So much confusion! Let me try to fix it.

Photon Torps do moderate damage, but have a higher rate of fire. This gives them the highest DPS.

Quantums do much more damage, but fire slower.

When you add 3x Purple Projectile Warfare Officers, however, torpedoes recharge much faster. Quantums (and to some extent, plasma as well) have several advantages over photon torpedoes when using these Duty officers:

1. Because quantums have a longer recharge rate than photon torps, they benefit more than photons from the PWOs. In fact, the observed DPS from a single quantum is about the same as a single photon while running these PWOs (so, the PWOs help the photon torp, but help the quantum MORE, enough to roughly equalize the DPS).

2. When running multiple torpedoes (remember that they share a 1-sec GCD), the fact that quantums (and plasmas) have a longer base cooldown means you can slot more of them without them "stepping on each other" and causing diminishing returns. The sweet spot for quantum torpedo launchers is probably 3 (possibly 2 if your other front weapons are DHCs - more on this in #3). For photon torpedoes, however, even 2 will often GCD each other when running so many PWOs.

3. Quantum DPS considerations: 3x Purple PWOs will increase the Rate of Fire on a quantum torp from 1 shot every 8 seconds (1/8) to 2.83 shots every 8 seconds. If you have 2 Quantum torpedoes fitted, then you'll see an observed RoF of around 5.4/8 seconds (note: that's less than the 5.66 you might expect, due to the fact that sometimes they will GCD each other). If you have 3 Quantums fitted, you'll see around 7 torps fired every 8 seconds (again, you lose efficiency because of the GCD). This means the following: look at the tooltip DPS of your quantum torpedo (while you are in space). Multiply it by 2.8, 5.4, and 7 respectively. That's the effective DPS of those 1, 2, or 3 quantum launchers you have fitted. If you are wondering if it's ever worth it to put a 4th quantum tube in an arc: no it's not. If you are wondering about that 3rd torp, then take your Tooltip Quantum Torp DPS, multiply it by 1.6 (the rough difference between 2 and 3 launchers), and compare that to the Tooltip DPS of another weapon (DHC, dual beam, Kinetic Cutting Beam, whatever). If the 1.6xQuantum Tooltip DPS is greater, use the torpedo. If the other weapon is greater, then just use 2 quantums and use the other weapon instead.

TL;DR: 1 torp? No PWOs? Use a photon torp. Multiple torps? PWOs? Go with quantum.