# What is the math behind quantum entanglement

## Viennese researchers find a completely new concept for measuring quantum entanglement

Thanks to the entanglement of quantum particles, the vision of a completely tap-proof transmission of information is becoming more and more within reach. If a message encrypted with the help of this quantum physical phenomenon is transmitted, eavesdropping would not only have to crack the transmission channel itself, but also circumvent the laws of physics, which ensure that every attempt to intercept the message can be detected immediately due to the entanglement of the particles.

In the last few years in particular, research in the field of this secure quantum communication has made great strides. In particular, it was possible to use the so-called multidimensional entanglement of quantum particles to encode significantly larger amounts of information than was possible in the past.

However, there are still some hurdles to overcome before this technology can be used in practice. One of these concerns the lack of efficient measurement methods that are required for the detection of a multidimensional entanglement between quantum particles: the more information can be transported with quantum particles, the more measurements are necessary, which has so far severely limited the practical use of high-dimensional entanglement.

Two questions, many answers

Researchers at the Institute for Quantum Optics and Quantum Information (IQOQI) Vienna of the Austrian Academy of Sciences around Marcus Huber have now been able to find a way out of this situation. The interdisciplinary team of researchers from theoretical physics, experimental physics, mathematics and computer science developed a new method for the efficient detection of high-dimensional quantum entanglement and was able to confirm this successfully in experiments, as the team has now published in the specialist journal "Nature Physics" portrays.

First, the researchers approached the problem from a mathematical perspective. On the basis of so-called pairwise complementary measurements, they succeeded in drastically reducing the number of measurements required to prove a high-dimensional entanglement: While every single conventional measurement on a quantum system often only yields a yes or no, measurements are also possible that provide significantly more answers deliver.

But even with such measurements, the more dimensions are involved, the more questions one would have to ask. The ÖAW researchers therefore identified a mathematical property of two special measurement settings. With these it was then possible for them to receive a large number of answers, which in turn can clearly determine the existence of an entanglement. “We were able to find the answer to all sorts of questions about the state of quantum particles with just two questions,” explains group leader Marcus Huber.

Experiment confirms concept

The team then provided experimental proof of this concept in the laboratory of the IQOQI Vienna of the Austrian Academy of Sciences. For this, the experimental physicist Mehul Malik resorted to light particles that were entangled in high dimensions via their angular momentum.

These light particles or photons were subjected to the new type of measurement and the scientists were able to confirm the high-dimensional entanglement with the data obtained. The highlight: "While hundreds to thousands of measurement settings were needed for such an experiment to prove the high-dimensional entanglement, we managed with just two," says OeAW quantum physicist Jessica Bavaresco, first author of the publication in "Nature Physics".

The advantage of the new measuring method is not only in the drastically increased efficiency. At the same time, it proves to be robust against disturbances and to be much safer than previous methods that always had to make assumptions about the system to be measured. All in all, the researchers are convinced that the new measurement concept opens up a multitude of applications that can massively simplify future research on high-dimensional quantum lines.

Marcus Huber

Institute for Quantum Optics and Quantum Information Vienna

Austrian Academy of Sciences

1090 Vienna, Boltzmanngasse 5

T + 43-4277-29562

[email protected]

"Measurements in two bases are sufficient for certifying high-dimensional entanglement", Jessica Bavaresco, Natalia Herrera Valencia, Claude Klöckl, Matej Pivoluska, Paul Erker, Nicolai Friis, Mehul Malik and Marcus Huber, Nature Physics, 2018.

DOI:

https://dx.doi.org/10.1038/s41567-018-0203-z

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