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Optimal Displacement Sensing with Spin-Dependent Squeezed States

Liam J. Bond1,2,*, Christophe H. Valahu3,4, Athreya Shankar5,6, Ting Rei Tan3,4, and Arghavan Safavi-Naini1,2

  • *Contact author: L.J.Bond@uva.nl
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PRX Quantum 7, 020368 – Published 23 June, 2026

DOI: https://doi.org/10.1103/mhvv-pr5d

Abstract

Displacement sensing is a fundamental task in metrology. However, the development of quantum-enhanced sensors that fully utilize the available degrees of freedom in many-body quantum systems remains an outstanding challenge. We propose many-body displacement sensing schemes that use spin-dependent squeezed (SDS) states—hybrid spin-boson states whose bosonic squeezed quadrature is conditioned on an auxiliary spin. We prove that SDS states are optimal, i.e., their quantum Cramér-Rao bound saturates the Heisenberg limit. We propose explicit measurement sequences that can be readily implemented in systems such as trapped ions. We also introduce a scalable state-preparation protocol and numerically demonstrate the preparation of 8.7 dB of spin-dependent squeezing 15 times faster than the standard approach using second-order sidebands in trapped ions. The potential applications of our sensing protocols range from measuring single-photon scattering to searches for dark matter.

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Popular Summary

Mechanical oscillators are crucial for searches of physics beyond the Standard Model because interactions between Standard Model fields and axionic dark matter are theorized to induce measurable oscillator displacements. Although quantum-enhanced sensing provides a route to unprecedented sensitivity, existing displacement sensing protocols do not take full advantage of the many-body nature of current quantum hardware platforms. This paper introduces optimal many-body protocols for sensing either a displacement’s amplitude or its real and imaginary components.

The protocols use spin-dependent squeezed (SDS) states—states whose bosonic squeezed quadrature is conditioned on the state of auxiliary spins. The protocols are proven to be optimal and can be realized on existing quantum hardware platforms. Also provided is a fast and scalable scheme for preparing SDS states in trapped ions.

The metrology protocols introduced in this paper could help researchers to measure single-photon scattering rates or to search for dark matter. In parallel, the scheme for preparing SDS states has applications beyond quantum metrology, for example, in quantum computing where spin-dependent squeezing can reduce the depth of quantum circuits.

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PRX Quantum 7, 020368– Published 23 June, 2026
  • Received 17 November 2025
  • Revised 17 March 2026
  • Accepted 28 April 2026
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