Will two identical antennas next to each other pickup the exact same noise?
Treating the signals received on more than one antenna is known as beamforming. It relies on the antennae being in different places, so that aspects of the noise and signal they receive are sufficiently different to be suitable for processing, usually to enhance the SNR (signal to noise ratio).

The two most common processes are to steer a beam in the direction of the wanted signal, and to steer a null in the direction of an identified unwanted signal source. 'Steering' is achieved by giving the signals different delays, and adding them, sometimes with weights other than unity.

This is a much-studied technique, and there is a huge amount of literature out there. Many people have done their PhDs in this field.