Delayed measurement of entangled states

Question

If we have two entangled particles $A$ and $B$ and we separate them (supose that after entanglement, both travel at same speed in lab reference frame in opposite directions), then we measure a property of particle $A$ at time $t_0$ (lab reference).

Are we 100% sure that the particle $B$, if it didn't interact with anything, will show the opposite state measured on particle $A$, at any time $t$?

Is the state of the system $A$-$B$ already collapsed or will any further measurument of particle $B$ recollapse the state of $A$?

Answer 1

An unstated assumption you're making here is that the combined entangled state is with the two particles that are in opposite states, e.g. spin system $\frac{1}{\sqrt{2}}\left(\lvert+,-\rangle + \lvert-,+\rangle\right)$. This is a specific kind of an entangled state—the general meaning of it is much broader (and has multiple equivalent definitions, which I won't get into here).

If we assume QM holds, then yes, given such a state, the particle $B$, if it didn't interact with anything, will show the opposite state measured on particle $A$, at any time $t$. The spin system is collapsed at this point, and further measurements on $A$ or $B$ will no longer affect the probability distribution of any measurement on the other. All experimental evidence to date, as far as I know of, does not contradict this—whether or not you consider this to be "100% sure" without the assumption QM holds is more a matter of epistemology.

Answer 2

If we have two entangled particles $A$ and $B$ [...] then we measure a property of particle $A$

The sequel of your question suggests that to the "property" (value of measured quantity) asserted of the state of partcle $A$ (or perhaps of the state of particle $A$ along with attending setup instrumentation, such as an analyzer) there also exists an "opposite value" (or at least a value differing from the aforementioned "property" in the value range of the measured quantity) of a corresponding "opposite state" of particle $B$, incl. setup.

Are we 100% sure that the particle $B$, if it didn't interact with anything, will show the opposite state [...] ?

Yes if: by the two particles (along with the requisite instrumentation, or reference frame) being "entangled" and "not interacting with anything (except the setup instrumentation)" you mean precisely the described outcome, namely that in 100 % of all trials there had been "opposite values" obtained of particles $A$ und $B$, incl. setup; whereby "opposite states" were being attributed to the two particles in each trial (which obviously also involves suitable alignment of the distinct and separate analyzers of the setup).

The corresponding state of such an entire system could therefore be symbolized as certain Bell states, conventionally denoted as type (3) or (4).

Is the state of the system $A$-$B$ already collapsed or will any further measurument of particle $B$ recollapse the state of $A$ ?

The state attributions to particles $A$ and $B$, in relation to each other and as a system involving the setup instrumentation and reference frame, is only certain after being derived from the certain measured values. (As far as such a derivation is characterized by the word "collapse", it seems to refer to a range of "potential" characterizations being reduced to only one certain result.)