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A quantum limit in physics is a limit on measurement accuracy at quantum scales. Depending on the context, the limit may be absolute , or it may only apply when the experiment is conducted with naturally occurring quantum states and can be circumvented with advanced state preparation and measurement schemes.
The usage of the term standard quantum limit or SQL is, however, broader than just interferometry. In principle, any linear measurement of a quantum mechanical observable of a system under study that does not commute with itself at different times leads to such limits. In short, it is the Heisenberg uncertainty principle that is the cause.
A more detailed explanation would be that any measurement in quantum mechanics involves at least two parties, an Object and a Meter. The former is the system whose observable, say x ^ {\displaystyle {\hat {x}}} , we want to measure. The latter is the system we couple to the Object in order to infer the value of x ^ {\displaystyle {\hat {x}}} of the Object by recording some chosen observable, O ^ {\displaystyle {\hat {\mathcal {O}}}} , of this system, e.g. the position of the pointer on a scale of the Meter. This, in a nutshell, is a model of most of the measurements happening in physics, known as indirect measurements. So any measurement is a result of interaction and that acts in both ways. Therefore, the Meter acts on the Object during each measurement, usually via the quantity, F ^ {\displaystyle {\hat {\mathcal {F}}}} , conjugate to the readout observable O ^ {\displaystyle {\hat {\mathcal {O}}}} , thus perturbing the value of measured observable x ^ {\displaystyle {\hat {x}}} and modifying the results of subsequent measurements. This is known as back action of the Meter on the system under measurement.
At the same time, quantum mechanics prescribes that readout observable of the Meter should have an inherent uncertainty, δ O ^ {\displaystyle \delta {\hat {\mathcal {O}}}} , additive to and independent of the value of the measured quantity x ^ {\displaystyle {\hat {x}}}. This one is known as measurement imprecision or measurement noise. Because of the Heisenberg uncertainty principle, this imprecision cannot be arbitrary and is linked to the back-action perturbation by the uncertainty relation:
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