We discuss the ultimate precision bounds on the multiparameter estimation of single- and two-mode pure Gaussian states. By leveraging on previous approaches that focused on the estimation of a complex displacement only, we derive the Holevo Cram & eacute;r-Rao bound (HCRB) for both displacement and squeezing parameter characterizing single and two-mode squeezed states. In the single-mode scenario, we obtain an analytical bound and find that it degrades monotonically as the squeezing increases. Furthermore, we prove that heterodyne detection is nearly optimal in the large squeezing limit, but in general the optimal measurement must include non-Gaussian resources. On the other hand, in the two-mode setting, the HCRB improves as the squeezing parameter grows and we show that it can be attained using double-homodyne detection.

Multi-parameter quantum estimation of single- and two-mode pure Gaussian states / G. Bressanini, M.G. Genoni, M.S. Kim, M.G.A. Paris. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 57:31(2024 Aug 02), pp. 315305.1-315305.21. [10.1088/1751-8121/ad6364]

Multi-parameter quantum estimation of single- and two-mode pure Gaussian states

M.G. Genoni
Secondo
;
M.G.A. Paris
Ultimo
2024

Abstract

We discuss the ultimate precision bounds on the multiparameter estimation of single- and two-mode pure Gaussian states. By leveraging on previous approaches that focused on the estimation of a complex displacement only, we derive the Holevo Cram & eacute;r-Rao bound (HCRB) for both displacement and squeezing parameter characterizing single and two-mode squeezed states. In the single-mode scenario, we obtain an analytical bound and find that it degrades monotonically as the squeezing increases. Furthermore, we prove that heterodyne detection is nearly optimal in the large squeezing limit, but in general the optimal measurement must include non-Gaussian resources. On the other hand, in the two-mode setting, the HCRB improves as the squeezing parameter grows and we show that it can be attained using double-homodyne detection.
quantum metrology; Holevo bound; Cramer Rao bound; Gaussian quantum information;
Settore PHYS-04/A - Fisica teorica della materia, modelli, metodi matematici e applicazioni
   Applications and Hardware for Photonic Quantum Information Processing
   AppQInfo
   European Commission
   Horizon 2020 Framework Programme
   956071

   Efficient simulation and design of quantum CONtrol sTRategies for mAny-Body quAntum SystemS (CONTRABASS)
   CONTRABASS
   MINISTERO DELL'UNIVERSITA' E DELLA RICERCA
   2022KB2JJM_001

   Recovering Information in Sloppy QUantum modEls (RISQUE)
   RISQUE
   MINISTERO DELL'UNIVERSITA' E DELLA RICERCA
   2022T25TR3_003
2-ago-2024
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1105064
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