locality, topologically non-triviality, and quantum interference. Those models could help us to classify the Majorana properties and to set up the boundaries and limitations of Majorana non-abelian tests: fusion tests, braiding tests and test set with joint measurements. We find a hierarchy among those Majorana tests with increasing experimental complexity.
Constructing local hidden variable (LHV) models for entangled quantum states is challenging, as the model should reproduce quantum predictions for all possible local measurements. Here we present a simple method for building LHV models, applicable to general entangled states, which consists in verifying that the statistics resulting from a finite set of measurements is local, a much simpler problem. This leads to a sequence of tests which, in the limit, fully capture the set of quantum states admitting a LHV model. Similar methods are developed for constructing local hidden state models. We illustrate the practical relevance of these methods with several examples, and discuss further applications.
Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many exhibit dynamics of node characteristics as well as of linking structure. Here we introduce and study natural temporal extensions of static hidden-variable network models with stochastic dynamics of hidden variables and links. The rates of the hidden variable dynamics and link dynamics are controlled by two parameters, and snapshots of networks in the dynamic models may or may not be equivalent to a static model, depending on the location in the parameter phase diagram. We quantify deviations from static-like behavior, and examine the level of structural persistence in the considered models. We explore tempor
I extend, apply, and generalize a model of a quantum radiator proposed by Griffiths to construct models of radiation fields that exhibit high entropy for long periods of time but approach pure states asymptotically. The models, which are fully consistent with the basic principles of quantum theory, provide coarse-grained models of both realistic physical systems and exotic space-times including black and white holes and baby and prodigal universes. Their analysis suggests experimental probes of some basic but subtle implications of quantum theory including interference between a particle and its own past, influence of quantum statistical entanglement on entropy flow, and residual entanglement connecting distant radiation with a degenerate source.
It was shown by Bell that no local hidden variable model is compatible with quantum mechanics. If, instead, one permits the hidden variables to be entirely non-local, then any quantum mechanical predictions can be recovered. In this paper, we consider general hidden variable models which can have both local and non-local parts. We then show the existence of (experimentally verifiable) quantum correlations that are incompatible with any hidden variable model having a non-trivial local part, such as the model proposed by Leggett.