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Photonic circuit for non-contextual inequalities tests via sequential measurements

Patrick Lima

Published Mar 15, 2022• 0 citations
OpenAlex

Abstract

In this work, we develop the details of experimental proposals for the verification of non-contextual inequalities in qutrits through sequential measurements using photonic circuits as physical platforms for implementing states and observables. Initially, an introduction to the concept of quantum contextuality and the relevance of non-contextuality inequalities was carried out. We explained the details of performing sequential measurements and the reason they were chosen as an experimental method as well as the details of the choice of photonic circuits as an experimental plataform to realize the experiments. Finally, we obtained the photonic circuit designs, and their respective experimental parameters, capable of performing non-contextuality tests through the observation of state-dependent and state-independent non-contextuality inequalities in three-level systems.

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In this work, we develop the details of experimental proposals for the verification of non-contextual inequalities in qutrits through sequential measurements using photonic circuits as physical platforms for implementing states and observables. Initially, an introduction to the concept of quantum contextuality and the relevance of non-contextuality inequalities was carried out. We explained the details of performing sequential measurements and the reason they were chosen as an experimental method as well as the details of the choice of photonic circuits as an experimental plataform to realize the experiments. Finally, we obtained the photonic circuit designs, and their respective experimental parameters, capable of performing non-contextuality tests through the observation of state-dependent and state-independent non-contextuality inequalities in three-level systems.
Recent experiments have demonstrated ququart state-independent quantum contextuality and qutrit state-dependent quantum contextuality. So far, the most basic form of quantum contextuality pointed out by Kochen and Specker, and Bell, has eluded experimental confirmation. Here we present an experimentally feasible test to observe qutrit state-independent quantum contextuality using single photons in a three-path setup. In addition, we show that if the same measurements are performed on two entangled qutrits, rather than sequentially on the same qutrit, then the noncontextual inequality becomes a Bell inequality. We show that this connection also applies to other recently introduced noncontextual inequalities.
In this paper, we present a protocol to obtain photonic circuits that can be used in the implementation of contextuality tests on qutrit systems. The use of photonic integrated circuits offers several advantages for performing this type of task. These include scalability, accuracy, robustness, high-speed and efficient quantum measurements, precise control over the phase properties of photons by using electrically driven heaters to induce a thermo-optic phase shift and resistance to noise. We relate the average values that appear in the inequalities with the probability of photon counting in the circuit outputs and present a realizable configuration for the desired device, taking into account state-dependent and state-independent contextuality tests.
Quantum contextuality provides a fundamental signature of nonclassical behavior that cannot be explained by noncontextual hidden-variable models. We propose and experimentally implement a linear-optical setup for demonstrating Kochen-Specker contextuality via a violation of the KCBS inequality using single photons. Our scheme employs sequential measurements realized with linear-optical networks and on-off photodetectors. The construction ensures that each co-measured observable is implemented by the same physical operation across different contexts. Our experimental results demonstrate a clear violation of the KCBS inequality and robustness against photon loss. Beyond fundamental investigations, the proposed setup provides a practical tool for probing non-classicality and photon-number statistics of quantum states, which in turn enables the verification of single-photon sources.
The violation of contextuality inequalities shows a strong conflict between the noncontextual hidden variable theory and quantum mechanics. A single qutrit is the simplest indivisible quantum system that can allow a state-dependent contextuality test with five observables and a state-independent contextuality test with 13 observables. For any qutrit states, except for the maximally mixed state, one can always find a set of nine observables for which the corresponding inequality is violated [P. Kurzynski and D. Kaszlikowski, Phys. Rev. A 86, 042125 (2012)]. In this paper, we demonstrate the violation of this inequality using single-photon experiments. Our experiments not only enrich the tests of quantum contextuality, but also deepen the understanding of the physical nature of quantum mechanics.
We report two fundamental experiments on three-level quantum systems (qutrits). The first one tests the simplest task for which quantum mechanics provides an advantage with respect to classical physics. The quantum advantage is certified by the violation of Wright's inequality, the simplest classical inequality violated by quantum mechanics. In the second experiment, we obtain contextual correlations by sequentially measuring pairs of compatible observables on a qutrit, and show the violation of Klyachko et al.'s inequality, the most fundamental noncontextuality inequality violated by qutrits. Our experiment tests exactly Klyachko et al.'s inequality, uses the same measurement procedure for each observable in every context, and implements the sequential measurements in any possible order.
Summary form only given. Contrarily to the classical physics picture, according to quantum mechanics the observable properties of the objects do not yield defined values, until a measurement is performed. The measurement outcome depends indeed also on the set of observables that is being measured [1]. Such a fundamental aspect of Nature is named quantum contextuality and it has been studied in several experimental systems, including single particles [2, 3]. Interestingly, it was recently suggested that even the non-classical power of quantum computing originates from contextuality [4]. Therefore, it is highly relevant to find experimental evidence of this aspect in technological platforms that may be adopted in future quantum computing devices, such as integrated photonics [5-7]. In this work we investigate experimentally quantum contextuality of a single photon on-a-chip, employing reconfigurable photonic circuits fabricated by femtosecond laser waveguide writing [7, 8].