The specific advance of this work is to propose a mechanism by which superpositions collapse during measurement of the separated subsystems of entangled quantum states. It is shown how the phase that locks together entangled states plays a special role in the measurement of isolated subsystems. This `contextual' phase is installed randomly into the entangled state, and decides the measurement outcomes for the subsystems by directing the collapse of each superposition to a particular classical outcome when a subsystem is measured. The measuring apparatus thus obtains a classical read-out of the quantum correlations embedded in an entangled state. More broadly, these results solidify the theory of measurement of quantum superpositions.
The specific advance of this work is to propose a mechanism by which superpositions collapse during measurement of the separated subsystems of entangled quantum states. It is shown how the phase that locks together entangled states plays a special role in the measurement of isolated subsystems. This `contextual' phase is installed randomly into the entangled state, and decides the measurement outcomes for the subsystems by directing the collapse of each superposition to a particular classical outcome when a subsystem is measured. The measuring apparatus thus obtains a classical read-out of the quantum correlations embedded in an entangled state. More broadly, these results solidify the theory of measurement of quantum superpositions.
One of the major remaining questions concerning foundations of the quantum mechanical theory is how superpositions are measured such that definite outcomes are obtained. Here a resolution to that issue is proposed. It is shown how to obtain state vectors associated with measurements on the separated subystems of an entangled state, revealing how a single wavefunction encodes a special kind of set of statistical measurement outcomes. The result explains why measurements on the subsystems give definite outcomes and why measurements on one subsystem are correlated with those on the other. It is therefore concluded that the theory of quantum mechanics, without nonlinearities or \emph{ad hoc} assertions, can explain both the mechanism of state vector collapse and the reason for the paradoxical nonlocal correlations between separated subsystems. The theory also explains why nonlocal correlations do not require any kind of interaction between the subsystems.
The entangled states of composite quantum systems are well studied. The particle-like nature of these systems also means that, while entangled, they can be physically separated and measurements performed on the separated subsystems. Measurements on the separated subsystems A and B should pertain to vectors in the local Hilbert space of each subsystem, but to date it has not been clear how to elucidate the relevant states of the separated subsystems because it is not obvious how to resolve them from states given in the tensor product basis, except for the separable states. Here it is shown that the projections of any general entangled state that are detected by measurements on the separated subsystems can be obtained considering the corresponding (cosets of) states in the free vector space from which the tensor product space is defined. The result eliminates the need to invoke random collapse, and from this perspective nonlocality arises because of the way measurements on each separated subsystem projects possible measurement outcomes.
This paper is an in depth implementation of the proposal (Ellis 2012 Ann. Phys. NY 327 1890–932) that the quantum measurement issue can be resolved by carefully looking at top-down contextual effects within realistic measurement contexts. The specific setup of the measurement apparatus determines the possible events that can take place. The interaction of local heat baths with a quantum system plays a key role in the process. In contrast to the usual attempts to explain quantum measurement by decoherence, we argue that the heat bath follows unitary time evolution only over limited length and time scales (Drossel 2017 His. Phil. Sci. B 58 12–21) and thus leads to localization and stochastic dynamics of quantum particles that interact with it. We show furthermore that a theory that describes all the steps from the initial arrival of the quantum particle to the final pointer deflection must use elements from classical physics. This proposal also provides a contextual answer to the puzzle of the origin of the arrow of time when quantum measurements take place: it derives from the cosmological direction of time. Overall, our proposal is for contextual wavefunction collapse.
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.
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 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.