Quantum Metrology of Noisy Spreading Channels

Journal Article · 07 December 2022 · Phys.Rev.Lett.

DOI:https://doi.org/10.1103/PhysRevLett.129.240503· OSTI ID:1906084

Górecki, Wojciech ^[1]; Riccardi, Alberto ^[2]; Maccone, Lorenzo ^[2]

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1. Warsaw U.
2. Pavia U.; INFN, Pavia

We provide the optimal measurement strategy for a class of noisy channels that reduce to the identity channel for a specific value of a parameter (spreading channels). We provide an example that is physically relevant: the estimation of the absolute value of the displacement in the presence of phase randomizing noise. Surprisingly, this noise does not affect the effectiveness of the optimal measurement. We show that, for small displacement, a squeezed vacuum probe field is optimal among strategies with same average energy. A squeezer followed by photodetection is the optimal detection strategy that attains the quantum Fisher information, whereas the customarily used homodyne detection becomes useless in the limit of small displacements, due to the same effect that gives Rayleigh’s curse in optical superresolution. There is a quantum advantage: a squeezed or a Fock state with $N$ average photons allow to asymptotically estimate the parameter with a $\sqrt{N}$ better precision than classical states with same energy.

• Research Organization: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• DOE Contract Number: AC02-07CH11359
• OSTI ID: 1906084
• Report Number(s): FERMILAB-PUB-22-867-SQMS-V; arXiv:2208.09386; oai:inspirehep.net:2139602
• Journal Information: Phys.Rev.Lett., Vol. 129, Issue 24
• Country of Publication: United States
• Language: English