Quantum contextuality of YO-13 rays

Quantum contextuality, a more general quantum correlation, is an important resource for quantum computing and quantum information processing. Meanwhile, quantum contextuality plays an important role in fundamental quantum physics. Yu and Oh (YO) proposed a proof of the Kochen–Specker theorem for a qutrit with only 13 rays. Here, we further study quantum contextuality of YO-13 rays using the inequality approach. The maximum quantum violation value of the optimal noncontextuality inequality constructed by YO-13 rays is increased to 11.9776 in the four-dimensional system, which is larger than 11.6667 in the qutrit system. The result shows that the set of YO-13 rays has stronger quantum contextuality in the four-dimensional system. Moreover, we provide an all-versus-nothing proof (i.e. Hardy-like proof) to study YO-13 rays without using any inequality, which is easily applied to experimental tests. Our results will further deepen the understanding of YO-13 rays.

Quantum Contextuality and Indeterminacy

The circumstances of measurement have more direct significance in quantum than in classical physics, where they can be neglected for well-performed measurements. In quantum mechanics, the dispositions of the measuring apparatus-plus-environment of the system measured for a property are a non-trivial part of its formalization as the quantum observable. A straightforward formalization of context, via equivalence classes of measurements corresponding to sets of sharp target observables, was recently given for sharp quantum observables. Here, we show that quantum contextuality, the dependence of measurement outcomes on circumstances external to the measured quantum system, can be manifested not only as the strict exclusivity of different measurements of sharp observables or valuations but via quantitative differences in the property statistics across simultaneous measurements of generalized quantum observables, by formalizing quantum context via coexistent generalized observables rather than only its subset of compatible sharp observables. Here, the question of whether such quantum contextuality follows from basic quantum principles is then addressed, and it is shown that the Principle of Indeterminacy is sufficient for at least one form of non-trivial contextuality. Contextuality is thus seen to be a natural feature of quantum mechanics rather than something arising only from the consideration of impossible measurements, abstract philosophical issues, hidden-variables theories, or other alternative, classical models of quantum behavior.

Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices

Violation of a noncontextuality inequality or the phenomenon referred to `quantum contextuality' is a fundamental feature of quantum theory. In this article, we derive a novel family of noncontextuality inequalities along with their sum-of-squares decompositions in the simplest (odd-cycle) sequential-measurement scenario capable to demonstrate Kochen-Specker contextuality. The sum-of-squares decompositions allow us to obtain the maximal quantum violation of these inequalities and a set of algebraic relations necessarily satisfied by any state and measurements achieving it. With their help, we prove that our inequalities can be used for self-testing of three-dimensional quantum state and measurements. Remarkably, the presented self-testing results rely on weaker assumptions than the ones considered in Kochen-Specker contextuality.

Indistinguishability and Negative Probabilities

In this paper, we examined the connection between quantum systems’ indistinguishability and signed (or negative) probabilities. We do so by first introducing a measure-theoretic definition of signed probabilities inspired by research in quantum contextuality. We then argue that ontological indistinguishability leads to the no-signaling condition and negative probabilities.