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Conference on Lasers and Electro-Optics

Certification of high-dimensional entanglement and Einstein-Podolsky-Rosen steering with quantum memory

Mateusz Mazelanik, Michał Dąbrowski, Michal P. Parniak, Adam Leszczyński, Michał Lipka, Wojciech Wasilewski

Published Jan 1, 2018• 0 citations
Publisher

Abstract

We experimentally generate a spatially-entangled state using a Raman multimode quantum memory setup and characterize it with the entropic EPR-steering inequality. We obtain genuine violation of 1.06 ± 0.05 bits and certify entanglement of formation of at least 0.70 ± 0.04 ebits.
DOI
10.1364/cleo_at.2018.jth2a.28

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The advent of complex, structured, and high-dimensional entangled states brings both new possibilities for experimental and theoretical scenarios and new challenges for the generation and characterization of such states. In particular, spatially structured photonic states offer applications in quantum imaging, information processing, and quantum key distribution. Here we experimentally generate a spatially entangled high-dimensional state composed of at least 10 Schmidt modes in a quantum memory setup and perform characterization using the entropic Einstein-Podolsky-Rosen (EPR)-steering inequality, yielding a genuine violation of $1.06\ifmmode\pm\else\textpm\fi{}0.15$ bits. The entanglement of formation of at least $0.70\ifmmode\pm\else\textpm\fi{}0.15$ ebit for the measured noisy state is certified using the entropic witness method. We point out and solve the difficulties in estimating the entropy, achieving characterization of the high-dimensional entangled state with highly undersampled data. Finally, the practical supremacy of the entropic EPR-steering witness over a variance-based witness is demonstrated for a wide class of states typical in an experimental scenario, giving prospects for EPR-steering demonstrations and applications in noisy systems or with lossy quantum channels.
Einstein-Podolsky-Rosen (EPR) steering, as a new form of nonlocality, stands between entanglement and Bell nonlocality, implying promising applications for quantum information tasks. The problem of detecting EPR steering plays an important role in characterization of quantum nonlocality. Despite some significant progress, one still faces a practical issue: how to detect EPR steering in an experimentally friendly fashion. Resorting to an EPR steering inequality, one is required to apply a strategy as efficiently as possible for any selected measurement settings on the two subsystems, one of which may not be trusted. Inspired by the recent powerful linear criteria proposed by Saunders et al. [D. J. Saunders, S. J. Jones, H. M. Wiseman, and G. J. Pryde, Nat. Phys. 6, 845 (2010).], we present an optimized method of certifying steering for an arbitrary-dimensional state in a cost-effective manner. We provide a practical way to signify steering via only a few settings to optimally violate the steering inequality. Our method leads to steering detections in a highly efficient way, and can be performed with any number of settings, for an arbitrary bipartite mixed state, which can reduce experimental overheads significantly.
In a measurement-device-independent or quantum-refereed protocol, a referee can verify whether two parties share entanglement or Einstein-Podolsky-Rosen (EPR) steering without the need to trust either of the parties or their devices. The need for trusting a party is substituted by a quantum channel between the referee and that party, through which the referee encodes the measurements to be performed on that party's subsystem in a set of non-orthogonal quantum states. In this work, an EPR-steering inequality is adapted as a quantum-refereed EPR-steering witness, and the trust-free experimental verification of higher dimensional quantum steering is reported via preparing a class of entangled photonic qutrits. Further, with two measurement settings, we extract 1.106±0.0231.106\pm0.0231.106±0.023 bits of private randomness from our observed data, which surpasses the one-bit limit for qubit systems. Our results advance research on quantum information processing tasks beyond qubits.
The Einstein-Podolsky-Rosen (EPR) steering is an intermediate quantum nonlocality between entanglement and Bell nonlocality, which plays an important role in quantum information processing tasks. In the past few years, the investigations concerning the EPR steering have been demonstrated in a series of experiments. However, these studies rely on the relevant steering inequalities and the choices of measurement settings. Here, we experimentally verify the EPR steering via entanglement detection without using any steering inequality and measurement setting. By constructing two new states from a two-qubit state, we observe the EPR steering by detecting the entanglement of these new states. The results show that the entanglement of the newly constructed states can be regarded as an unusual kind of steering witness for these states. Compared to the results of Xiao et al. [Phys. Rev. Lett. 118, 140404 (2017)], we find that the ability to detect the EPR steering in our scenario is stronger than that of two-setting projective measurements, which can observe more steerable states. Hence, our demonstrations can deepen the understanding of the connection between the EPR steering and entanglement.
Einstein-Podolsky-Rosen steering is an intermediate relationship between entanglement and Bell nonlocality in the hierarchical structure of quantum nonlocality. To certify the steerability of the entangled state, Mermin steering inequality is supposed to be violated by exceeding the inequality bound of 2. We present an experimental generation of post-selected three-photon entangled states and witness a maximal violation of the inequality up to 3.50±0.05. In the context of observing the maximal violation of Mermin steering inequality which requires measuring on the GHZ state, we derive a tight lower bound on the GHZ-fidelity that can be certified from the Mermin steering inequality violation. From this bound, it follows that the violation of Mermin steering inequality by 3.5 certifies the GHZ-fidelity of 78.66% at least. On the other hand, the above maximal violation of Mermin steering inequality observed in our experimental setup is produced by a post-selected entangled state having the GHZ-fidelity of 87.25 ± 0.34% through quantum tomography.