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Certification of high-dimensional entanglement generated in Hong-Ou-Mandel interference

Yuanyuan Chen, Sebastian Ecker, Jessica Bavaresco, Thomas Scheidl, Fabian Steinlechner, Marcus Huber, Rupert Ursin

Published Oct 17, 2019• 0 citations
OpenAlex

Abstract

Entanglement and quantum interference are key ingredients in a variety of quantum information processing tasks. Harnessing the generation and characterization of entanglement in high-dimensional state spaces is a necessary prerequisite towards practical quantum protocols. Here, we use quantum interference on a beam splitter to engineer hyperentanglement in polarization and discrete frequency degrees of freedom (DOF). We show how independent measurements of polarization and frequency DOF allow for both the verification and, strictly stronger requirement, also the certification of high-dimensional entanglement in the combined state space. These results may indicate new paths towards practical exploitation of entanglement stored in multiple degrees of freedom, in particular in the context of high-dimensional quantum information processing protocols.

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Entanglement and quantum interference are key ingredients in a variety of quantum information processing tasks. Harnessing the generation and characterization of entanglement in high-dimensional state spaces is a necessary prerequisite towards practical quantum protocols. Here, we use quantum interference on a beam splitter to engineer hyperentanglement in polarization and discrete frequency degrees of freedom (DOF). We show how independent measurements of polarization and frequency DOF allow for both the verification and, strictly stronger requirement, also the certification of high-dimensional entanglement in the combined state space. These results may indicate new paths towards practical exploitation of entanglement stored in multiple degrees of freedom, in particular in the context of high-dimensional quantum information processing protocols.
Entanglement and quantum interference are key ingredients in a variety of quantum information processing tasks. Harnessing the generation and characterization of entanglement in high-dimensional state spaces is a necessary prerequisite towards practical quantum protocols. Here, we use quantum interference on a beam splitter to engineer hyperentanglement in polarization and discrete frequency degrees of freedom (DOF). We show how independent measurements of polarization and frequency DOF allow for the verification of high-dimensional entanglement in the combined state space. These results may indicate new paths towards practical exploitation of entanglement stored in multiple degrees of freedom, in particular in the context of high-dimensional quantum information processing protocols.
Abstract High-dimensional quantum entanglement is currently one of the most prolific fields in quantum information processing due to its high information capacity and error resilience. A versatile method for harnessing high-dimensional entanglement has long been hailed as an absolute necessity in the exploration of quantum science and technologies. Here we exploit Hong-Ou-Mandel interference to manipulate discrete frequency entanglement in arbitrary-dimensional Hilbert space. The generation and characterization of two-, four- and six-dimensional frequency entangled qudits are theoretically and experimentally investigated, allowing for the estimation of entanglement dimensionality in the whole state space. Additionally, our strategy can be generalized to engineer higher-dimensional entanglement in other photonic degrees of freedom. Our results may provide a more comprehensive understanding of frequency shaping and interference phenomena, and pave the way to more complex high-dimensional quantum information processing protocols.
Hyperentanglement, the simultaneous and independent entanglement of quantum particles in multiple degrees of freedom, is a powerful resource that can be harnessed for efficient quantum information processing. In photonic systems, the two degrees of freedom (DOFs) often used to carry quantum and classical information are polarization and frequency, thanks to their robustness in transmission, both in free space and in optical fibers. Telecom-band hyperentangled photons generated in optical fibers are of particular interest because they are compatible with existing fiber-optic infrastructure and can be distributed over fiber networks with minimal loss. Here, we experimentally demonstrate the generation of telecom-band biphotons hyperentangled in both the polarization and frequency DOFs using a periodically poled silica fiber and observe entanglement concurrences above 0.95 for both polarization and frequency DOFs. Furthermore, by concatenating a Hong-Ou-Mandel interference test for frequency entanglement and full state tomography for polarization entanglement in a single experiment, we can demonstrate simultaneous entanglement in both the polarization and frequency DOFs. The states produced by our hyperentanglement source can enable protocols such as dense coding and high-dimensional quantum key distribution.
Quantum entanglement is a fundamental resource for secure information processing and communications. The canonical optical quantum information processing encodes a single qubit per photon, with remarkable demonstrations of secure quantum communications, linear optical quantum computing amongst others. Often the polarization qubit, a discrete variable with entangled Bell states, is used. Continuous variables such as energy-time modes and spatial modes, however, present a dramatically larger Hilbert space for quantum information processing. The high-dimensional entanglement capture more qubits per photon, enabling dramatically higher secure key rates over longer distances and with better error resilience. Here I will describe our results on high-dimensional entanglement in quantum frequency combs for dense quantum communications. We first demonstrate revival of the Hong-Ou-Mandel interferences, long postulated by theorists more than a decade ago, up to 19-dimensions and with visibilities up to 96.5%. The mode-locked two-photon state in high-dimensions is further witnessed through a stabilized Franson interferometer, as a generalized Bell’s inequality test and hyperentangled through multiple degrees-of-freedom. Entanglement revivals of the non-local interference at discrete time-bins are uncovered, up to 97.8% visibility, as a fundamental resource for dense secure information processing.
Abstract Higher dimensional Hilbert space along with ability to control multiple degrees of freedom of photon and entangle them has enabled new quantum protocols for various quantum information processing applications. Here, we propose a scheme to generate and control polarization-path-frequency entanglement using the operative elements required to implement a polarization-controlled quantum walk in the path (position) space and frequency domain. Hyperentangled states manifests in the controlled dynamics using an interferometric setup where half-wave plates, beam-splitters and frequency shifters such as those based on the electro-optic effect are used to manipulate the polarization, path and frequency degrees of freedom respectively. The emphasis is on utilizing the polarization to influence the movement to a specific value in the frequency and position space. Negativity between the subspaces is calculated to demonstrate the controllability of the entanglement between the three degrees of freedom and the effect of noise on the entanglement is modelled using the depolarizing channel. Progress reported with experimental demonstration of realization of quantum walk using quantum states of light makes quantum walks a practical approach to generate hyperentangled states.
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.