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Weighted Bures length uncovers quantum state sensitivity.

Paweł Kurzyński1

  • 1Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznańskiego 2, 61-614 Poznań, Poland and Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore.

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This summary is machine-generated.

Quantum mechanics may exhibit state sensitivity detectable by the Weighted Bures length (WBL). This metric reveals linear or exponential growth in WBL for perturbed quantum systems, depending on qubit arrangement.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Mathematical Physics

Background:

  • Quantum evolutions preserve state overlap, seemingly limiting state sensitivity.
  • Classical state sensitivity relies on trajectory distance, distinct from quantum state overlap.
  • A specialized metric may reveal quantum state sensitivity.

Purpose of the Study:

  • To investigate quantum state sensitivity using the Weighted Bures length (WBL).
  • To analyze the impact of single-qubit perturbations on WBL in a quantum system.

Main Methods:

  • Numerical investigation of a unitary cellular automaton with N interacting qubits.
  • Analysis of WBL evolution between perturbed and unperturbed quantum states.
  • Comparison of WBL growth on cyclic versus random bipartite graphs.

Main Results:

  • The Weighted Bures length effectively detects quantum state sensitivity.
  • WBL shows linear growth for qubits in a cyclic graph.
  • WBL exhibits exponential growth for qubits in a random bipartite graph.

Conclusions:

  • The Weighted Bures length is a viable metric for detecting quantum state sensitivity.
  • Qubit arrangement significantly influences the growth rate of WBL under perturbation.
  • This work offers new insights into quantum system dynamics and sensitivity.