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  • Open Access

Saturation of the quantum Cramér-Rao bound for distributed sensing via error sensitivity in SU(1,1)-SU(m) interferometry

Girish S. Agarwal*

  • Institute for Quantum Science and Engineering, Department of Physics and Astronomy, Department of Biological and Agricultural Engineering, Texas A&M University, College Station, Texas 77843, USA

  • *Contact author: girish.agarwal@ag.tamu.edu
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Phys. Rev. A 112, 032439 – Published 29 September, 2025

DOI: https://doi.org/10.1103/h2x6-dz96

Abstract

Breaking the standard quantum limit in the sensing of parameters at different spatial locations, such as in a quantum network, is of great importance. Using the framework of quantum Fisher information, many strategies based on squeezed quantum probes and multipath multiphoton or multiqubit entangled states have been considered. In this context there is always the question of what the simplest measurement is that would saturate the quantum Cramér-Rao bound (QCRB). The simplest quantity to measure would be characteristics of photon flux or population distribution in the case of qubits. Previous studies have shown that the error sensitivity in SU(1,1) interferometry, also known by several other terms such as nonlinear interferometry and time-reversed measurements, does saturate the QCRB for single parameters such as phase, displacement, and loss. In this work we reveal the great utility of generalized SU(1,1) interferometry in distributed sensing. Generalized SU(1,1) interferometry is a combination of SU(m) and SU(1,1) elements, where m is the number of nodes in the network. The SU(m) element is used to produce distributed entanglement starting from a squeezed photonic or matter probe. We demonstrate how error sensitivity measurement or more precisely the method of moment sensitivity at just one output port can saturate or nearly saturate the QCRB and thus results in Heisenberg sensitivity of network sensing.

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Phys. Rev. A 112, 032439– Published 29 September, 2025
  • Received 21 April 2025
  • Accepted 8 September 2025
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