I congratulate Kincaid et al. on their recent article,1 which nicely spells out the details of the measurement process for the important case of the double-slit experiment. I was impressed that the authors were able to carry out explicit calculations all the way through.
I agree entirely with the article's analysis, but it should be noted that the reduced state given in Eq. (11) is controversial among quantum foundations experts who debate the “quantum measurement problem,” which is primarily the problem of how to think about the entangled post-measurement state of Eq. (7). If the detection apparatus A is Schrodinger's cat in an arrangement designed to poison the cat when a radioactive nucleus decays, and if the quantum system S is that nucleus, then Eq. (7) appears to be a superposition of a dead and alive cat, in contradiction with reality.
The reduced state Eq. (11) is criticized on at least three grounds.2 First, it is said to be an “improper density operator” because it does not represent uncertainty about which state S is in but is instead a reduction from the known pure state Eq. (7). Second, this reduced density operator is thought to be ambiguous because it has no “preferred basis”; it is simply 1/2 times the identity operator in S's Hilbert space so that any basis of S's Hilbert space forms a basis for this operator. Third, and most importantly, the pure state of Eq. (7) appears to be a state with no “definite outcomes” because it is a superposition, rather than a mixture, of two composite states (decayed nucleus/dead cat; undecayed nucleus/live cat) that themselves do represent definite outcomes so that the composite system SA appears to be in both of these macroscopic states at the same time, implying that the two definite outcomes indicated by Eq. (11) must be spurious.
These criticisms have for decades led the quantum foundations community to reject analyses such as that of Kincaid et al., and to declare instead that the measurement problem has no resolution within standard quantum theory. The measurement problem is widely regarded as a stumbling block in the foundations of quantum physics.3 This circumstance has led to a plethora of hypothesized alterations and re-interpretations of the theory, such as the GRW spontaneous collapse hypothesis,4 the many-worlds interpretation,5 and the de Broglie/Bohm pilot-wave theory.6
These criticisms have been leveled ever since Jauch's 1968 proposal that Eq. (11) actually does resolve the measurement problem since it says that, when S and A are in the composite state given by Eq. (7), a “local” observer of the nucleus alone must observe the nucleus to be either decayed or undecayed; thus, the expected conclusion (decayed or undecayed nucleus, dead or alive cat) cannot be inconsistent with Eq. (7).7 These criticisms can all be answered within the framework of standard quantum physics, and in fact, non-local experiments with entangled photons demonstrate that Eq. (7) is non-problematic.8 Nevertheless, these criticisms represent the consensus of the quantum foundations community, and should be noted in any analysis that derives the reduced state Eq. (11) from the composite state Eq. (7).