Analysis of Multimode Squeezing in Three-Qubit Systems

Introduction:
The ability to generate and control quantum states is fundamental for the development of quantum information theory and its applications. Key quantum features, such as superposition, entanglement, and squeezing, are essential resources in quantum communication, metrology, and information processing. In particular, understanding the relationship between entanglement and squeezing is crucial for a better characterisation of nonclassical states. This work focuses on multimode squeezing in three-qubit systems exhibiting genuine tripartite entanglement.

Methods:
We consider a theoretical model of three-qubit states, including classes of states characterised by non-zero tripartite entanglement. Following the established classification of three-qubit entangled states, we analyse different categories of these states. Entanglement is quantified using negativity [1], while squeezing properties are described by quadrature operators and principal squeezing variances [2, 3]. We derive and evaluate the conditions for two-mode and three-mode squeezing, both analytically and numerically, paying particular attention to the structure of the quantum states.

Results:
Our analysis shows that two- and three-mode squeezing can be observed for certain configurations. Furthermore, relationships between squeezing parameters and entanglement measures are established, demonstrating how the presence of multipartite entanglement influences multimode squeezing properties.

Conclusions:
Our results confirm that multimode squeezing can be realised in three-qubit systems and is closely related to the structure of entanglement. The identified connections between squeezing and entanglement measures provide additional insight into nonclassical correlations in multipartite systems and may be useful for future developments in quantum information and quantum optics.

[1] M. Horodecki, P. Horodecki, R. Horodecki, Phys. Lett. A 223, 1–8 (1996).
[2] A. Lukš, V. Peřinová, J. Peřina, Opt. Commun. 67, 149 (1988).
[3] J. K. Kalaga, J. Peřina Jr., Quantum Inf Process 24, 339 (2025)