Quantum contextuality of a qutrit state

Abstract

We present a study of quantum contextuality of three-dimensional mixed states for the Klyachko-Can-Binicioglu-Shumovsky (KCBS) and the Kurzyński-Kaszlikowski (KK) noncontextuality inequalities. For any class of states whose eigenvalues are arranged in decreasing order, a universal set of measurements always exists for the KK inequality, whereas none does for the KCBS inequality. This difference can be reflected from the spectral distribution of the overall measurement matrix. Our results would facilitate the error analysis for experimental setups, and our spectral method in the paper combined with graph theory could be useful in future studies on quantum contextuality.

Plug-and-play measurement-device-independent quantum key distribution

“…Moreover, our proof-ofprinciple experiment clearly shows the feasibility of using a single laser for implementing P&P MDI-QKD. With the rigours security proof of P&P MDI-QKD [31] and our results, we believe that P&P MDI-QKD will facilitate practical implementation of MDI-QKD, and contribute to the ultimate secure communication.…”

“…It is necessary to discuss how the plug-and-play architecture affects the security of MDI-QKD. A rigorous security proof for P&P MDI-QKD has been provided recently [31]. The only thing we must consider now is the security of P&P MDI-QKD system being implemented with realistic devices.…”

Quantum contextuality of a single neutrino under interactions with matter

“…Three-dimensional systems-qutrits-are the simplest objects exhibiting contextuality yet rich enough to attract attention [26,58]. A 'natural qutrits'-neutrinos-exhibiting often unexpected properties and attracting researchers from very different sub-disciplines of physics are a stage of the most fundamental properties of a quantum world.…”

“…Due to its simplicity, in our work we focus only on the Klyachko-Can-Binicioglu-Shumovsky test (KCBS test) [24]. It is state-dependent [8] but requires only five observables to be measured and it is designed for the three-dimensional system [26] which is exactly the one considered in this paper. The KCBS inequality is constructed as follows.…”

Simple state preparation for contextuality tests with few observables

“…First, for some states, the noncontextuality inequality is satisfied with any set of observables obeying the required compatibility relations. Second, for the other states, the observables must be chosen according to the state, in order to violate the inequality [13][14][15][16][17]. A noncontextuality inequality involves a sum of expectation values.…”