Is it ever possible to determine if an unknown or partially unknown two-qubit state is entangled using only a single copy of that state? Given many copies of an unknown two-qubit state we can perform state tomography and determine basis independent properties which will tell us if a state is entangled.
But what if you only have one copy of this state?  Is there, in principle, a reason why it would be impossible to determine whether or not this state is entangled if you only have access to one copy?  What if you have partial knowledge, for example, you know it's one of two states, one entangled one unentangled?
 A: Interesting question. The TL;DR is: it's possible under some assumptions.
First of all, it is definitely possible in general to certify the entanglement of a state with much less resources than those required for a full state tomography.
A common way to do this is to use an entanglement witness, which is an operator whose expectation value can tell you whether your state is entangled.
More specifically, it can be shown that for any non separable state $\rho$ there is an (hermitian) operator $W$ such that $\operatorname{tr}(\rho W) < 0$ but $\operatorname{tr}(\sigma W) \ge 0$ for all separable states $\sigma$.
Such operator is called a witness for $\rho$.
What this tells you is that, provided you can find a witness for the considered class of states, then the expectation value of a single projective measurement can be enough to tell you whether a state is entangled (note however that this only provides a sufficient condition: $\operatorname{tr}(\rho W)\ge0$ is not enough to say that the state is not entangled).
While the above is a quite efficient way to assess entanglement, and requires way less resources than a full tomography, it also requires more than one copy of the state, as you need to collect some statistics to estimate the expectation value of the measurement corresponding to $W$.
On the other hand, imposing enough restrictions on your state (that is, assuming some prior knowledge on the possible states you have), then it becomes trivial that in some cases it is possible to assess the separability with a single copy of the state.
Say for example that you are assuming your state to be either $\lvert\psi\rangle=\lvert00\rangle$ or $\lvert\psi\rangle=\left(\sqrt{1-0.9^2}\lvert00\rangle+0.9\lvert11\rangle\right)$.
Then just measuring any of the two qubits in the computational basis will tell you whether your state is entangled or not with high probability (if you get $0$ the state is likely separable, if you get $1$ it's likely entangled).
More generally, in this paper are given examples of more realistic classes of states for which separability can be assessed with a single copy of the state: Dimić and Dakić (2017), Single-copy entanglement detection.
If instead the question is whether it is possible to devise a protocol that, given any state $\rho$, can certify its separability with high probability and a single copy of the state, then I don't see how this can be possible, even though I'm not sure how to prove it easily right now.
