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arXiv:2209.09942 · Physical Review Letters

Contextuality as a Precondition for Quantum Entanglement

Martin Plávala, Otfried Gühne

Published Mar 7, 2024• 16 citations
arXivHTMLPDF

Abstract

Quantum theory features several phenomena which can be considered as resources for information processing tasks. Some of these effects, such as entanglement, arise in a nonlocal scenario, where a quantum state is distributed between different parties. Other phenomena, such as contextuality, can be observed if quantum states are prepared and then subjected to sequences of measurements. We use robust remote state preparation to connect the nonlocal and sequential scenarios and provide an intimate connection between different resources: We prove that entanglement in a nonlocal scenario can arise only if there is preparation and measurement contextuality in the corresponding sequential scenario and that the absence of entanglement implies the absence of contextuality. As a direct consequence, our result allows us to translate any inequality for testing preparation and measurement contextuality into an entanglement test; in addition, entanglement witnesses can be used to design novel contextuality inequalities.

DOI
10.1103/physrevlett.132.100201

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Quantum theory features several phenomena which can be considered as resources for information processing tasks. Some of these effects, such as entanglement, arise in a nonlocal scenario, where a quantum state is distributed between different parties. Other phenomena, such as contextuality, can be observed if quantum states are prepared and then subjected to sequences of measurements. We use robust remote state preparation to connect the nonlocal and sequential scenarios and provide an intimate connection between different resources: We prove that entanglement in a nonlocal scenario can arise only if there is preparation and measurement contextuality in the corresponding sequential scenario and that the absence of entanglement implies the absence of contextuality. As a direct consequence, our result allows us to translate any inequality for testing preparation and measurement contextuality into an entanglement test; in addition, entanglement witnesses can be used to design novel contextuality inequalities.
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 reveal that the entropic uncertainty relation with a quantum memory is able to intrinsically connect local generic contextuality addressed in the pioneering work by Spekkens and nonlocal quantum resources such as entanglement and Bell nonlocality. Based on the constructed optimal set for any given single-qubit state, we prove rigorously a faithful criterion to witness the generic contextuality in the scenario of local quantum state preparation. Furthermore, within the framework of quantum resource distribution, it is proved that there exist quantitative trade-off relations between local preparation contextuality and bipartite entanglement or Bell nonlocality in a shared quantum system, which are captured by two inequalities where the local and nonlocal quantum resources can coexist. The faithful criterion and quantitative inequalities are all experimentally testable, which are verified through two independent well-designed experiments on the Quafu quantum cloud platform.
Contextuality provides a unifying paradigm for nonclassical aspects of quantum probabilities and resources of quantum information. Unfortunately, most forms of quantum contextuality remain experimentally unexplored due to the difficulty of performing sequences of projective measurements on individual quantum systems. Here we show that two-point correlations between binary compatible observables are sufficient to reveal any form of contextuality. This allows us to design simple experiments that are more robust against imperfections and easier to analyze, thus opening the door for observing interesting forms of contextuality, including those requiring quantum systems of high dimensions. In addition, it allows us to connect contextuality to communication complexity scenarios and reformulate a recent result relating contextuality and quantum computation.
Contextuality provides a unifying paradigm for nonclassical aspects of quantum probabilities and resources of quantum information. Unfortunately, most forms of quantum contextuality remain experimentally unexplored due to the difficulty of performing sequences of projective measurements on individual quantum systems. Here we show that two-point correlations between binary compatible observables are sufficient to reveal any form of contextuality. This allows us to design simple experiments that are more robust against imperfections and easier to analyze, thus opening the door for observing interesting forms of contextuality, including those requiring quantum systems of high dimensions. In addition, it allows us to connect contextuality to communication complexity scenarios and reformulate a recent result relating contextuality and quantum computation.
Contextuality and measurement incompatibility are two fundamental aspects of nonclassicality, and their manifestations in observed quantum correlations are often deeply interconnected. Recently, measurement incompatibility has been studied in connection with nonlocality, particularly in terms of their robustness under various quantum channels. This line of investigation helps establish a connection between the channels that break nonlocality and those that break incompatibility. In this study, we focus on an asymmetric bipartite Bell scenario involving three and four inputs on Alice and Bob sides, respectively, with each of these inputs having dichotomous outcomes. Under the assumption of locality, the observed statistics in this asymmetric scenario obeys the Elegant Bell inequality (EBI). Here, we use a different version of the EBI that relies on the assumption of the preparation noncontextuality. By taking the violation of this noncontextual version of EBI as a witness of preparation contextuality we establish a connection between the channels that break contextuality and the channels that break triple-wise measurement incompatibility. Our results suggest that any channel which breaks EBI contextuality will also break Clauser-Horne-Shimony-Holt (CHSH) nonlocality; however, the reverse does not hold. We also show that a depolarising channel that breaks N-wise incompatibility can also break a certain form of contextuality, witnessed by a generalised inequality involving N measurements on one wing of a bipartite Bell scenario.
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.