I've seen the company Positron Dynamics claim they have a potential solution to interstellar travel through their proposed antimatter propulsion system. More often then not these advanced propulsion proposals are met with widespread criticism, but I can't find anyone «debunking» their plans.
In short: are they on to something?
From Next Big Future:
They are on to something... else than they try to claim on their site.
The paper on the actual science explains the concepts.
This is not intended to be the "holy grail", genuine antimatter drive (a photon drive utilizing gamma rays from annihilation of positron and electon; specific impulse of the maximal ${c}\over{g_0}$ and 100% mass to energy conversion), but a ion thruster, with positrons used to produce muons for muon-catalyzed fusion as source of ion propulsion (instead of electric field).
Muon-catalyzed fusion is a "cold fusion" process which, while working, was considered (similarly to many other similar) useless practically, the reason being a relatively low number of deuterium or tritium atoms catalyzed into fusion to helium, per positron, and obviously prohibitive price of antimatter-generating isotopes. In other words, the wattage of the process is minuscule, and energy needed to produce the anti-matter - way higher than the energy output of this fusion.
Still, products of the muon-catalyzed fusion are extremely hot (=fast) ions (= charged particles which can be directed using magnetic fields). In other words, it can be used for a ion engine of quite extreme specific impulse - heat of nuclear fusion replacing accelerating ions through electric field.
Unfortunately, the poor wattage problem remains. The site the asker linked provides beautiful visions, "months to Pluto, Proxima Centauri in 5 years, a craft accelerating at sustained 1g". The paper makes much more modest claims:
One significant actual breakthrough they claim to have made is production of "cold positrons" (usable for catalyzing the fusion) at a rate an order of magnitude greater than currently available, and with promise for improvement. This could indeed reduce the amount (=cost) of antimatter-producing isotope needed for this to work.
It's still a lot of very tall claims, especially for the schedule, without even a decent test article device for the thruster. It's still a viable (if not realistically near) concept for a fusion-powered ion drive, which would indeed surpass everything we have in terms of specific impulse and delta-V total. Regardless, there's nothing that would suggest thrust in newton range, never mind the claimed kilonewtons. While the energy density of the fuel (deuterium+tritium) is fantastic, the catalyst-producing isotopes (e.g $^{22}Na$) are still prohibitively expensive and must be used in macroscopic amounts to trigger release of any macroscopic amounts of energy.
(and this is just a tip of the iceberg of problems, like half-life of the fuel, powering magnetic fields to handle the high-energy ions, all the accidental hard gamma radiation from positron-electron annihilation (which WILL happen, wanted or not), and lots and lots the authors of the proposal conveniently remained silent about.)
As written, this question is far too broad. "Are they on to something?" is a nearly meaningless question.
Is antimatter propulsion theoretically feasible? Yes.
Does it make interstellar travel possible? Not by itself.
Does Positron Dynamics know how to make an antimatter-powered thruster useful for interstellar travel? No.
Will Positron Dynamics demonstrate an antimatter-powered thruster in the near future? I have no idea.
