Measurement^[1] is an action to assess certain qualities or properties of a system or object. This is highly related to the notion of test. One of the most essential ideas in measurement is the notion of invariance. It means that measurement must be done against some non-changing unit or reference. This non-changing, or invariant requirement is a form of symmetry. Therefore, it is fair to say that all measurements must be conducted under some form of symmetries.

Measurement and Maxwell's Demon

One can think of Maxwell's Demon(MxD) as a primitive form of measuring device. It provides two possible states that enable the observer or MxD to give a single bit of answer. In other words, every MxD is the measuring device for one bit of information in a given physical spacetime context.

Quantum Measurements

An introductory talk on quantum bits and measurements can be found here^[2]. All measurements can be defined in terms of logic models. William Phillips gave a talk on Quantum Reform of the Modern Metric System^[3], which can be useful to learn about measurement.