## This new approach is applicable to any class of astronomical observations.

**Physicists have applied quantum information to the problem of direct observation of exoplanets. They showed that measurement in the quantum limit mode can reduce the likelihood of a false negative error, and also showed which of the existing methods for detecting new exoplanets can achieve this in practice. **

**Detecting new exoplanets using new methods: Everything you need to know**

### Detecting new exoplanets

Astronomers began to detect exoplanets relatively recently and today their number is about four and a half thousand. Most of these are detectable by transit photometry, and only about a percent can be seen directly. The reason for this is that the emission of light from exoplanets is weaker than the emission of a star next to them.

### Direct observations of new exoplanets

In direct observation of stellar systems, their images are collected in the focal plane of the telescope. Due to the diffraction limit, the image of celestial bodies turns out to be blurred, which inevitably leads to errors, both false positive (they saw the planet where it is not) and false negative (did not see the planet, although it is there). Due to the rarity of exoplanets, errors of the second type are much more critical, so astronomers try to avoid them in the first place.

### Quantum information theory

Physicists Zixin Huang of Macquarie University and Cosmo Lupo of Sheffield University decided to apply a quantum information theory approach to this problem. They took the parameter ε as a basis, which is equal to the ratio of the intensity of light scattered by an exoplanet to the intensity of light from the entire system and showed that in the limit of a small parameter, the quantum approach to estimating errors will have advantages over the classical one. The authors also showed in what types of measurements the quantum limit can be reached.

### False negative error

The probability of a false negative error is determined in information theory through the relative entropy, expressed in terms of the probabilities of encountering a photon on the screen for the cases of the presence and absence of an exoplanet.

### Lower probability of error

Physicists presented calculations for the classical and quantum relative entropies and found that if the distribution from a point source on the screen is Gaussian (normal), they depend on small ε in a quadratic and linear manner, respectively. In practice, this would mean that in the case of a weak signal from an exoplanet, a measurement that takes into account the quantum nature of light has a lower probability of error.

### Measurement approaches

The authors considered several measurement approaches that could reach the quantum limit. Having performed the appropriate calculations, they showed that this is possible in the spatial demultiplexing mode (SPADE) and in the inversion interferometry mode (SLIVER).

### Methods

The first method is based on decomposing the incoming light into spatial Hermite-Gauss modes and calculating the probabilities for each of them. It could be implemented in interferometers using holographic technology and multimode waveguides. The second method evaluates the influence of the parameter ε on the probability of obtaining one or another parity when the incoming signal is inverted. This mode can also be implemented in interferometers. In both cases, the measured relative entropy depends linearly on ε.

### Photon spread

Physicists have also investigated the effect of the statistical spread in the number of photons within a single mode, which characterizes classical equilibrium light, on the above estimates. It turned out that even a large number of photons in equilibrium light does not significantly increase the error.

### Weak optical signals

Moreover, astronomers most often deal with weak optical signals, which contain few photons. In this limit, the obtained expressions for the entropies practically coincide with the formulas derived by the authors at the very beginning.

### Detecting new exoplanets and identifying celestial objects

The researchers note that the developed approach is applicable not only to astronomical observations like detecting new exoplanets but in general to any class of problems where it is necessary to optically resolve one weak source against the background of another strong one. As an example, they cite the search for dimers in microscopy, as well as the identification of objects that are very close to each other.

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**Sources:**

• Huang, Z., & Lupo, C. (2021, September 23). *Quantum hypothesis testing for exoplanet detection*. Physical Review Letters.

• Stephens, M. (2021, September 23). *Finding exoplanets with Quantum Imaging*. Physics.