https://doi.org/10.1140/epjd/s10053-023-00629-1
Regular Article – Quantum Optics
Wehrl entropy of entangled oscillators from the Segal–Bargmann formalism
1
Departamento de Física Teórica, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Plaza de Ciencias 1, 28040, Madrid, Spain
2
Institute of Particle and Cosmos Physics (IPARCOS), Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Plaza de Ciencias 1, 28040, Madrid, Spain
Received:
1
November
2022
Accepted:
7
March
2023
Published online:
15
March
2023
In this manuscript, we study the Wehrl entropy of entangled oscillators. This semiclassical entropy associated with the phase-space description of quantum mechanics can be used for formulating uncertainty relations and for a quantification of entanglement. We focus on a system of two coupled oscillators described within its Segal–Bargmann space. This Hilbert space of holomorphic functions integrable with respect to a given Gaussian-like measure is particularly convenient to deal with harmonic oscillators. Indeed, the Stone–von Neumann theorem allows us to work in this space in a full correspondence with the ladder operators formalism. In addition, the Husimi pseudoprobability distribution is directly computed within the Segal–Bargmann formalism. Once we obtain the Husimi function, we analyse the Wehrl entropy and mutual information.
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