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Updated: Dec 24, 2025

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Probabilistic bound on extreme fluctuations in isolated quantum systems.

Joshua M Deutsch¹, Dominik Šafránek², Anthony Aguirre²

¹Department of Physics, University of California, Santa Cruz, California 95064, USA.

Physical Review. E

|April 16, 2020

Summary

Isolated quantum systems can contract into smaller Hilbert subspaces. For real initial states, this contraction probability approaches 50%, indicating a significant entropy reduction.

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Area of Science:

Quantum mechanics
Statistical mechanics
Cosmology

Background:

Quantum systems evolve within Hilbert spaces.
Understanding entropy reduction and fluctuations is key in statistical and quantum mechanics.
Cosmological models consider long-term system evolution.

Purpose of the Study:

To determine the maximum probability of an isolated quantum system contracting into a specified Hilbert subspace.
To investigate the implications of this contraction for entropy reduction.

Main Methods:

Starting with an initial random quantum state.
Calculating the probability of particles being measured within a fixed subspace.
Maximizing this probability over all possible times.

Main Results:

Maximal contraction probability approaches 1/2 for real initial wave functions.
Maximal contraction probability approaches π²/16 for complex initial wave functions.
This contraction corresponds to an entropy reduction by a factor of approximately 2.

Conclusions:

Isolated quantum systems can exhibit significant contraction into smaller subspaces.
This phenomenon bounds large downward entropy fluctuations from generic initial states.
The findings have relevance for understanding quantum system evolution in cosmological contexts.