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Physical Review Letters

Realization of the Contextuality-Nonlocality Tradeoff with a Qubit-Qutrit Photon Pair

Xiang Zhan, Xin Zhang, Jian Li, Yong-Sheng Zhang, Barry C. Sanders, Peng Xue

Published Feb 29, 2016• 57 citations
Publisher

Abstract

We report our experimental results on the no-disturbance principle, which imposes a fundamental monogamy relation on contextuality versus nonlocality. We employ a photonic qutrit-qubit hybrid to explore no-disturbance monogamy at the quantum boundary spanned by noncontextuality and locality inequalities. In particular, we realize the single point where the quantum boundary meets the no-disturbance boundary. Our results agree with quantum theory and satisfy the stringent monogamy relation thereby providing direct experimental evidence of a tradeoff between locally contextual correlations and spatially separated correlations. Thus, our experiment provides evidence that entanglement is a particular manifestation of a more fundamental quantum resource.

DOI
10.1103/physrevlett.116.090401

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We report our experimental results on the no-disturbance principle, which imposes a fundamental monogamy relation on contextuality versus nonlocality. We employ a photonic qutrit-qubit hybrid to explore no-disturbance monogamy at the quantum boundary spanned by noncontextuality and locality inequalities. In particular, we realize the single point where the quantum boundary meets the no-disturbance boundary. Our results agree with quantum theory and satisfy the stringent monogamy relation thereby providing direct experimental evidence of a tradeoff between locally contextual correlations and spatially separated correlations. Thus, our experiment provides evidence that entanglement is a particular manifestation of a more fundamental quantum resource.
We show that the no-disturbance principle imposes a tradeoff between locally contextual correlations violating the Klyachko-Can-Biniciogˇlu-Shumovski inequality and spatially separated correlations violating the Clauser-Horne-Shimony-Holt inequality. The violation of one inequality forbids the violation of the other. We also obtain the corresponding monogamy relation imposed by quantum theory for a qutrit-qubit system. Our results show the existence of fundamental monogamy relations between contextuality and nonlocality that suggest that entanglement might be a particular form of a more fundamental resource.
The quantum no-disturbance principle imposes a fundamental monogamy relation on quantum contextuality and quantum nonlocality. We experimentally demonstrated the simulation of this monogamy relation on a ququart-qubit system using three NMR qubits. We constructed experimental tests of the violation of the Klyachko-Can-Binicioglu-Shumovski (KCBS) inequality and the Clauser-Horne-Shimony-Holt (CHSH) inequality. We measured the average CHSH and KCBS values at the single point where the quantum boundary meets the no-disturbance boundary, at which point the tradeoff inequality becomes an equality. The tradeoff relation is always satisfied, implying that the violation of either the KCBS or the CHSH inequality automatically forbids the violation of the other.
The Clauser-Horne-Shimony-Holt (CHSH) inequality and the Klyachko-Can-Binicioglu-Shumovski (KCBS) inequality present a tradeoff on the no-disturbance (ND) principle. Recently, the fundamental monogamy relation between contextuality and nonlocality in quantum theory has been demonstrated experimentally. Here we show that such a relation and tradeoff can also be simulated in classical optical systems. Using polarization, path and orbital angular momentum of the classical optical beam, in classical optical experiment we have observed the stringent monogamy relation between the two inequalities by implementing the projection measurement. Our results show the application prospect of the concepts developed recently in quantum information science to classical optical system and optical information processing.
Abstract Contextuality and entanglement are fundamental quantum resources for quantum information processing, and contextuality has been identified as a necessary precondition for entanglement. However, direct implementation of this connection in a realistic experiment remains to be demonstrated. In addition, previous experiments face practical challenges in explicitly satisfying the linear constraints required for contextuality tests. In this work, we present an experimental investigation of this relationship using polarization-entangled photons. First, remote state preparation arising from entanglement allows the required linear constraints to be satisfied structurally. Second, our results provide an operational demonstration of the relationship’s asymmetrical nature. While all four tested Bell states violate a general noncontextuality inequality, confirming they are all contextual resources, only a single Bell state violates the specific entanglement witness mapped from it. This work provides a proof-of-principle experimental implementation of the contextuality-entanglement connection and illustrates how remote state preparation can be used to realize the relevant linear constraints in this setting.
We report a state-independent experimental test of quantum contextuality of a single-photon qutrit. The experimental results demonstrate violations of an inequality originally formulated by Yu and Oh [Phys. Rev. Lett. 108, 030402 (2012)] and further optimized by Cabello et al. [Phys. Rev. A 85, 032108 (2012)]; this inequality is satisfied by all noncontextual hidden variable models and is violated by all qutrit states. Our experiment shows quantum contextuality of this nature in a most fundamental way: A way that is independent of state and unrelated to entanglement.
Quantum nonlocality can be revealed ``via local contextuality'' in qudit-qudit entangled systems with d>2d>2d>2, that is, through the violation of inequalities containing Alice-Bob correlations that admit a local description, and Alice-Alice correlations (between the results of sequences of measurements on Alice's subsystem) that admit a local (but contextual) description. A fundamental question to understand the respective roles of entanglement and local contextuality is whether nonlocality via local contextuality exists when the parties have only qubit-qubit entanglement. Here we respond affirmatively to this question. This result further clarifies the connection between contextuality and nonlocality and opens the door for observing nonlocality via local contextuality in actual experiments.