# Coplanar Antenna Design for Microwave Entangled Signals Propagating in Open Air

Tasio Gonzalez-Raya1,2 and Mikel Sanz1,2,3,4

1Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
2EHU Quantum Center, University of the Basque Country UPV/EHU
3Basque Center for Applied Mathematics (BCAM), Alameda de Mazarredo 14, 48009 Bilbao, Basque Country, Spain
4IKERBASQUE, Basque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Spain

### Abstract

Open-air microwave quantum communication and metrology protocols must be able to transfer quantum resources from a cryostat, where they are created, to an environment dominated by thermal noise. Indeed, the states carrying such quantum resources are generated in a cryostat characterized by a temperature $T_\text{in} \simeq 50$ mK and an intrinsic impedance $Z_\text{in} = 50 \, \Omega$. Then, an antenna-like device is required to transfer them with minimal losses into open air, characterized by an intrinsic impedance of $Z_\text{out} = 377 \, \Omega$ and a temperature $T_\text{out} \simeq 300$ K. This device accomplishes a smooth impedance matching between the cryostat and the open air. Here, we study the transmission of two-mode squeezed thermal states, developing a technique to design the optimal shape of a coplanar antenna to preserve the entanglement. Based on a numerical optimization procedure, we find the optimal shape of the impedance, and we propose a functional ansatz to qualitatively describe this shape. Additionally, this study reveals that the reflectivity of the antenna is very sensitive to this shape, so that small changes dramatically affect the outcoming entanglement, which could have been a limitation in previous experiments employing commercial antennae. This work is relevant in the fields of microwave quantum sensing and quantum metrology with special application to the development of the quantum radar, as well as any open-air microwave quantum communication protocol.

In the last years, the advances in controllability, scalability and coherence of superconducting circuits have led to the blossoming of the propagating quantum microwave technology. This had a deep  impact on the fields of quantum communication and quantum sensing. Indeed, an improved toolbox of quantum devices, comprising JPAs, HEMTs, photodetectors and photocounters, has benefited  experiments in these fields, which are now in the verge of moving into free space. This is supported by early experiments on the direction of a quantum radar in open air by the groups of C. M. Wilson and J. M. Fink, as well as some theoretical proposals for open-air microwave quantum communication.

These experiments and proposals rely on effective entanglement distribution. In the microwave regime, entangled states are generated in a cryostat at temperatures below 50 mK in order to reduce thermal noise. The impedance employed in superconducting circuit technology is 50 Ω, since this is adapted to available classical control electronics. In contrast, the impedance in open air is around 377 Ω and the temperature approximately 300 K. Then, the wireless transmission of quantum signals requires an antenna, essentially an inhomogeneous medium that performs the impedance matching while keeping the entanglement properties. Remarkably, the efficiency of the entanglement transfer is extremely sensible to the impedance function inside the cavity, and consequently, to the shape of the antenna. In our manuscript, we obtain the optimal shape of a coplanar antenna especially  designed for entanglement distribution in open air and show its high sensitivity to small imperfections in the shape of the antenna. For instance, following our calculations, the use of commercial antennae in the aforementioned experiments towards quantum radars has dramatically contributed to the unsuccessful entanglement distribution, since deviation over 3% from the optimal shape completely destroy quantum correlations.

This work has applications in wireless microwave quantum communication protocols requiring efficient entanglement distribution techniques, as well as in quantum sensing and quantum metrology protocols working in the microwave regime, especially for quantum radars.

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### Cited by

[1] Mateo Casariego, Yasser Omar, and Mikel Sanz, "Bi‐Frequency Illumination: A Quantum‐Enhanced Protocol", Advanced Quantum Technologies 5 11, 2100051 (2022).

[2] Tasio Gonzalez-Raya, Mateo Casariego, Florian Fesquet, Michael Renger, Vahid Salari, Mikko Möttönen, Yasser Omar, Frank Deppe, Kirill G. Fedorov, and Mikel Sanz, "Open-Air Microwave Entanglement Distribution for Quantum Teleportation", Physical Review Applied 18 4, 044002 (2022).

[3] Mateo Casariego, Emmanuel Zambrini Cruzeiro, Stefano Gherardini, Tasio Gonzalez-Raya, Rui André, Gonçalo Frazão, Giacomo Catto, Mikko Möttönen, Debopam Datta, Klaara Viisanen, Joonas Govenius, Mika Prunnila, Kimmo Tuominen, Maximilian Reichert, Michael Renger, Kirill G. Fedorov, Frank Deppe, Harriet van der Vliet, A. J. Matthews, Yolanda Fernández, R. Assouly, R. Dassonneville, B. Huard, Mikel Sanz, and Yasser Omar, "Propagating Quantum Microwaves: Towards Applications in Communication and Sensing", arXiv:2205.11424, (2022).

[4] Florian Fesquet, Fabian Kronowetter, Michael Renger, Qiming Chen, Kedar Honasoge, Oscar Gargiulo, Yuki Nojiri, Achim Marx, Frank Deppe, Rudolf Gross, and Kirill G. Fedorov, "Perspectives of microwave quantum key distribution in open-air", arXiv:2203.05530, (2022).

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