The amount of data required to observe quantum phenomena such as entanglement and interference depends on various factors, including the specific experimental setup and the nature of the quantum system involved. Let's consider the case of a small Johnson-Nyquist electric noise source, which typically generates random voltage fluctuations due to thermal effects.
In general, to observe quantum phenomena, you would need to ensure that the system under investigation satisfies certain conditions, such as being isolated from external influences and being operated at low temperatures to suppress thermal noise. The coherence time of the system, which determines how long quantum effects can be observed before they degrade, is also crucial.
To quantify the amount of data needed, it is common to consider the concept of a "quantum state tomography." Quantum state tomography is a process that involves characterizing the quantum state of a system by performing measurements on a large number of identically prepared copies of that system.
The number of measurements required for accurate quantum state tomography grows exponentially with the size of the quantum system. For example, if you have a quantum system with N quantum bits or qubits, you would typically need to perform measurements on 2^N copies of the system to reconstruct the quantum state accurately.
In the case of a small Johnson-Nyquist electric noise source, which typically involves a macroscopic number of particles, it would be challenging to directly observe quantum phenomena like entanglement or interference due to the presence of thermal noise and the lack of proper isolation and control over the system. The dominant noise source in this case is usually classical in nature.
However, if you were interested in detecting and studying quantum effects using a small Johnson-Nyquist noise source, you would need to devise an experimental setup that can isolate the relevant quantum subsystems from the classical noise and control their interactions. This would require sophisticated techniques such as quantum state preparation, manipulation, and measurement.
In summary, observing quantum phenomena in the context of a small Johnson-Nyquist electric noise source would typically require advanced experimental techniques and control over the system's quantum subsystems. The amount of data needed would depend on the specific experiment, the complexity of the quantum system, and the desired level of accuracy in characterizing the quantum state.