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A magic monotone for faithful detection of non-stabilizerness in mixed states

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arxiv 2409.18570 v1 pith:TQ35NZUR submitted 2024-09-27 quant-ph

Krzysztof Warmuz , Ernest Dokudowiec , Chandrashekar Radhakrishnan , Tim Byrnes This is my paper · ORCID
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keywords magicmonotonemixedboundariesfaithfulgiveshyperplaneintroduce
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We introduce a monotone to quantify the amount of non-stabilizerness (or magic for short), in an arbitrary quantum state. The monotone gives a necessary and sufficient criterion for detecting the presence of magic for both pure and mixed states. The monotone is based on determining the boundaries of the stabilizer polytope in the space of Pauli string expectation values. The boundaries can be described by a set of hyperplane inequations, where violation of any one of these gives a necessary and sufficient condition for magic. The monotone is constructed by finding the hyperplane with the maximum violation and is a type of Minkowski functional. We also introduce a witness based on similar methods. The approach is more computationally efficient than existing faithful mixed state monotones such as robustness of magic due to the smaller number and discrete nature of the parameters to be optimized.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Evaluating many-body stabilizer R\'enyi entropy by sampling reduced Pauli strings: singularities, volume law, and nonlocal magic

    quant-ph 2025-01 conditional novelty 8.0 of 10

    A sign-problem-free quantum Monte Carlo algorithm computes stabilizer Rényi entropy derivatives, revealing critical-point singularities and volume-law corrections that show discontinuity across phase transitions.

  2. Quantum States with Maximal Magic

    quant-ph 2024-12 conditional novelty 7.0 of 10

    For every stabilizer entropy of order α ≥ 2, a state attains the maximum if and only if it is a fiducial state of a Weyl-Heisenberg covariant SIC.

  3. Extremal Magic States from Symmetric Lattices

    quant-ph 2025-06 conditional novelty 6.0 of 10

    Vectors from symmetric lattices E8, BW16, and E6 map onto stabiliser and maximal-magic states, yielding explicit three-qubit and one-qutrit magic states and conjectured complete counts.

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