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We introduce thauma measures to quantify nonstabilizerness in quantum states, crucial for quantum computation. These measures provide efficient benchmarks for magic-state distillation and resolve key questions in nonstabilizer state theory.

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Area of Science:

  • Quantum Information Science
  • Quantum Computation Theory
  • Resource Theories

Background:

  • Magic-state distillation is essential for scalable, fault-tolerant quantum computation.
  • Characterizing and quantifying nonstabilizerness is a key goal in the resource theory of nonstabilizer states.

Purpose of the Study:

  • Introduce the family of thauma measures to quantify nonstabilizerness.
  • Address open questions in the resource theory of nonstabilizer states.
  • Develop efficient benchmarks for magic-state distillation.

Main Methods:

  • Introduced the family of thauma measures (min-thauma, max-thauma, hypothesis testing thauma).
  • Utilized hypothesis testing thauma to benchmark one-shot distillable nonstabilizerness.
  • Employed max-thauma for efficient benchmarking of magic-state distillation efficiency.
  • Applied min-thauma to bound the regularized relative entropy of magic.

Main Results:

  • Established hypothesis testing thauma as an efficiently computable benchmark for one-shot distillable nonstabilizerness.
  • Demonstrated that max-thauma outperforms mana-based approaches for benchmarking distillation efficiency.
  • Proved that two classes of states with maximal mana cannot be interconverted at a rate of one in the asymptotic regime.

Conclusions:

  • Thauma measures offer efficient and powerful tools for analyzing nonstabilizerness in quantum states.
  • The results provide new bounds on magic-state distillation overhead and rates.
  • Resolved a fundamental question regarding state interconversion in the resource theory of nonstabilizer states, highlighting differences from other resource theories.