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  • Open Access

Algorithm for estimating α-stabilizer Rényi entropies via purity

Benjamin Stratton*

  • Quantum Engineering Centre for Doctoral Training, H. H. Wills Physics Laboratory and Department of Electrical & Electronic Engineering, University of Bristol, BS8 1FD, United Kingdom and H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom

  • *Contact author: ben.stratton@bristol.ac.uk
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Phys. Rev. A 113, 022434 – Published 20 February, 2026

DOI: https://doi.org/10.1103/tl6w-hbnx

Abstract

Nonstabilizerness, or “magic,” is a resource for universal quantum computation in most fault-tolerant architectures; access to states with nonstabilizerness allows for nonclassically simulable quantum computation to be performed. Quantifying this resource for unknown states is therefore essential to assessing their utility in quantum computation. The stabilizer Rényi entropies have emerged as a leading tool for achieving this, having already enabled one efficient algorithm for measuring nonstabilizerness. In addition, the stabilizer Rényi entropies have proven useful in developing connections between nonstabilizerness and other quantum phenomena. In this work, we introduce an alternative algorithm for measuring the stabilizer Rényi entropies of an unknown quantum state. First, we show the existence of a state, produced from the action of a channel on α copies of some state ρ, that encodes the α-stabilizer Rényi entropy of ρ into its purity. We detail several methods of applying this channel, and then, by employing existing purity-measuring algorithms, provide an algorithm for measuring the α-stabilizer Rényi entropies for all integers α>1. This algorithm is benchmarked for qubits and the resource requirements compared to other known algorithms. Finally, a nonstabilizerness-entanglement relationship is shown to exist in the algorithm, demonstrating a relationship between the two resources, before an instance of resource hiding is found.

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Phys. Rev. A 113, 022434– Published 20 February, 2026
  • Received 21 July 2025
  • Accepted 23 January 2026
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