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Operational exploration of quantum contextuality by simultaneous control of complementary photon polarizations

Kengo Matsuyama, Ming Ji, Holger Friedrich Hofmann, M. Iinuma

Published Jan 1, 2023• 0 citations
Publisher

Abstract

Contextual relations between complementary pairs of polarization components of two photons were observed by controlling the degree of entanglement and the local polarizations, highlighting the non-classical aspects of the relations between measurement contexts.
DOI
10.1364/quantum.2023.qth2a.17

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We experimentally investigate nonlocal contextual relations between complementary photon polarizations by adapting the entanglement and the local polarizations of a two-photon state to satisfy three deterministic conditions demonstrating both quantum contextuality and nonlocality. The key component of this adaptive input state control is the variable degree of entanglement of the photon-pair source. Local polarization rotations can optimize two of the three correlations, and the variation of the entanglement optimizes the third correlation. Our results demonstrate that quantum contextuality is based on a nontrivial trade-off between local complementarity and quantum correlations.
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In this work we propose two experimental setups to observe fractional topological phases in qudits. The degree of freedom in which the qudits are encoded is the transverse position of photon pairs generated by spontaneous parametric down-conversion after being transmitted through multiple slits. The photons generated in this phenomenonare quantum correlated in energy and momenta. Initially we discuss the basic theory about topological phases, the context in which they are fractional, and its relation with entanglement. Then, we see how local unitary operations can be applied in this degree of freedom with the aid of spatial light modulators that introduce a programmable phase prole on the wavefront of the photons. Thus, the desired fractional phases canbe observed through polarization-controlled two-photon interference. The roles played by entanglement and Hilbert space dimension are revealed by the behavior of the interference fringes as the unitary operations are continuously changed. These ideas are supported by analytical and numerical calculations of the expected interference fringes. We also show how the so called Hong-Ou-Mandel eect is present in the proposed interferometer, which requires simultaneity on the recombination of the photons generated to allow for the interference