How much matter is equivalent to a single photon?

Typically not a lot.

Firstly I'll get out of the way that a "single photon" is indeed a meaningful concept and there are various detectors that can pick up individual photons hitting them.

Then, the lightest particle in ordinary matter is the electron. When an electron annihilates with its antiparticle (a positron) you get two gamma ray photons. The higher the frequency and shorter the wavelength of light, the higher the energy and equivalently mass of each photon.

Thus normal light photon, and even UV and some X-ray photons, have less energy than any matter particle. It takes short-wavelength X-rays or gamma ray for the photons to have energies comparable to electrons or protons.

a really small amount, a photon is a light particle and light is energy so and since E=mc^2 then divide it by m^2 and you get a really small amount.

"How much matter is equivalent to a single photon?"

An energetic UV photon could "pretend" give rise to a neutrino-anti-neutrino pair., But photons do not interact with neutrinos, and so do not produce those low energy pairs. The lowest energy massive particle pair (that I know of) would be electron-positron, at more than 1 GeV (well into gamma ray range).

"Or does particle-wave duality make the notion of a single photon meaningless?"

CCD cameras take pictures with single photons, so it is not meaningless. The silver emulsion films used to take at least two photons to score an exposure... CCDs do not have this problem.

"I'm not sure."

I am not sure what you are actually trying to get to...

Zero, as in null-set. There is no matter in a photon or mass to a photon.

A photon is actually a highly truncated standing wave of energy E = hF, where F is its fundamental frequency. It's truncated because of destructive interference by its own harmonics.

But energy, all energy no matter what, has a rest mass equivalent m = E/c^2, which is why, for example, a hot cup of coffee weighs more than a cold one, all other things equal.

So as the other answer correctly put it m = E/c^2 = hf/c^2 is the invariant mass equivalent of a photon with energy E = hf.

well,

it is not possible to isolate a single photon and capture it in a bottle or anything like that

but

we can still think of a photon as the ultimate unit of light

so

from E = h f we can get the energy value of a single photon of a known frequency

then

E = m c^2 lets us calculate the mass equivalent of that photon

If someone gives you a good answer,

please consider giving a best answer.

This is the only reward we get.

hf/c^2, where f is the frequency of the photon and c velocity of light in vacuum.