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arXiv:2207.09990 · Physical Review Applied

Entanglement Verification of Hyperentangled Photon Pairs

Christopher K. Zeitler, Joseph C. Chapman, Eric Chitambar, Paul G. Kwiat

Published Nov 9, 2022• 11 citations
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Abstract

We experimentally investigate the properties of hyperentangled states displaying simultaneous entanglement in multiple degrees of freedom and find that Bell tests beyond the standard Clauser-Horne-Shimony-Holt inequality can reveal a higher-dimensional nature in a device-independent way. Specifically, we show that hyperentangled states possess more than just simultaneous entanglement in separate degrees of freedom but also entanglement in a higher-dimensional Hilbert space. We also verify the steerability of hyperentangled quantum states by steering different photonic degrees of freedom.

DOI
10.1103/physrevapplied.18.054025

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We experimentally investigate the properties of hyperentangled states displaying simultaneous entanglement in multiple degrees of freedom and find that Bell tests beyond the standard Clauser-Horne-Shimony-Holt inequality can reveal a higher-dimensional nature in a device-independent way. Specifically, we show that hyperentangled states possess more than just simultaneous entanglement in separate degrees of freedom but also entanglement in a higher-dimensional Hilbert space. We also verify the steerability of hyperentangled quantum states by steering different photonic degrees of freedom.
We experimentally demonstrate the first quantum system entangled in every degree of freedom (hyperentangled). Using pairs of photons produced in spontaneous parametric down-conversion, we verify entanglement by observing a Bell-type inequality violation in each degree of freedom: polarization, spatial mode, and time energy. We also produce and characterize maximally hyperentangled states and novel states simultaneously exhibiting both quantum and classical correlations. Finally, we report the tomography of a 2 x 2 x 3 x 3 system (36-dimensional Hilbert space), which we believe is the first reported photonic entangled system of this size to be so characterized.
We demonstrate hybrid entanglement of photon pairs via the experimental violation of a Bell inequality with two different degrees of freedom (DOF), namely, the path (linear momentum) of one photon and the polarization of the other photon. Hybrid entangled photon pairs are created by spontaneous parametric down conversion and coherent polarization to path conversion for one photon. For that photon, path superposition is analyzed, and polarization superposition for its twin photon. The correlations between these two measurements give an SSS parameter of $S=2.653\ifmmode\pm\else\textpm\fi{}0.027$ in a Clauser-Horne-Shimony-Holt inequality and thus violate local realism for two different DOF by more than 24 standard deviations. This experimentally supports the idea that entanglement is a fundamental concept which is indifferent to the specific physical realization of Hilbert space.
We experimentally demonstrate the first quantum system entangled in every degree of freedom (hyper-entangled). Using pairs of photons produced in spontaneous parametric downconversion, we verify entanglement by observing a Bell-type inequality violation in each degree of freedom: polarization, spatial mode and time-energy. We also produce and characterize maximally hyper-entangled states and novel states simultaneously exhibiting both quantum and classical correlations. Finally, we report the tomography of a 2x2x3x3 system (36-dimensional Hilbert space), which we believe is the first reported entangled system of this size to be so characterized.
Multidimensional entangled photon states represent a useful resource for large-scale quantum communication networks. By leveraging multiple degrees of freedom (DoFs) of photons, the dimensionality of the Hilbert space can be expanded without increasing the number of particles, enhancing the efficiency of quantum information processing. Specifically, hyperentanglement, i.e. simultaneous entanglement across multiple DoFs, is robust against decoherence, thus providing strengthened performance in noisy quantum communication protocols with respect to n-photon quantum states [1].
Exploiting the simultaneous entanglement (hyperentanglement) in multiple degrees of freedom of an entangled photon pair increases the dimensionality of the Hilbert space for quantum information processing. However, the generation of hyperentangled photon pairs collinearly, while capable of high brightness, results in a smaller Hilbert space due to the two photons being in the same spatial mode. In this paper, we show that one can recover the full dimensionality of such hyperentanglement through a simple interference setup, similar to the time-reversed Hong-Ou-Mandel (TR-HOM) process. In contrast to the standard TR-HOM, we point out that a critical phase condition has to be satisfied in order to recover the hyperentanglement. We theoretically analyze the realization of this approach and discuss the feasibility of generating truly hyperentangled photon pairs. Our proposed approach does not require postselection and hence enables efficient hyperentangled photon pair generation for high-dimensional quantum applications.
Multi-dimensional entangled photon states represent an important resource in quantum communication networks. Specifically, hyperentangled states presenting simultaneous entanglement in several degrees of freedom (DoF) stand out for their noise resilience and information capacity. In this work, we demonstrate the generation of hyperentangled photon pairs in the time and frequency-bin domain by spontaneous four-wave mixing from the coherent driving of two integrated silicon microresonators. We demonstrate entanglement in each DoF by proving the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality by more than 27 standard deviations (STDs) in each reduced space. Genuine hyperentanglement is then assessed from the negativity of a hyperentanglement witness, which is verified by more than 60 STDs. These results mark the first, to the best of our knowledge, demonstration of time-frequency bin hyperentanglement in an integrated silicon photonic device.