This is a vague statement that could mean two different things.

1. That quantum mechanics is deterministic (as far as wavefunctions go) and time-reversible. Knowing the state of a system at any given point, you can use the differential equation (Schrodinger's equation) that determines the evolution of the system, to find the state any other time.

2. The should in the statement is referring to the philosphical idea that we expect that the true laws of physics will always be deterministic and time-reversible.

This is where my layperson's intuition totally breaks down.

Matter goes into black hole. Black hole destroys everything because too much gravity and spacetime itself might or might not literally have a break in it. Eventually the remnants of said matter radiates out as random particles.

That seems totally logical and not paradoxical at all to me. My uneducated mental models of black holes and information theory are so crude that I can't even see what the problem with this is. All I can figure is that the conclusions of a theorem in Research Area A turn out to violate an axiom that is used and dependend-on in Research Area B.

I did however find this very interesting document that seems to cover some of what I'm missing: https://plato.stanford.edu/entries/spacetime-singularities/. I'll have to make my way through it over the next few days, maybe it will benefit other people, too.

I'm a layman, so I'm not 100% certain on this, but I think this is a quantum version of Laplace's Demon; where if you know all the information about the state of a system, you can calculate what the system will look like at any point in the past, present, or future.

Does this imply that if we knew the total state of the universe, we could calculate its future state?

Basically, does this imply the universe is deterministic, or that we're living in a simulation?

It implies that the universe is deterministic, with the caveat that what’s deterministic is the universe as a whole, which includes umpteenillion extra “timelines” which we can’t see, in addition to our own.

There’s remains indexical uncertainty, as we can’t predict which timelines we’ll see. The answer is of course all of them.

Unknown: https://physics.stackexchange.com/questions/63811/is-the-uni...

Also, has been argued philosophically for thousands of years https://plato.stanford.edu/entries/freewill/

It's known that the universe is deterministic, just not all people agree.

The evolution of the wave function is deterministic. However, the observables of the wave function are not deterministic. So if I tell you the state of a photon moving toward your eye, you can determine the probability distribution of what color you will see, but not the actual color, because there's randomness during collapse.

(Alternately, there's indexical uncertainty in timelines, which rouuuughly comes out to the same thing if you handwave about game theory a bit https://plus.maths.org/content/playing-games-part-i )

It sounds like just the Schrodinger Equation, Quantum Mechanics 101

Mathematically, thee solutions to the differential equation have a “time evolution operator” that allow the quantum states to be pushed forward or backward in time.

This is basically stating an assumption of determinism with respect to physical dynamics.

Determinism.

The laws of physics are mostly fully deterministic, even quantum laws.