Hong,
I am not sure that I know what you mean by multidimensional. All objects are (at least) three dimensional - even planar devices such as graphene-based sensors.
So, in a sense, the possibility is '1'.
Could you explain what you mean by multidimensional? I presume, but am not sure, that it does not mean 'having more than one physical dimension'.
Hong,
Data have no dimensions. Dimensions, are by their definition orthogonal measures - and the density of a liquid is not orthogonal to its temperature, for example.
Many sensors measure more than one property of a material. A thin wire in a fluid can measure both temperature and thermal diffusivity. A capacitor with platinum RTD plates delivers both temperature, dielectric constant, and resistivity.
Hong,
I now understand.
But there are many sensors that can reveal multiple simultaneous properties - the thin wire in a liquid can be used to deduce not only temperature but also thermal diffusivity (if the density is known).
So, are you wanting to find a sensor for an application, or do you have a new sensor and wish to tell us about it?
It is more generally true that any given sensor has *some* sensitivity to more than one property.
eg.
A strain gauge has a temperature dependence (based on the expansion coefficient of the substrate)
A pressure gauge (such as a pirani sensor) is sensitive to the nature of the gas as well as its pressure.
etc.
Some friends of mine using microbalances to separate male and female chromosomes , to program births in agricultural environment. That is like Quantum-multiverse, male and femal worlds.....
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