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Optica

Experimental certification of quantum dimensions and irreducible high-dimensional quantum systems with independent devices

Yong-Nan Sun, Zhao‐Di Liu, Joseph Bowles, Geng Chen, Xiao-Ye Xu, Jian‐Shun Tang, Chuan‐Feng Li, Guang‐Can Guo

Published Jul 20, 2020• 15 citations
Publisher

Abstract

Dimensionality plays an important role in various information-theoretic tasks and can be seen as a key resource for quantum information processing. In this work, for the first time to the best of our knowledge, we report an experimental test of classical and quantum dimensions in a prepare-and-measure scenario through a nonlinear dimension witness (NDW), where the preparer and the measurer have no shared randomness. We propose a theoretical method to certify whether the generated states can be decomposed as products of lower dimensional states with the NDW, certify the dimension of the high-dimensional system, and identify whether the quantum system is irreducible in a unified picture in our experiment. To demonstrate the practicability of this method, we experimentally witness the generation of classical and quantum systems encoded in the high-dimensional orbital angular momentum (OAM) state under the effects of atmospheric turbulence. Our results show that this nonlinear dimension witness is highly robust and can be used in the presence of noise and low detection efficiency; hence, we estimate the dimension in our experiment in a detection-loophole-free manner through the NDW. We believe our work opens new avenues for dimension witnesses, especially for device-independent estimation of quantum systems and quantum communications.

DOI
10.1364/optica.396932

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Dimensionality plays an important role in various information-theoretic tasks and can be seen as a key resource for quantum information processing. In this work, for the first time to the best of our knowledge, we report an experimental test of classical and quantum dimensions in a prepare-and-measure scenario through a nonlinear dimension witness (NDW), where the preparer and the measurer have no shared randomness. We propose a theoretical method to certify whether the generated states can be decomposed as products of lower dimensional states with the NDW, certify the dimension of the high-dimensional system, and identify whether the quantum system is irreducible in a unified picture in our experiment. To demonstrate the practicability of this method, we experimentally witness the generation of classical and quantum systems encoded in the high-dimensional orbital angular momentum (OAM) state under the effects of atmospheric turbulence. Our results show that this nonlinear dimension witness is highly robust and can be used in the presence of noise and low detection efficiency; hence, we estimate the dimension in our experiment in a detection-loophole-free manner through the NDW. We believe our work opens new avenues for dimension witnesses, especially for device-independent estimation of quantum systems and quantum communications.
When increasing the dimensionality of quantum systems, high-dimensional quantum state certification becomes important in quantum information science and technology. However, how to certify ensembles of high-dimensional quantum states in a black-box scenario remains a challenging task. In this work, we report an experimental test of certifying ensembles of high-dimensional quantum states based on prepare-and-measure experiments with \textit{independent devices}, where the state preparation device and the measurement device have no shared randomness. In our experiment, the prepared quantum states are high-dimensional orbital angular momentum states of single photons, and both the preparation fidelity and the measurement fidelity are about 99.0%\%% for the six-dimensional quantum states. We also measure the crosstalk matrices and calculate the similarity parameter for up to ten dimensions. We not only experimentally certify the ensemble of high-dimensional quantum states in a semi-device-independent manner, but also experimentally investigate the effect of atmospheric turbulent noise on high-dimensional quantum state certification. Our experimental results clearly show that the certification of high-dimensional quantum states can still be achieved even under the influence of atmospheric turbulent noise. Our findings have potential implications in quantum certification and quantum random number generation.
Certifying quantum behavior from classically accessible data is essential for secure communication and scalable quantum technologies. While powerful certification methods such as Bell nonlocality and quantum steering exist, their implementation typically requires entanglement or additional assumptions, and experimental demonstrations mainly focus on low-dimensional systems. In minimal prepare-and-measure scenarios, where a sender encodes information into quantum states and a receiver performs a single measurement, robust certification becomes particularly challenging, especially in the presence of noise and in higher-dimensional Hilbert spaces. Here, we propose, design, and experimentally implement a protocol that certifies quantumness between two distant parties without the need for preshared resources or measurement incompatibility. The experiments are carried out using the orbital angular momentum degrees of freedom of single photons, chosen for providing increased dimensionality that is scalable. We demonstrate the robustness of the protocol through rank-stability analysis of the observed correlations, which enables the certification of non-classicality even in the presence of noise. Our results provide a practical route to validate high-dimensional quantum communication systems and open new possibilities for secure and dimension-efficient quantum information processing.
We report on a new class of dimension witnesses, based on quantum random access codes, which are a function of the recorded statistics and that have different bounds for all possible decompositions of a high-dimensional physical system. Thus, it certifies the dimension of the system and has the new distinct feature of identifying whether the high-dimensional system is decomposable in terms of lower dimensional subsystems. To demonstrate the practicability of this technique, we used it to experimentally certify the generation of an irreducible 1024-dimensional photonic quantum state. Therefore, certifying that the state is not multipartite or encoded using noncoupled different degrees of freedom of a single photon. Our protocol should find applications in a broad class of modern quantum information experiments addressing the generation of high-dimensional quantum systems, where quantum tomography may become intractable.
Abstract The certification of entanglement dimensionality is of great importance in characterizing quantum systems. Recently, it was pointed out that quantum correlation of high-dimensional states can be simulated with a sequence of lower-dimensional states. Such a problem may render existing characterization protocols unreliable—the observed entanglement may not be a truly high-dimensional one. Here, we introduce the notion of irreducible entanglement to capture its dimensionality that is indecomposable in terms of a sequence of lower-dimensional entangled systems. We prove this new feature can be detected in a measurement-device-independent manner with an entanglement witness protocol. To demonstrate the practicability of this technique, we experimentally apply it on a 3-dimensional bipartite state, and the result certifies the existence of irreducible (at least) 3-dimensional entanglement.
We characterize sets of fractional orbital angular momentum (OAM) modes of a light beam using unitary-invariant properties encoded by two-mode overlaps. Using basis-independent coherence and dimension witnesses, we experimentally certify, on a triple of fractional modes, both the presence of coherence and that the states necessarily span a space of dimension 3. We propose and implement a practical, fast experimental method to extract two-mode overlaps requiring only a single intensity image per interference pair. These results lay the groundwork for using fractional OAM states in high-dimensional quantum information protocols.
The use of high-dimensional systems for quantum communication opens interesting perspectives, such as increased information capacity and noise resilience. In this context, it is crucial to certify that a given quantum channel can reliably transmit high-dimensional quantum information. Here we develop efficient methods for the characterization of high-dimensional quantum channels. We first present a notion of dimensionality of quantum channels and develop efficient certification methods for this quantity. We consider a simple prepare-and-measure setup and provide witnesses for both a fully and a partially trusted scenario. In turn, we apply these methods to a photonic experiment and certify dimensionalities up to 59 for a commercial graded-index multimode optical fiber. Moreover, we present extensive numerical simulations of the experiment, providing an accurate noise model for the fiber and exploring the potential of more sophisticated witnesses. Our work demonstrates the efficient characterization of high-dimensional quantum channels, a key ingredient for future quantum communication technologies.