Squeezed States Quantum Metrology Heisenberg Limit

Short answer: Quantum metrology uses quantum states to measure quantities more precisely than classical strategies allow. With N independent probes, precision improves as 1 over the square root of N, the standard quantum limit. Entanglement or squeezing can in principle reach the Heisenberg scaling of 1 over N, a quadratic gain. Squeezed light, which has reduced noise in one quadrature, is one practical route, and a 2025 review surveys its use in sensing. The Heisenberg gain is a theoretical bound, and noise can limit it in practice.

The two scalings

A 2014 review in the Journal of Physics A summarizes quantum metrology with cold gases, trapped atoms and photons. It reviews setups using spin-squeezed, GHZ, Dicke and singlet states, and presents the key notions: shot-noise scaling, Heisenberg scaling, the quantum Fisher information and the Cramer-Rao bound. The authors show that entanglement is needed to surpass shot-noise scaling in very general metrological tasks with a linear interferometer. They also explain how uncorrelated noise limits the highest achievable precision in very general metrological tasks. They add that if the dynamics has interaction terms, even better scaling than Heisenberg scaling is possible.

A framework for squeezing

A 2020 paper in Quantum says metrology theory had mostly focused on gains from entanglement among N probes, typically a quadratic gain from the 1 over root N of the central limit theorem to the 1 over N of the Heisenberg bound. The authors focus instead on squeezing and give a unified framework. They show that one can generally attain a quadratic gain when comparing a squeezed probe with the best classical N-probe strategy using the same energy, and they quantify a Heisenberg squeezing bound for arbitrary estimation strategies that use squeezing. They state the theory recovers known results in quantum optics and spin squeezing and holds for arbitrary quantum systems.

Squeezed light in sensing

A 2025 review in Applied Sciences describes squeezed light as a non-classical state with reduced quantum noise in one quadrature component, below the standard quantum limit. In optical interferometry, it explains, vacuum fluctuations of the electromagnetic field set the standard quantum limit for phase sensitivity, which scales as 1 over the square root of the average photon number for classical light. The review covers how squeezed light is generated in atomic ensembles, nonlinear crystals and fibres, and its role in interferometry, gravitational wave detection, magnetometry, force sensing, biomedical sensing and quantum radar. It also discusses future challenges and opportunities.

What this does not tell you

These papers give bounds and reviews. They do not give the precision any particular instrument achieves, and the 2014 review stresses that noise limits the benefit. A bound that holds in theory is not a measured improvement in a device.

FAQ

What is the standard quantum limit?

The precision scaling of 1 over the square root of N for N independent probes, set by the central limit theorem.

What is the Heisenberg limit?

Scaling as 1 over N, a quadratic gain, reachable in principle with entanglement or squeezing.

Does squeezing help?

The 2020 paper shows a quadratic gain over the best classical strategy using the same energy, within its framework.

What limits it in practice?

Noise. The 2014 review explains how uncorrelated noise limits achievable precision.

Where is squeezed light used?

The 2025 review lists interferometry, gravitational wave detection, magnetometry, force sensing, biomedical sensing and quantum radar.