The entangled “measurement state” (MS), predicted by von Neumann to arise during quantum measurement, seems to display paradoxical properties such as multiple macroscopic outcomes. But analysis of interferometry experiments using entangled photon pairs shows that entangled states differ surprisingly from simple superposition states. Based on standard quantum theory, this paper shows that the MS (i) does not represent multiple detector readings but instead represents nonparadoxical multiple statistical correlations between system states and detector readings, (ii) implies that exactly one outcome actually occurs, and (iii) implies that when one outcome occurs, the other possible outcomes simultaneously collapse nonlocally. Point (iii) resolves an issue first raised in 1927 by Einstein who demonstrated that quantum theory requires instantaneous state collapse. This conundrum’s resolution requires nonlocal correlations, which from today’s perspective suggests the MS should be an entangled state. Thus, contrary to previous presumed proofs of the measurement problem’s insolubility, we find the MS to be the collapsed state and just what we expect upon measurement.
The entangled “measurement state” (MS), predicted by von Neumann to arise during quantum measurement, seems to display paradoxical properties such as multiple macroscopic outcomes. But analysis of interferometry experiments using entangled photon pairs shows that entangled states differ surprisingly from simple superposition states. Based on standard quantum theory, this paper shows that the MS (i) does not represent multiple detector readings but instead represents nonparadoxical multiple statistical correlations between system states and detector readings, (ii) implies that exactly one outcome actually occurs, and (iii) implies that when one outcome occurs, the other possible outcomes simultaneously collapse nonlocally. Point (iii) resolves an issue first raised in 1927 by Einstein who demonstrated that quantum theory requires instantaneous state collapse. This conundrum’s resolution requires nonlocal correlations, which from today’s perspective suggests the MS should be an entangled state. Thus, contrary to previous presumed proofs of the measurement problem’s insolubility, we find the MS to be the collapsed state and just what we expect upon measurement.
The entangled Schrodinger cat state obtained immediately upon measurement of a superposed two-state quantum system is often considered paradoxical because it appears to predict two macroscopically different outcomes, such as an alive and dead cat. However, nonlocal interferometry experiments testing momentum-entangled photon pairs over all phases demonstrate that the cat state does not fit this description and is not paradoxical. Both experiment and theory imply that it instead represents a superposition of two nonlocally coherent (i.e. phase-dependent) statistical correlations between its sub-systems. This is not paradoxical. Standard quantum theory rigorously predicts the experimentally-observed outcomes of this state. Neither sub-system is superposed; rather, the correlations between the states of the subsystems are superposed. This resolves the problem of definite outcomes. The nonlocal properties of entanglement then ensure that only one outcome occurs while the other outcome simultaneously does not occur, resolving a problem posed by Einstein in 1927. The single outcome that occurs then triggers an irreversible process leading to macroscopic registration of the outcome. This resolves the quantum measurement problem. Collapse occurs because of entanglement and does not require a special collapse postulate. Collapse is a consequence of standard quantum physics and the irreversible nature of the macroscopic registration.
The fully entangled Schrodinger cat state obtained immediately upon measurement of a superposed two state quantum system by a detector is often said to paradoxically predict macroscopically different outcomes simultaneously. However, nonlocal interferometry experiments and their accompanying quantum theoretical analyses, testing momentum entangled photon pairs over the full range of phases, demonstrate that the cat state does not fit this description. This state instead represents two nonlocally coherent correlations between its subsystems. Even if the detector is a cat, this state is not paradoxical. Furthermore, standard quantum theory correctly predicts the experimentally observed nonparadoxical outcomes. Thus both quantum theory and quantum experiments show there is no Schrodinger cat paradox associated with measurement. This resolves the problem of definite outcomes and, with it, the measurement problem. Upon entanglement with a detector, superpositions collapse nonlocally and unitarily to one definite macroscopic outcome. No special collapse postulate is needed.
