Quantum signatures such as level-spacing statistics and Loschmidt echo decay satisfy operationally equivalent definitions of chaos without requiring classical state space structures.

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Chaos (in physics)(as used in physics and dynamical systems): A state of disorder where tiny changes in starting conditions lead to completely different outcomes, making systems unpredictable—like how a butterfly's wings might theoretically cause a tornado.
Classical state space structures(what the quantum signatures don't need to rely on): The traditional way of describing how regular, everyday-sized systems (not quantum ones) change over time and what states they can be in.
Level-spacing statistics(as an example of quantum signatures): A measurement of the gaps between different energy levels in a quantum system—basically, how spread out or clustered the possible energy states are.
Loschmidt echo(as an example of quantum signatures): A physics concept that measures how sensitive a system is to tiny changes in its starting conditions, named after physicist Ernst Loschmidt.

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