Contextuality and the probability representation of quantum states

Abstract

The contextuality and noncontextuality notions are considered in framework of probability representation of quantum states. Example of qutrit states and violation of the noncontextuality inequalities are presented by using the spin tomogram and tomographic symbols of the observables.

Multilevel superconducting circuits as two-qubit systems: Operations, state preparation, and entropic inequalities

“…Quantum correlations for states of composite systems are successfully described in terms of various information and entropic characteristics, including the von Neumann entropy and quantum mutual information [9], discord related measures [10][11][12], informational asymmetry [13], contextuality [14], entropic inequalities [15][16][17], and subadditivity and strong subadditivity conditions [17][18][19][20]. Entropic characteristics of quantum states have been widely studied [18,20,21] in the framework of q-deformed entropic functions, e.g., Rényi [22] and Tsallis entropies [23], depending on a single extra parameter, as well as a larger number of parameters [24].…”

Contextuality in Tree-Like Graphs

“…For qudit systems these distributions are associated with finite probability vectors. The problem of relationship between contextuality and tomographic probability vectors was discussed in [10]. There exist the problem of constructing a joint probability distribution if the marginal distributions are known [11].…”

Multilevel superconducting circuits as two-qubit systems: Operations, state preparation, and entropic inequalities

“…Fundamental results on generalization of the Shannon classical information theory in the quantum domain have been obtained [6][7][8]. Quantum correlations for states of composite systems are successfully described in terms of various information and entropic characteristics, including the von Neumann entropy and quantum mutual information [9], discord related measures [10][11][12], informational asymmetry [13], contextuality [14], entropic inequalities [15][16][17], subadditivity and strong subadditivity conditions [17][18][19][20]. Entropic characteristics of quantum states have been widely studied [18,20,21] in the framework of q-deformed entropic functions, e.g., Rényi [22] and Tsallis entropies [23], depending on single extra parameter, as well as a larger number of parameters [24].…”