PBR cite the above paragraph fromEinstein's 1935 letter to Schrödinger saying that for the same state of B there are twoequally justified ψB"

But note that the general ideathat two distinct quantum states may describe the same state of reality has a longhistory going back to Einstein. For example, in a letter to Schrödinger containing avariant of the famous EPR (Einstein-Podolsky-Rosen) argument, Einstein argues fromlocality to the conclusion that [... quoting Einstein's argument]. In this version of theargument, Einstein really is concerned with the idea that there are two distinctquantum states for the same reality, and not with the idea that there are two differentstates of reality corresponding to the same quantum state (the more commonlyunderstood notion of incompleteness)".

wouldmean that in that case connections between Nature’s choices of the outcomesof measuring q2 or alternatively p2 cannot be assumed not to depend uponwhether q1 or p1 is measured

Applied to the particular example that EPR considered,this consideration was shown to entail that if one sets up the system so thatq1 + q2 and p1 − p2 are both well defined, as EPR specify, then one can mea-sure either q1 or p1, but not both, and hence become able to predict eitherq2 or p2 but not both.

R I V I S T A D E L NUOVO CIMENTO VOL. 4, N. 2 1981Quantum Mechanics Reality and Separability.F. SELLERII s t i t u t o d i E i s i e a dell' Universitd - B a r iI s t i t u t o lqazionale di F i s i e a _Nueleare - Sezione d i B a r iO. T~mozzi(')I s t i t u t o d i F i l o s o / i a dell' Universitd - P e r u g i a(rieevuto il 19 Iqovembre 1980)

Thenonlocal connection is manifested only in the correlations (revealed througha comparison of the experimental data independently gathered at each of thetwo particles) and not at the level of statistical properties of the particles ateach end of the connection

For Einstein, the crucial part of the argument was the demonstration of nonlocality, that the choice of measurement done in particle A, either position or momentum, would lead to two different quantum states of particle B. He argued that, because of locality, the real state of particle B couldn't depend on which kind of measurement was done in A, and therefore the quantum states cannot be in one-to-one correspondence with the real states.[5]