Bell's theorem states that no local hidden-variable model is compatible with quantum mechanics. Surprisingly, even if we release the locality constraint, certain nonlocal hidden-variable models, such as the one proposed by Leggett, may still be at variance with the predictions of quantum physics. Here, we report an experimental test of Leggett's nonlocal model with solid-state spins in a diamond nitrogen-vacancy center. We entangle an electron spin with a surrounding weakly coupled $^{13}\mathrm{C}$ nuclear spin and observe that the entangled states violate Leggett-type inequalities by more than four and seven standard deviations for six and eight measurement settings, respectively. Our experimental results are in full agreement with quantum predictions and violate Leggett's nonlocal hidden-variable inequality with a high level of confidence.
Bell's theorem states that no local hidden-variable model is compatible with quantum mechanics. Surprisingly, even if we release the locality constraint, certain nonlocal hidden-variable models, such as the one proposed by Leggett, may still be at variance with the predictions of quantum physics. Here, we report an experimental test of Leggett's nonlocal model with solid-state spins in a diamond nitrogen-vacancy center. We entangle an electron spin with a surrounding weakly coupled 13C nuclear spin and observe that the entangled states violate Leggett-type inequalities by more than four and seven standard deviations for six and eight measurement settings, respectively. Our experimental results are in full agreement with quantum predictions and violate Leggett's nonlocal hidden-variable inequality with a high level of confidence.
According to Bell’s theorem, every theory based on local realism is at variance with certain predictions of quantum mechanics. A theory that maintains realism but abandons reliance on locality, which has been proposed by Leggett, is incompatible with experimentally observable quantum correlations. In our experiment correlation measurements of spin-energy entangled single-neutrons violate a Leggett-type inequality by more than 7.6 standard deviations. The experimental data falsify the contextual realistic model and are fully in favor of quantum mechanics.
Leggett inequality states that nonlocal hidden-variable models might still be incompatible with the predictions of quantum physics. However, its theoretical and experimental demonstration is only in the scenario of 2-dimensional maximally entangled systems. An open question remains as to whether the Leggett inequality can be violated by nonmaximally entangled states. Here, we answer this question both in theory and experiment. Specifically, from the point of view of geometry, we theoretically map the problem of maximizing the correlation measure in the Leggett inequality to maximizing the sum of an ellipse’s diameter and semi-diameter axes, accordingly, demonstrating that the violation of the Leggett inequality requires a more robust entanglement than that of Bell’s theory. Experimentally, by leveraging the controllable photonic orbital angular momentum entanglement, we demonstrate the violation of Leggett-type inequalities by more than 8.7 and 4.5 standard deviations under concurrence C = 0.95 and 0.9, respectively. Our observations indicate that, the requirement for quantum correlation should be increased to exclude a particular class of non-local hidden variable theories that abide by Leggett’s model, providing insights into the boundaries of quantum correlation and the limitations imposed by non-local hidden variables.
According to Bell's theorem, no theory based on the joint assumption of realism and locality can reproduce certain predictions of quantum mechanics. Another class of realistic models, proposed by Leggett, that demands realism but abandons reliance on locality, is predicted to be in conflict with quantum mechanics. In this paper, we report on an experimental test of a contextual realistic model analogous to the model of Leggett performed with matter waves, more precisely with neutrons. Correlation measurements of the spin-energy entangled single-particle system show violation of a Leggett-type inequality by more than 7.6 standard deviations. Our experimental data falsify the contextual realistic model and are fully in favor of quantum mechanics.
We report the experimental violation of Leggett-type inequalities for a hybrid entangled state of spin and orbital angular momentum of a single photon. These inequalities give a physical criterion to verify the possible validity of a class of hidden-variable theories, originally named ``crypto nonlocal,'' that are not excluded by the violation of Bell-type inequalities. In our case, the tested theories assume the existence of hidden variables associated with independent degrees of freedom of the same particle, while admitting the possibility of an influence between the two measurements, i.e., the so-called contextuality of observables. We observe a violation of the Leggett inequalities for a range of experimental inputs, with a maximum violation of seven standard deviations, thus ruling out this class of hidden-variable models with a high level of confidence.
Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for some realistic models with hidden variables. There are, however, two powerful theorems against the hidden-variable theories showing that certain quantum features cannot be reproduced based on two rationale premises of classicality, the Bell theorem, and noncontextuality, due to Bell, Kochen and Specker (BKS) . Tests of the Bell inequality and the BKS theorem are both of fundamental interests and of great significance . The Bell theorem has already been experimentally verified extensively on many different systems , while the quantum contextuality, which is independent of nonlocality and manifests itself even in a single object, is experimentally more demanding. Moreover, the contextuality has been shown to play a critical role to supply the `magic' for quantum computation, making more extensive experimental verifications in potential systems for quantum computing even more stringent. Here we report an experimental verification of quantum contextuality on an individual atomic nuclear spin-1 system in solids under ambient condition. Such a three-level system is indivisible and thus the compatibility loophole, which exists in the experiments performed on bipartite systems, is closed. Our experimental results confirm that the quantum contextuality cannot be explained by nonlocal entanglement, revealing the fundamental quantumness other than locality/nonlocality within the intrinsic spin freedom of a concrete natural atomic solid-state system at room temperature.
In this thesis we experimentally investigate quantum nonlocality: entangled states of spatially separated objects. Entanglement is one of the most striking consequences of the quantum formalism developed in the 1920's; the predicted outcomes of independent measurements on entangled objects reveal strong correlations that cannot be explained by classical physics. Early on, such predictions led physicists to doubt the validity and completeness of quantum theory. At the same time, entanglement is a key resource for applications in quantum information processing and a pre-requisite for many tasks in quantum communication and computation. This thesis attempts to answer two application driven questions: Firstly, can we generate useful entangled states of solid state spins for applications in quantum information processing? Secondly, can we use such entangled states as a resource to teleport an unknown quantum state? Finally, we ask a foundational question: Are our entangled states indeed inconsistent with the classical notions of free choice, locality and realism? Can we prove this experimentally, under the minimal assumptions of a loophole-free Bell test? To answer these questions we use single spins in ultra-pure diamonds. In particular, we use the electronic and nuclear spins associated with single nitrogen-vacancy (NV) defects. The NV centre is a point defect in diamond, consisting of a substitutional nitrogen (N) atom and a neighbouring missing carbon atom (vacancy, V). The NV centre possesses bound electronic states, whose energy levels lie well within the bandgap of the diamond host and whose spin degree of freedom can be used as a quantum bit (qubit). Because of the large diamond bandgap and the 99% spin free carbon-12 environment, the electronic spin qubit has exceptional coherence properties even at room temperature. Optical and microwave fields allow control of the electronic spin, which in turn allows control of nearby nuclear spins (the host nitrogen nuclear spin, and nearby carbon-13 spins). At liquid helium temperatures, spin-preserving optical transitions provide a powerful optical interface to the electronic spin, allowing, for example, projective readout of the spin state. By employing a protocol where entanglement is heralded by the detection of a single photon from each of two NV centres in diamonds separated by three metres, we find we can answer the first question in the affirmative. We show for the first time heralded entanglement between solid state quantum systems separated by a human-scale distance. Then, by combining the heralded entanglement with a deterministic local Bell state measurement and fast feed-forward, we show for the first time unconditional quantum teleportation over human-scale distances. We teleport an unknown quantum state from a nuclear spin in one diamond to an electronic spin in a diamond three meters away. Finally, by employing techniques from the previous experiments, we implement the first loophole-free Bell test. We separate two diamonds by 1.3 kilometres and optimize all operational fidelities, collection efficiencies and rates. This allows us to generate heralded entanglement between them approximately once an hour. The distance provides us with time to read out the electronic spin state in each diamond, faster than any lightlike signal could travel between them. The high-fidelity entangled state preparation and spin readout are sufficient to violate the Clauser-Horne-Shimony-Holt Bell-inequality. Combined with fast random number generators and a robust statistical analysis, we find a significant rejection of the local-realist hypothesis, without requiring additional experimental assumptions. The results in this thesis open the door to various applications in quantum information processing. In particular, a remote photonic entangling operation may enable future quantum networks. In such a network the nodes would be formed by the NV centre's combined electronic and nuclear spin register. The nodes would be linked by photonic entanglement operations. Such a network could be used for long distance secure communication, provide a connection between separated quantum computers, or form the basis of a fault tolerant quantum computer by itself. Furthermore, a loophole-free Bell test demonstrates the possibility to do device independent randomness generation and key distribution, that could form the basis for future secure communication channels.