Abstract
The consensus regarding quantum measurements rests on two statements: (i) von Neumann’s standard quantum measurement theory leaves undetermined the basis in which observables are measured, and (ii) the environmental decoherence of the measuring device (the “meter”) unambiguously determines the measuring (“pointer”) basis. The latter statement means that the environment monitors (measures) selected observables of the meter and (indirectly) of the system. Equivalently, a measured quantum state must end up in one of the “pointer states” that persist in the presence of the environment. We find that, unless we restrict ourselves to projective measurements, decoherence does not necessarily determine the pointer basis of the meter. Namely, generalized measurements commonly allow the observer to choose from a multitude of alternative pointer bases that provide the same information on the observables, regardless of decoherence. By contrast, the measured observable does not depend on the pointer basis, whether in the presence or in the absence of decoherence. These results grant further support to our notion of Quantum Lamarckism, whereby the observer’s choices play an indispensable role in quantum mechanics.
Highlights
Attempts to banish the observer from quantum mechanics have motivated approaches [1,2,3,4] whereby the environment observes a quantum system
M does not affect the measured observable, which remains unique, whether in the absence or in the presence of decoherence (Section 3). We illustrate these results for the case of a qubit meter decohered by a bath when this meter measures a two-level system (Section 4). These results are discussed as arguments in favor of the central role of the observer in quantum mechanics in the spirit of Quantum Lamarckism [24] (Section 5)
Pointer states have been defined by Zurek [3,6,7,8] as the ones that are minimally entangled with the bath following their interaction
Summary
Attempts to banish the observer from quantum mechanics have motivated approaches [1,2,3,4] whereby the environment observes a quantum system. Subsequent theory, notably Zurek’s, has pleaded the case for “the environment as the observer” by stressing the importance of system-environment correlations in determining the information obtainable on the system through the notions of “einselection” [4,6] and “the environment as a witness” [7,8] and the mechanism of enforcing classicality [9,10,11] These approaches must cope with the issue that the decomposition of a (closed) “supersystem” into an open quantum system and its environment is often neither unique nor inevitable, but rather a matter of expediency and choice for the observer: Depending on the computational and experimental resources, the observer can choose which degrees of freedom pertain to the system to be measured (or otherwise manipulated) and which ones are part of the inaccessible environment (“bath”). These results are discussed as arguments in favor of the central role of the observer in quantum mechanics in the spirit of Quantum Lamarckism [24] (Section 5)
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