A misunderstanding of entangled states has spawned decades of concern about quantum measurements and a plethora of quantum interpretations. The "measurement state" or "Schrodinger's cat state" of a superposed quantum system and its detector is nonlocally entangled, suggesting that we turn to nonlocality experiments for insight into measurements. By studying the full range of superposition phases, these experiments show precisely what the measurement state does and does not superpose. These experiments reveal that the measurement state is not, as had been supposed, a paradoxical superposition of detector states. It is instead a nonparadoxical superposition of two correlations between detector states and system states. In this way, the experimental results resolve the problem of definite outcomes ("Schrodinger's cat"), leading to a resolution of the measurement problem. However, this argument does not yet resolve the measurement problem because it is based on the results of experiments, while measurement is a theoretical problem: How can standard quantum theory explain the definite outcomes seen experimentally? Thus, we summarize the nonlocality experiments' supporting theory, which rigorously predicts the experimental results directly from optical paths. Several previous theoretical analyses of the measurement problem have relied on the reduced density operators derived from the measurement state, but these solutions have been rejected due to criticism of reduced density operators. Because it avoids reduced density operators, the optical-path analysis is immune to such criticism.
The quantum measurement problem still finds no consensus. Nonlocal interferometry provides an unprecedented experimental probe by entangling two photons in the ``measurement state'' (MS). The experiments show that each photon measures the other; the resulting entanglement decoheres both photons; decoherence collapses both photons to unpredictable but definite outcomes; and the two-photon MS continues evolving coherently. Thus, when a two-part system is in the MS, the outcomes actually observed at both subsystems are definite. Although standard quantum physics postulates definite outcomes, two-photon interferometry verifies them to be not only consistent with, but also actually a prediction of, the other principles. Nonlocality is the key to understanding this. As a consequence of nonlocality, the states we actually observe are the local states. These actually observed local states collapse, whereas the global MS, which can be ``observed'' only after the fact by collecting coincidence data from both subsystems, continues its unitary evolution. This conclusion implies a refined understanding of the eigenstate principle: Following a measurement, the actually observed local state instantly jumps into the observed eigenstate. We also discuss and rebut objections to this.
Nonlocal interferometry, in which two photons are entangled in the (MS) of quantum measurement theory, illuminates the measurement problem. Experiments done in 1990 by Rarity and Tapster and by Mandel's group, in which each photon measures the other, probe the effect of a variable phase factor inserted between the two superposed terms of the MS. The results show that, when a bipartite (two-part) system is in the MS, its subsystems are not in superpositions but are instead in collapsed, or mixed, states with each subsystem exhibiting a definite, but unpredictable, outcome. Standard quantum theory (without the collapse postulate) predicts this MS and thus correctly predicts these observations. The experiment confirms that, when a quantum system and a measuring apparatus are entangled in the MS, the state actually detected by an observer of either subsystem is the local or reduced state of the subsystem. The global superposition state, which continues evolving unitarily, merely records the nonlocal correlations and does not contradict the definite, non-superposed, outcomes. Thus Schrodinger's cat, example, is in a non-paradoxical mixture of being alive on trials when the nucleus didn't decay, and dead on trials when the nucleus decayed. This resolves the problem of definite outcomes, with no assistance from human minds, other worlds, hidden variables, the environment, a collapse postulate, collapse mechanisms, or for all practical purposes arguments.
Theory and experiment both demonstrate that an entangled quantum state of two subsystems is neither a superposition of states of its subsystems nor a superposition of composite states but rather a coherent superposition of nonlocal correlations between incoherently mixed local states of the two subsystems. Thus, even if one subsystem happens to be macroscopic as in the entangled "Schrodinger's cat" state resulting from an ideal measurement, this state is not the paradoxical macroscopic superposition it is generally presumed to be. It is, instead, a "macroscopic correlation," a coherent quantum correlation in which one of the two correlated sub-systems happens to be macroscopic. This clarifies the physical meaning of entanglement: When a superposed quantum system A is unitarily entangled with a second quantum system B, the coherence of the original superposition of different states of A is transferred to different correlations between states of A and B, so the entangled state becomes a superposition of correlations rather than a superposition of states. This transfer preserves unitary evolution while permitting B to be macroscopic without entailing a macroscopic superposition. This resolves the "problem of outcomes" but is not a complete resolution of the measurement problem because the entangled state is still reversible.