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arXiv:quant-ph/0503009

Quantum Measurement, a coherent description

Bas Janssens

Published Mar 1, 2005• 3 citations
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Abstract

It is widely known that `collapse of the wave function' on a quantum system A may be brought about by an interaction with another quantum system B. We will prove that this is not just a possible, but a necessary consequence of information transfer from A to B. We generalize this in order to explain why coherences are normally not observed in macroscopic quantum systems. Finally, we provide a quantitative insight into the balance between information gain and state disturbance. We define the quality of an information transfer. For all information transfers of a certain quality, we find a minimum amount of state collapse. Along the way, we obtain generalizations of the Joint Measurement Theorem and of the Heisenberg Principle.

DOI
10.48550/arxiv.quant-ph/0503009

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It is widely known that `collapse of the wave function' on a quantum system A may be brought about by an interaction with another quantum system B. We will prove that this is not just a possible, but a necessary consequence of information transfer from A to B. We generalize this in order to explain why coherences are normally not observed in macroscopic quantum systems. Finally, we provide a quantitative insight into the balance between information gain and state disturbance. We define the quality of an information transfer. For all information transfers of a certain quality, we find a minimum amount of state collapse. Along the way, we obtain generalizations of the Joint Measurement Theorem and of the Heisenberg Principle.
We exhibit three inequalities involving quantum measurement, all of which are sharp and state independent. The first inequality bounds the performance of joint measurement. The second quantifies the trade-off between the measurement quality and the disturbance caused on the measured system. Finally, the third inequality provides a sharp lower bound on the amount of decoherence in terms of the measurement quality. This gives a unified description of both the Heisenberg principle and the collapse of the wave function.
We exhibit three inequalities involving quantum measurement, all of which are sharp and state independent. The first inequality bounds the performance of joint measurement. The second quantifies the trade-off between the measurement quality and the disturbance caused on the measured system. Finally, the third inequality provides a sharp lower bound on the amount of decoherence in terms of the measurement quality. This gives a unified description of both the Heisenberg uncertainty principle and the collapse of the wave function.
We attempt to clarify certain puzzles concerning state collapse. In open quantum systems decoherence is a necessary consequence of the transfer of information to the outside; we prove an upper bound for the amount of coherence which can survive such a transfer. In large closed systems decoherence is not observed, but we will show that it is usually harmless to assume its occurrence. An independent physical collapse mechanism over and above Schrödinger's equation and the probability interpretation of quantum states is therefore redundant.
We attempt to clarify certain puzzles concerning state collapse and decoherence. In open quantum systems decoherence is shown to be a necessary consequence of the transfer of information to the outside; we prove an upper bound for the amount of coherence which can survive such a transfer. We claim that in large closed systems decoherence has never been observed, but we will show that it is usually harmless to assume its occurrence. An independent postulate of state collapse over and above Schroedinger's equation and the probability interpretation of quantum states, is shown to be redundant.
Information‐theoretical restrictions on the information transferred in quantum measurements, are regarded for the measurement of quantum object S performed via its interaction with information system O. This information restrictions, induced by Heisenberg commutation relations, are derived in the formalism of inference maps in Hilbert space. O restricted states ξo are calculated from Shroedinger S, O dynamics and the structure of O observables set (algebra); O decoherence by its environment is also accounted for some S, O systems. It's shown that this principal constraints on the information transfer result in the stochasticity of measurement outcomes. Consequently, ξo describes the random 'pointer' outcomes qj, which correspond to the collapse of S pure state.
Information-theoretical restrictions on the information transferred in quantum measurements are regarded for the measurement of object S performed via its interaction with information system O. This information restrictions, induced by Heisenberg commutation relations, are derived in the formalism of inference maps in Hilbert space. O restricted states ξ O are calculated from S,O quantum dynamics and the structure of O observables set (algebra). It’s shown that this principal constraints on the information transfer result in the appearance of stochasticity in the measurement outcomes. Consequently, ξ O describes the random ’pointer ’ outcomes qj, which correspond to the collapse of S pure state. O decoherence by its environment is studied for some S, O systems, it’s shown that it doesn’t change this results principally. 1