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arXiv:1306.0096 · Proceedings of the National Academy of Sciences

Generation and confirmation of a (100 × 100)-dimensional entangled quantum system

Mario Krenn, Marcus Huber, Robert Fickler, Radek Łapkiewicz, Sven Ramelow, Anton Zeilinger

Published Mar 27, 2014• 330 citations
arXivHTMLPDF

Abstract

Entangled quantum systems have properties that have fundamentally overthrown the classical worldview. Increasing the complexity of entangled states by expanding their dimensionality allows the implementation of novel fundamental tests of nature, and moreover also enables genuinely new protocols for quantum information processing. Here we present the creation of a (100 × 100)-dimensional entangled quantum system, using spatial modes of photons. For its verification we develop a novel nonlinear criterion which infers entanglement dimensionality of a global state by using only information about its subspace correlations. This allows very practical experimental implementation as well as highly efficient extraction of entanglement dimensionality information. Applications in quantum cryptography and other protocols are very promising.

DOI
10.1073/pnas.1402365111

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Entangled quantum systems have properties that have fundamentally overthrown the classical worldview. Increasing the complexity of entangled states by expanding their dimensionality allows the implementation of novel fundamental tests of nature, and moreover also enables genuinely new protocols for quantum information processing. Here we present the creation of a (100 × 100)-dimensional entangled quantum system, using spatial modes of photons. For its verification we develop a novel nonlinear criterion which infers entanglement dimensionality of a global state by using only information about its subspace correlations. This allows very practical experimental implementation as well as highly efficient extraction of entanglement dimensionality information. Applications in quantum cryptography and other protocols are very promising.
Entangled quantum systems have properties that have fundamentally overthrown the classical worldview. Increasing the complexity of entangled states by expanding their dimensionality allows the implementation of novel fundamental tests of nature, and moreover also enables genuinely new protocols for quantum information processing. Here we present the creation of a (100x100)-dimensional entangled quantum system, using spatial modes of photons. For its verification we develop a novel nonlinear criterion which infers entanglement dimensionality of a global state by using only information about its subspace correlations. This allows very practical experimental implementation as well as highly efficient extraction of entanglement dimensionality information. Applications in quantum cryptography and other protocols are very promising.
Complex transverse spatial modes of photons are very interesting for both, foundations and applications of quantum information. In a first experiment, we generate two-dimensional bi-partite entanglement where each photon carries an orbital angular momentum of a quantum number up to 300. Secondly, we demonstrate (100 × 100)-dimensional entanglement, using again the spatial modes of photons and a novel nonlinear criterion which uses only information about two-dimensional subspace correlations. In a third test, we increase the complexity of the state by entangling ”vector photons” that show a transverse varying polarization. Thereby, we demonstrate a surprising property: Such photons can be both entangled and not entangled in polarization depending on their transverse spatial position.
This paper proposes a novel approach to verifying quantum entanglement with significantly improved fidelity compared to traditional Bell tests. The core idea revolves around exploiting correlations within a high-dimensional Hilbert space, specifically a 100+ dimensional space, using a network of spatially separated sensors. Each sensor measures a correlated set of quantum states. Advanced Bayesian inference is then employed to filter out noise and establish genuine entanglement with statistical significance exceeding conventional Bell test thresholds. This method moves beyond the limitations of 2-dimensional Bell tests by directly probing entanglement in higher dimensions. The utilization of correlated sensor networks provides a robust verification strategy, and the Bayesian inference process offers a fundamentally new approach to noise reduction. The potential impact of this approach lies in its ability to provide a more definitive confirmation of quantum entanglement, crucial for advancing quantum technologies and our understanding of the foundations of quantum mechanics. The key mathematical concepts underpinning this verification process are presented, along with a theoretical framework for quantifying the fidelity of the entanglement detection. ---
The quantum world differs from our classical experience in many ways. Perhaps most curious is the phenomenon of quantum entanglement, where measuring the state of one particle can instantaneously define the state of another, even though the second particle is arbitrarily distant. For much of the 20th century, it was debated whether entanglement really exists. The issue was quantified by Bell’s formulation of the Bell inequality (1), and the subsequent flurry of experiments by Clauser, Aspect, and others, demonstrating that quantum entanglement was real (2⇓–4). All of these early tests were applied to systems where the measured state of one particle can only take one of two values, but such systems are not representative of the wider world. In PNAS, Krenn et al. derive a new entanglement test for systems where the measured state can take on one of many values (Fig. 1) (5). The authors apply their test to the spatial structure (i.e., state) of two separated photons. Krenn et al. confirmed that the photons are entangled over at least 100 of these spatial states. This large number of states allows entanglement in higher dimensions, which can increase both the security of communication and the efficiency of computing protocols (6).
Most of the attention given to continuous variable systems for quantum information processing has traditionally been focused on Gaussian states. However, non-Gaussianity is an essential requirement for universal quantum computation and entanglement distillation, and can improve the efficiency of other quantum information tasks. Here we report the experimental observation of genuine non-Gaussian entanglement using spatially entangled photon pairs. The quantum correlations are invisible to all second-order tests, which identify only Gaussian entanglement, and are revealed only under application of a higher-order entanglement criterion. Thus, the photons exhibit a variety of entanglement that cannot be reproduced by Gaussian states.
Spatially entangled light has proven to be a critical resource in high-dimensional quantum information applications such as quantum cryptography, quantum sensing, and quantum computing. However, progress in the generation of arbitrary spatially entangled states for these protocols via spontaneous parametric down-conversion has been hindered due to the complex relationship between the nonlinear coupling and the generated quantum state. Here, we employ an inverse-design algorithm for the generation of non-trivial maximally entangled bi-photon qubit and qutrit states in the azimuthal index via spontaneous parametric down-conversion. These states are obtained by shaping the pump spatial distribution as a superposition of Laguerre-Gaussian radial modes. The generated bi-photon states are experimentally characterized through quantum state tomography, with their entanglement verified by breaking generalized Bell inequalities. Finally, we performed a proof-of-principle experiment demonstrating the potential utility of the inverse-designed states in entanglement-based quantum key distribution protocols, measuring quantum error rates of 3.95% and 7.03% for the generated qubit and qutrit states, respectively. Our results validate the inverse-design model in a free-space optical setup and pave the way for high-dimensional spatial-mode entangled state design and generation for quantum network applications.