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arXiv:1505.06825 · Optica

Experimental generalized contextuality with single-photon qubits

Xiang Zhan, Eric G. Cavalcanti, Jian Li, Zhihao Bian, Yong-Sheng Zhang, Howard M. Wiseman, Peng Xue

Published Aug 8, 2017• 31 citations
arXivHTMLPDF

Abstract

Contextuality is a phenomenon at the heart of the quantum mechanical departure from classical behaviour, and has been recently identified as a resource in quantum computation. Experimental demonstration of contextuality is thus an important goal. The traditional form of contextuality -- as violation of a Kochen-Specker inequality -- requires a quantum system with at least three levels, and the status of the assumption of determinism used in deriving those inequalities has been controversial. By considering `unsharp' observables, Liang, Spekkens and Wiseman (LSW) derived an inequality for generalized noncontextual models that doesn't assume determinism, and applies already to a qubit. We experimentally implement the LSW test using the polarization states of a heralded single photon and three unsharp binary measurements. We violate the LSW inequality by more than 16 standard deviations, thus showing that our results cannot be reproduced by a noncontextual subset of quantum theory.

DOI
10.1364/optica.4.000966

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Contextuality is a phenomenon at the heart of the quantum mechanical departure from classical behaviour, and has been recently identified as a resource in quantum computation. Experimental demonstration of contextuality is thus an important goal. The traditional form of contextuality -- as violation of a Kochen-Specker inequality -- requires a quantum system with at least three levels, and the status of the assumption of determinism used in deriving those inequalities has been controversial. By considering `unsharp' observables, Liang, Spekkens and Wiseman (LSW) derived an inequality for generalized noncontextual models that doesn't assume determinism, and applies already to a qubit. We experimentally implement the LSW test using the polarization states of a heralded single photon and three unsharp binary measurements. We violate the LSW inequality by more than 16 standard deviations, thus showing that our results cannot be reproduced by a noncontextual subset of quantum theory.
Abstract Contextuality is a phenomenon at the heart of quantum mechanics different from classical behavior and has been recently identified as a resource in quantum information processing. Experimental demonstration of contextuality is thus an important goal. We experimentally demonstrate a test of state-independent contextuality in a four-dimensional Hilbert space with single photons and violate the inequality by at least 387 standard deviations. Despite imperfections and possible measurement disturbance, our results cannot be explained in non-contextual models. We also provide a theoretical analysis of a test of contextuality with a coherent light field and show how the definitions affect the emergence of non-classical correlations. Our result sheds new light on the conflict between quantum and classical physics.
We show that three unsharp binary qubit measurements are enough to violate a generalized noncontextuality inequality, the Liang-Spekkens-Wiseman inequality, in a state-dependent manner. For the case of trine spin axes we calculate the optimal quantum violation of this inequality. In addition, we show that unsharp qubit measurements do not allow a state-independent violation of this inequality. We thus provide a minimal state-dependent proof of measurement contextuality requiring one qubit and three unsharp measurements. Our result rules out generalized noncontextual models of these measurements which were previously conjectured to exist. More importantly, this class of generalized noncontextual models includes the traditional Kochen-Specker (KS) noncontextual models as a proper subset, so our result rules out a larger class of models than those ruled out by a violation of the corresponding KS inequality in this scenario.
Abstract Contextuality is a striking feature of our nature predicted by quantum theory and tested by various experiments. In a qubit system, testing contextuality requires scenarios distinct from traditional ones for systems with dimension of three or greater. In this paper, we consider the noncontextuality inequality developed by Liang-Spekkens-Wiseman and Yu-Oh, and investigate the set of three qubit measurements that can be used to test and violate this inequality. Our numerical results show that two of the three measurements can be almost arbitrary. Moreover, we have singled out several extremely interesting sets of measurements, e.g. one measurements can be white noise while the other two are arbitrarily close to white noise. These sets fulfill our knowledge about contextuality in this minimum quantum system.
Contextuality provides one of the fundamental characterizations of quantum phenomena, and can be used as a resource in lots of quantum information processing. In this paper, we summarize and derive some equivalent noncontextual inequalities from different noncontextual models of the proofs for the Kochen-Specker theorem based on Greenberger-Horne-Zeilinger states. These noncontextual inequalities are equivalent up to some correlation items which hold both for noncontextual hidden variable theories and quantum mechanics. Therefore, using single-photon hyperentangled Greenberger-Horne-Zeilinger states encoded by spin, path, and orbital angular momentum, we experimentally verify several state-dependent noncontextual models of the proofs for the Kochen-Specker theorem by testing an extreme simplest Mermin-like inequality.
Whereas complementarity manifests itself via two incompatible observables, quantum contextuality can only be revealed via the joint measurements among at least three observables. By incorporating unsharp measurements and joint measurements into a realistic model, we reestablish an inequality due to Liang, Spekkens, and Wiseman rigorously based on the assumption of noncontextuality alone. Its violation therefore unambiguously pinpoints the quantum contextuality of a two-level system. The maximal violation is attained by three triplewise jointly measurable observables that are pairwise jointly measured in an incompatible way. We also present the necessary and sufficient condition of triplewise joint measurability of three unbiased observables of a qubit.
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.