Measuring dimensionality and purity of high-dimensional entangled states

Isaac Nape (), Valeria Rodríguez-Fajardo, Feng Zhu, Hsiao-Chih Huang, Jonathan Leach and Andrew Forbes
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Isaac Nape: University of the Witwatersrand
Valeria Rodríguez-Fajardo: University of the Witwatersrand
Feng Zhu: Heriot-Watt University
Hsiao-Chih Huang: National Taiwan University
Jonathan Leach: Heriot-Watt University
Andrew Forbes: University of the Witwatersrand

Nature Communications, 2021, vol. 12, issue 1, 1-8

Abstract: Abstract High-dimensional entangled states are promising candidates for increasing the security and encoding capacity of quantum systems. While it is possible to witness and set bounds for the entanglement, precisely quantifying the dimensionality and purity in a fast and accurate manner remains an open challenge. Here, we report an approach that simultaneously returns the dimensionality and purity of high-dimensional entangled states by simple projective measurements. We show that the outcome of a conditional measurement returns a visibility that scales monotonically with state dimensionality and purity, allowing for quantitative measurements for general photonic quantum systems. We illustrate our method using two separate bases, the orbital angular momentum and pixels bases, and quantify the state dimensionality by a variety of definitions over a wide range of noise levels, highlighting its usefulness in practical situations. Importantly, the number of measurements needed in our approach scale linearly with dimensions, reducing data acquisition time significantly. Our technique provides a simple, fast and direct measurement approach.

Date: 2021
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DOI: 10.1038/s41467-021-25447-0

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