Weighted Bures Length Uncovers Quantum State Sensitivity
- URL: http://arxiv.org/abs/2106.14081v1
- Date: Sat, 26 Jun 2021 20:06:30 GMT
- Title: Weighted Bures Length Uncovers Quantum State Sensitivity
- Authors: Pawel Kurzynski
- Abstract summary: Unitarity of quantum evolutions implies that the overlap between two initial states does not change in time.
We numerically study a cellular automaton-like unitary evolution of N qubits, known as Rule 54, and apply WBL to show that a single-qubit perturbation of a random initial state appears to grow exponentially in time.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The unitarity of quantum evolutions implies that the overlap between two
initial states does not change in time. This property is commonly believed to
explain the lack of state sensitivity in quantum theory, a feature that is
prevailing in classical chaotic systems. However, a distance between two points
in classical phase space is a completely different mathematical concept than an
overlap distance between two points in Hilbert space. There is a possibility
that state sensitivity in quantum theory can be uncovered with a help of some
other metric. Here we show that the recently introduced Weighted Bures Length
(WBL) achieves this task. In particular, we numerically study a cellular
automaton-like unitary evolution of N qubits, known as Rule 54, and apply WBL
to show that a single-qubit perturbation of a random initial state: (a) grows
linearly in time under the nearest neighbour interaction on a cycle, (b)
appears to grow exponentially in time under interaction given by a random
bipartite graph.
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