I read this antenna theory statement somewhere:
And, for next-step or future thoughts: a receiving antenna can be as small as you can imagine, without loss of signal to noise.
Is this BS or not?
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Mostly true, with a number of significant practical caveats.
The problem with making an antenna small is that it becomes inefficient. But for receiving this may not be a problem, as antenna inefficiency attenuates signal as well as noise. It is the ratio of signal to noise, not simply signal power, that determines if reception is successful or not.
However, as the antenna becomes less efficient it adds thermal noise. Consider the limiting case of inefficient antennas: the dummy load. A 50 ohm dummy load produces thermal noise equivalent to a 50 ohm resistor, because it is a 50 ohm resistor. An ideal, 100% efficient antenna produces no thermal noise at all. An inefficient antenna is somewhere between.
This may not matter. On HF, the ambient thermal noise is very high, and the worst-case thermal noise of a dummy load is utterly irrelevant when compared to the ambient RF noise the antenna will pick up regardless.
At the other extreme, for a deep-space antenna this would be terrible. The antenna is pointed into space where the ambient noise is orders of magnitude lower, and these antennas tend to utilize cryogenically cooled LNAs. Adding thermal noise would significantly raise the noise floor of the antenna system.
For further reading, see How can I calculate the effects of an LNA, antenna gain, etc. on noise performance?
Additionally, in practice any very small antenna is going to require matching components and/or active circuitry to extract any useful signal from it. This additional circuitry will add noise and nonlinear distortion. It's possible to make receiving antennas pretty small and still get good performance. But there is a point where the antenna becomes so small that the engineering challenges become impractical.
Yes (No BS).
Transmitter antenna without loss, think of a black box that has coax input and in the box is a loss-free antenna. There is no dissipation; all the power is converted into EM-field that is radiated. A directivity pattern can be measured.
---> From reciprocity, or passive two-port theory: that same antenna used as reception antenna converts the received EM-field into available power, in your feedline to the receiver. Same assumption: loss-free matching!
Of course there is a practical limitation. A small antenna can't be matched without losses. As soon as the size is below 10 % of the wavelength, the losses explode almost. Also the bandwidth of the matching network is narrow-band for smaller antennas.
Mentioned is a receiver antenna: Power loss is very important for transmission. For reception however some loss is acceptable since received noise can (LF, SW) be stronger than the thermal noise from the losses. Radiation resistance apparent temperature is thousands or even million degrees Kelvin. Losses in a matching unit are at room temperature.
True only if you do not want to detect or receive the signal.
Any physically realizable (e.g. made out of atoms) feedline, passive network, or receiver input connected to the antenna will add thermal and quantum noise, which can overwhelm a small enough signal from even a perfect noiseless source (theoretic infinitesimal antenna).
At that point there will exist quantum uncertainty about whether an RF photon even existed in the vicinity of the antenna within the reception timeframe.