High-Dimensional Pixel Entanglement: Efficient Generation and Certification

Natalia Herrera Valencia,Will Mccutcheon,Matej Pivoluska,Vatshal Srivastav,Mehul Malik,Nicolai Friis,Marcus Huber

doi:10.22331/q-2020-12-24-376

Abstract

Photons offer the potential to carry large amounts of information in their spectral, spatial, and polarisation degrees of freedom. While state-of-the-art classical communication systems routinely aim to maximize this information-carrying capacity via wavelength and spatial-mode division multiplexing, quantum systems based on multi-mode entanglement usually suffer from low state quality, long measurement times, and limited encoding capacity. At the same time, entanglement certification methods often rely on assumptions that compromise security. Here we show the certification of photonic high-dimensional entanglement in the transverse position-momentum degree-of-freedom with a record quality, measurement speed, and entanglement dimensionality, without making any assumptions about the state or channels. Using a tailored macro-pixel basis, precise spatial-mode measurements, and a modified entanglement witness, we demonstrate state fidelities of up to 94.4% in a 19-dimensional state-space, entanglement in up to 55 local dimensions, and an entanglement-of-formation of up to 4 ebits. Furthermore, our measurement times show an improvement of more than two orders of magnitude over previous state-of-the-art demonstrations. Our results pave the way for noise-robust quantum networks that saturate the information-carrying capacity of single photons.

Highlights

Quantum entanglement plays a pivotal role in the development of quantum technologies, resulting in revolutionary concepts in quantum communication such as superdense coding [1] and device-independent se-In order to make full use of the potential of highdimensional entanglement, it is of key importance to achieve the certification of entanglement with as few measurements as possible
We demonstrate the speed of our measurement technique, which is enabled by the use of phase-only pixel-basis holograms and our entanglement witness that allows the use of any two pixel mutually unbiased bases (MUBs) for certifying entanglement
We have demonstrated the certification of photonic high-dimensional entanglement in the transverse position-momentum degree-of-freedom with a record quality, measurement time, and entanglement dimensionality

Summary

Introduction

Quantum entanglement plays a pivotal role in the development of quantum technologies, resulting in revolutionary concepts in quantum communication such as superdense coding [1] and device-independent se-In order to make full use of the potential of highdimensional entanglement, it is of key importance to achieve the certification of entanglement with as few measurements as possible. More efficient tools for quantifying high-dimensional entanglement involve entanglement witnesses that use semi-definite programming [16], matrix completion techniques [17], or compressed sensing [18]. In this context, it is crucial to certify entanglement without compromising the security and validity of the applications by introducing assumptions on the state, e.g., purity of the generated state [19] or conservation of quantities [20]. Recent work has shown how measurements in mutually unbiased bases (MUBs) allow the efficient certification of high-dimensional entanglement [21, 22], without any such assumptions on the underlying quantum state. We employ and extend this method to improve upon the quality and speed of high-dimensional entanglement certification

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