The Triangle Criterion detects mixed-state magic, proves multi-qubit distillation is strictly stronger than single-qubit schemes, and identifies a purity bound plus undetectable unfaithful magic states.
Efficient witnessing and testing of magic in mixed quantum states
7 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Nonstabilizerness or `magic' is a crucial resource for quantum computers which can be distilled from noisy quantum states. However, determining the magic of mixed quantum has been a notoriously difficult task. Here, we provide efficient witnesses of magic based on the stabilizer R\'enyi entropy which robustly indicate the presence of magic and quantitatively estimate magic monotones. We also design efficient property testing algorithms to reliably distinguish states with high and low magic, assuming the entropy is bounded. We apply our methods to certify the number of noisy T-gates under a wide class of noise models. Additionally, using the IonQ quantum computer, we experimentally verify the magic of noisy random quantum circuits. Surprisingly, we find that magic is highly robust, persisting even under exponentially strong noise. Our witnesses can also be efficiently computed for matrix product states, revealing that subsystems of many-body quantum states can contain extensive magic despite entanglement. Finally, our work also has direct implications for cryptography and pseudomagic: To mimic high magic states with as little magic as possible, one requires an extensive amount of entropy. This implies that entropy is a necessary resource to hide magic from eavesdroppers. Our work uncovers powerful tools to verify and study the complexity of noisy quantum systems.
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The stabilizer Rényi entropy governs the exponential rate at which Clifford orbits become indistinguishable from Haar-random states and sets the optimal distinguishability from stabilizer states in property testing.
Analytical and numerical study of stabilizer nullity and Rényi entropies in monitored Clifford circuits shows quantized decay for computational measurements and size-dependent relaxation to a non-trivial steady state for rotated bases.
Introduces a purity-encoding algorithm for estimating α-Stabilizer Rényi Entropies of unknown quantum states for integer α > 1, with benchmarks and a non-stabilizerness/entanglement link.
Amplitude damping generates nonstabilizerness in qubit systems unlike depolarizing noise, with local injection washed out collectively after encoding, decoding, and postselection.
A tunable mixing parameter p in random quantum circuits controls the transition from classically simulable to expressive quantum reservoir dynamics via entanglement and nonstabilizer content.
A review of how quantum information science is expected to provide new tools and insights for nuclear and high-energy physics phenomenology and quantum simulations.
citing papers explorer
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Triangle Criterion: a mixed-state magic criterion with applications in distillation and detection
The Triangle Criterion detects mixed-state magic, proves multi-qubit distillation is strictly stronger than single-qubit schemes, and identifies a purity bound plus undetectable unfaithful magic states.
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Operational interpretation of the Stabilizer Entropy
The stabilizer Rényi entropy governs the exponential rate at which Clifford orbits become indistinguishable from Haar-random states and sets the optimal distinguishability from stabilizer states in property testing.
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Rise and fall of nonstabilizerness via random measurements
Analytical and numerical study of stabilizer nullity and Rényi entropies in monitored Clifford circuits shows quantized decay for computational measurements and size-dependent relaxation to a non-trivial steady state for rotated bases.
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An Algorithm for Estimating $\alpha$-Stabilizer R\'enyi Entropies via Purity
Introduces a purity-encoding algorithm for estimating α-Stabilizer Rényi Entropies of unknown quantum states for integer α > 1, with benchmarks and a non-stabilizerness/entanglement link.
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Nonstabilizerness and Error Resilience in Noisy Quantum Circuits
Amplitude damping generates nonstabilizerness in qubit systems unlike depolarizing noise, with local injection washed out collectively after encoding, decoding, and postselection.
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Optimal quantum reservoir learning in proximity to universality
A tunable mixing parameter p in random quantum circuits controls the transition from classically simulable to expressive quantum reservoir dynamics via entanglement and nonstabilizer content.
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Quantum Complexity and New Directions in Nuclear Physics and High-Energy Physics Phenomenology
A review of how quantum information science is expected to provide new tools and insights for nuclear and high-energy physics phenomenology and quantum simulations.