# Scope

In research and many areas of our daily lives, sensors target the precise measurement of a large variety of physical quantities. One example is the measurement of tiny forces such as in atomic force microscopes and in detectors for gravitational waves, which were produced far from earth in astrophysical events. Other examples are the measurement of rotations in planes, vibrations in industrial plants and automotive industry, and mechanical motion as well as magnetic and electric fields in cell biology.

Sensing performance and metrology itself are ultimately limited by the fundamental laws of quantum mechanics. The arising limitations have been named for instance *quantum measurement noise limit*, *quantum back-action noise limit*, *photon counting noise limit*, *Heisenberg limit*, *energetic quantum limit*, and the *standard quantum limit*. Some of these terms describe the same physical boundary whereas others are fundamentally different.

The fundamental principle saying that interaction is quantized leads to an intrinsic uncertainty in the measurements of quantum states. For example, a perfectly stabilized laser beam being in a coherent state exhibits fundamental quantum noise when its amplitude and phase is measured. This noise is often called ‘photon counting noise’ or simply ‘shot noise’. Gravitational-wave detectors operate close to the shot-noise limit at signal frequencies above a few hundreds of hertz’. Since 2010, squeezed states of light improve the sensitivity of the gravitational-wave detector GEO600 [Nat. Phys. 7,962 (2011)], which now achieves a sensitivity beyond the shot noise limit above 700Hz.

Electron spins prepared in a superposition state are another example of a sensor operating at limits set by quantum uncertainties. Recent studies have even suggested the generation of spin squeezing in an ensemble of NV centres or the formation of phononic squeezing of a mechanical oscillator coupled to NV centres. Such squeezed states of spins and phonons will allow for magnetic field sensing and possible inertial sensing beyond the quantum limits.

Future gravitational-wave detectors will also be limited by back-action noise, i.e. by *photon radiation pressure noise* producing a random force that acts on the test mass mirrors. The gravitational-wave community defines the ‘*standard quantum limit*’ as the minimum of the sum of photon shot noise and photon radiation pressure noise when those two are uncorrelated and the light power is varied. Other communities in quantum optics use the same term to describe just the photon shot noise.

If shot noise and back action noise are correlated even the standard quantum limit can be beaten. This opens a fully new regime of sensing which is often called the *quantum non-demolition* or *back-action evading* regime. It is already part of the design of the future European gravitational-wave detector, the Einstein Telescope.

Squeezed light is not the only state by which the shot noise limit can be broken. Using so-called NOON states combined with NOON state detection or by using single photon states in a feedback loop, the shot limit can be also surpassed. In fact, using such systems, it is possible to reach the so-called *Heisenberg limit*, which is the ultimate limit for a given total number of quanta per measuring time. For this reason it is also called the *energetic quantum limit*. However, due to the fragility of NOON states, these states are non-optimal in realistic noisy systems.

The overarching aim of the seminar is to discuss ‘quantum limits’ in relation to each other as well as in relation to state-of-the art sensing experiments to help developing a unified terminology within this broad field of research.