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Entanglement, decoherence, and measurement

Art Hobson

Published Apr 10, 2019• 1 citation
OpenAlex

Abstract

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.

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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.
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.
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.
This paper reviews and suggests a resolution of the problem of definite outcomes of measurement. This problem, also known as ‘Schrodinger’s cat’, has long posed an apparent paradox because the state resulting from a measurement appears to be a quantum superposition in which the detector is in two macroscopically distinct states (alive and dead in the case of the cat) simultaneously. Many alternative interpretations of the quantum mathematical formalism, and several alternative modifications of the theory, have been proposed to resolve this problem, but no consensus has formed supporting any one of them. Applying standard quantum theory to the measurement state, together with the analysis and results of decades of nonlocality experiments with pairs of entangled systems, this paper shows the entangled measurement state is not a paradoxical macroscopic superposition of states. It is instead a phase-dependent superposition of correlations between states of the subsystems. Thus Schrodinger’s cat is a non-paradoxical ‘macroscopic correlation’ in which one of the two correlated systems happens to be a detector. This insight resolves the problem of definite outcomes but it does not entirely resolve the measurement problem because the entangled state is still reversible.
The entangled state that results when a detector measures a superposed quantum system has spawned decades of concern about the problem of definite outcomes or "Schrodinger's cat." This state seems to describe a detector in an indefinite or "smeared" situation of indicating two macroscopic configurations simultaneously. This would be paradoxical. Since all entangled states are known to have nonlocal properties, and since measurements have obvious nonlocal characteristics, it's natural to turn to nonlocality experiments for insight into this question. Unlike the measurement situation where the phase is fixed at zero for perfect correlations, nonlocality experiments cover the full range of superposition phases and can thus show precisely what entangled states superpose. For two-state systems, these experiments reveal that the measurement state is not a superposition of two macroscopically different detector states but instead a superposition of two coherent correlations between distinct detector states and corresponding system states. In the measurement situation (i.e. at zero phase), and assuming the Schrodinger's cat scenario, the entangled state can be read as follows: An undecayed nucleus is perfectly correlated with an alive cat, AND a decayed nucleus is perfectly correlated with a dead cat, where "AND" indicates the superposition. This is not paradoxical.
This paper resolves the problem of definite outcomes, also known as "Schrodinger's cat" and the "problem of wavefunction collapse." It's the problem of understanding how nature goes from a coherent superposition of possible outcomes to a single definite outcome. This "measurement problem" has not to my knowledge been solved. The analysis stems from an insight into entanglement demonstrated in two nonlocality experiments involving pairs of momentum-entangled photons. These show that an entangled state of two subsystems is not a superposition of products of paired states, but instead a superposition of correlations between paired states. The "premeasurement state" is just such a superposition with the proviso that one subsystem is the detector of the other subsystem. This state is not a paradoxical superposition of macroscopic detector states; it is instead a superposition of correlations between detector states and microscopic quantum states. Thus, Schrodinger's cat isn't "smeared" between dead and alive but instead represents a nonlocal superposition of correlations between states of the cat and states of the nucleus: This is what we want. We also critique one previously claimed resolution of the measurement problem and seven previously claimed proofs that the measurement problem is unsolvable.
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.