Gentle Measurement as a Principle of Quantum Theory
- URL: http://arxiv.org/abs/2103.15110v3
- Date: Mon, 2 Aug 2021 08:12:14 GMT
- Title: Gentle Measurement as a Principle of Quantum Theory
- Authors: Eyuri Wakakuwa
- Abstract summary: We propose the gentle measurement principle (GMP) as one of the principles at the foundation of quantum mechanics.
We show, within the framework of general probabilistic theories, that GMP imposes strong restrictions on the law of physics.
- Score: 9.137554315375919
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We propose the gentle measurement principle (GMP) as one of the principles at
the foundation of quantum mechanics. It asserts that if a set of states can be
distinguished with high probability, they can be distinguished by a measurement
that leaves the states almost invariant, including correlation with a reference
system. While GMP is satisfied in both classical and quantum theories, we show,
within the framework of general probabilistic theories, that it imposes strong
restrictions on the law of physics. First, the measurement uncertainty of a
pair of observables cannot be significantly larger than the preparation
uncertainty. Consequently, the strength of the CHSH nonlocality cannot be
maximal. The parameter in the stretched quantum theory, a family of general
probabilistic theories that includes the quantum theory, is also limited.
Second, the conditional entropy defined in terms of a data compression theorem
satisfies the chain inequality. Not only does it imply information causality
and Tsirelson's bound, but it singles out the quantum theory from the stretched
one. All these results show that GMP would be one of the principles at the
heart of quantum mechanics.
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