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Objectivity of Quantum Measurement in Many-Observer World

Chang-Pu Sun

Published Aug 3, 2015• 0 citations
OpenAlex

Abstract

The objectivity of quantum measurement is treated as an emergent phenomenon with $N$ observers who can agree to the same result of measurement, and meanwhile, they can identify their records with each other. In this many-observer world (MOW), an objective quantum measurement is dealt with as a multipartite [$(N+1)$-body] quantum correlation among the measured system and $N$ observers when its bipartite reductions are the same classical correlations. With this conceptual clarification, we find that, an objective quantum measurement is implemented if and only if the MOW is initially factorized in a pure state and then the total system can evolve into a generalized GHZ state with respect to the orthogonal basis preferred by each observer. Especially, such objective quantum measurement is recast in ideal classical correlation when the observer world is macroscopic for $N\rightarrow\infty$.

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The objectivity of quantum measurement is treated as an emergent phenomenon with NNN observers who can agree to the same result of measurement, and meanwhile, they can identify their records with each other. In this many-observer world (MOW), an objective quantum measurement is dealt with as a multipartite [(N+1)(N+1)(N+1)-body] quantum correlation among the measured system and NNN observers when its bipartite reductions are the same classical correlations. With this conceptual clarification, we find that, an objective quantum measurement is implemented if and only if the MOW is initially factorized in a pure state and then the total system can evolve into a generalized GHZ state with respect to the orthogonal basis preferred by each observer. Especially, such objective quantum measurement is recast in ideal classical correlation when the observer world is macroscopic for N→∞N\rightarrow\inftyN→∞.
Quantum measurement is a physical process. What physical resources and constraints does quantum mechanics require for measurement to produce the classical world we observe? Treating measurement as a fully unitary quantum process, our goal is to show that objective, redundant, and correctly aligned outcomes are possible iff the environment begins in a specially structured, correlated subspace. We start with a minimal set of assumptions: unitarity, orthogonality of conditional environment branches, and finite-dimensional Hilbert spaces. Using these, we demonstrate that generic environmental states cannot support redundant and mutually consistent records of the signal, the measured quantum system. The admissible initial states form a subspace on which the measurement maps obey the Knill-Laflamme error-correction conditions, revealing that the emergence of classical objectivity relies on the environment behaving like a quantum error-correcting code. The post-measurement subspace naturally factorizes into a ``pointer'' to hold measurement outcomes and ``memory'' to retain pre-measurement quantum information about the environment's state, thereby respecting the no-deletion theorem. This further allows the identification of correlation as a finite resource consumed during measurement. Through an explicit qudit model with local interactions, we demonstrate how correlated environments yield redundant observer networks. Simulations show that record fidelity and redundancy depend on the initial correlations in the environment. This perspective links quantum Darwinism to error correction and raises the possibility that natural processes may prepare and evolutionarily favour environments capable of supporting reliable measurement.
Measurement is an important scientific activity. In most of science, including classical physics, is may be understood as a way of finding out about the physical world and representing the results numerically. No-go theorems show that measurement of quantum observables is not like that: the recorded outcome is typically created rather than revealed in a quantum measurement, in which case there is no objective fact about the observable's prior value. Other no-go theorems show that unitary quantum theory can generally neither explain nor even represent a unique recorded outcome, thereby threatening that outcome's objectivity. Methodological norms inherent in quantum physical practice nevertheless institute the objectivity, not only of unique recorded outcomes of quantum measurements, but also of non-quantum features of the world that physicists and other scientists take their models to represent.
The starting point of this dissertation is that a quantum state represents the observer's knowledge about the system of interest. As it has been pointed out several times by the opponents of this epistemic interpretation, it is difficult to reconcile this point of view with our common notion of “physical reality”, which exists independently of our monitoring, and can be discovered without disturbance. Indeed, if quantum theory is correct, it should apply to classical systems—including measurement devices—as well as to any other system. In this dissertation, we will study the quantum mechanisms responsible for our perception of the world and demonstrate how they lead to the emergence of an operational objective reality from within quantum theory: several observers gathering information through these mechanisms will arrive at a common consensus about the properties of the world. The two mechanisms we study in great detail are the redundant proliferation of information in the environment and the direct measurement of a macroscopic observable. An example of the first mechanism is the photon environment which provides us with our visual data about the world. Several independent observers learning about their surroundings in this indirect fashion will agree on their findings. An example of the second mechanism is our tactile information: when the tip of our finger touches an object, it interacts collectively with a very large number of molecules. Again, under realistic assumptions, this type of information acquisition will lead to a classical perception of the world.
We provide an alternative approach to the decoherence-by-environment paradigm in the field of the quantum measurement process and the appearance of a classical world. In contrast to the decoherence approach we argue that the transition from pure states to mixtures and the appearance of macro objects (and macroscopic properties) can be understood without invoking the measurement-like influence of the environment on the pointer-states of the measuring instrument. We show that every generic many-body system contains within the class of microscopic quantum observables a subalgebra of macro observables, the spectrum of which comprises the macroscopic properties of the many-body system. Our analysis is based (among other things) on two ingenious papers by v.Neumann and v.Kampen.
This paper is concerned with the description of the process of measurement within the context of a quantum theory of the physical world. It is noted that quantum mechanics permits a quasi-classical description (classical in the limited sense implied by the correspondence principle of Bohr) of those macroscopic phenomena in terms of which the observer forms his perceptions. Thus, the process of measurement in quantum mechanics can be understood on the quasi-classical level by transcribing from the strictly classical observables of Newtonian physics to their quasi-classical counterparts the known rules for the measurement of the former. The remaining physical problem is the delineation of the circumstances in which the correlation of a peculiarly quantum mechanical observable A with a classically measurable observable B can result in a significant measurement of A. This is undertaken within the context of quantum theory. The resulting clarification of the process of measurement has important implications relative to the philosophic interpretation of quantum mechanics.
Quantum theory is applicable, in principle, to both the microscopic and macroscopic realms. It is therefore worthwhile to investigate whether it is possible to evolve a quantum-compatible view of the properties and states of macroscopic objects in everyday thinking. It will allow a realistic interpretation of quantum theory in a manner directly consistent with the observations. The construction of such a view will provide a solution to what I term the observation problem. Toward solving the observation problem, I identify a category of new objective properties called 'relational properties' that are (so to speak) in-between primary and secondary properties. We regularly associate such properties with everyday objects, and I discuss how in fact these are quantum-compatible. If this relational-property viewpoint could be worked into quantum theory, it would altogether avoid the measurement problem, which is an artifact of our current inconsistent (albeit pragmatically successful) strategy of retaining a classical view of the macroscopic world while applying quantum theory to the microscopic world. Some implications of the relational property viewpoint to neurobiological issues underlying cognition are touched upon.