Operational interpretation of the Stabilizer Entropy

Abstract

Magic-state resource theory is a fundamental framework with far-reaching applications in quantum error correction and the classical simulation of quantum systems. Recent advances have significantly deepened our understanding of magic as a resource across diverse domains, including many-body physics, nuclear and particle physics, and quantum chemistry. Central to this progress is the stabilizer Rényi entropy, a computable and experimentally accessible magic monotone. Despite its widespread adoption, a rigorous operational interpretation of the stabilizer entropy has remained an open problem. In this work, we provide such an interpretation in the context of quantum property testing. By showing that the stabilizer entropy is the most robust measurable magic monotone, we demonstrate that the Clifford orbit of a quantum state becomes exponentially indistinguishable from Haar-random states, at a rate governed by the stabilizer entropy $M_{\alpha }(\psi )$ and the number of available copies. This implies that the Clifford orbit forms an approximate state $k$-design, with an approximation error $\exp (-\Theta (M_{\alpha }(\psi )))$ for $\alpha \ge 2$. Conversely, we establish that the optimal probability of distinguishing a given quantum state from the set of stabilizer states is also governed by its stabilizer entropy. These results reveal that the stabilizer entropy quantitatively characterizes the transition from stabilizer states to universal quantum states, thereby offering a comprehensive operational perspective of the stabilizer entropy as a quantum resource.

References in corpus (57)

• Topological entanglement entropy
• Improved Simulation of Stabilizer Circuits
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Quantum Resource Theories
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Restrictions on Transversal Encoded Quantum Gate Sets
• Evenly distributed unitaries: on the structure of unitary designs
• Magic state distillation with low overhead
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Stabilizer Rényi entropy
• Information-theoretic bounds on quantum advantage in machine learning
• Quantifying nonstabilizerness of matrix product states
• Stabilizer entropies and nonstabilizerness monotones
• Robustness of Magic and Symmetries of the Stabiliser Polytope
• Measuring magic on a quantum processor
• Schur-Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations
• Efficiently computable bounds for magic state distillation
• Quantum Chaos is Quantum
• Stabilizer entropies are monotones for magic-state resource theory
• Magic-state resource theory for the ground state of the transverse-field Ising model
• Nonstabilizerness via matrix product states in the Pauli basis
• Bound States for Magic State Distillation in Fault-Tolerant Quantum Computation
• Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
• Simulation of Qubit Quantum Circuits via Pauli Propagation
• Magic spreading in random quantum circuits
• Efficient quantum algorithms for stabilizer entropies
• Stabilizer entropy dynamics after a quantum quench
• Critical behaviors of non-stabilizerness in quantum spin chains
• Nonstabilizerness in U(1) lattice gauge theory
• Stabilizer entropy in non-integrable quantum evolutions
• Quantum Magic and Multi-Partite Entanglement in the Structure of Nuclei
• Nonstabilizerness of Permutationally Invariant Systems
• Improved Stabilizer Estimation via Bell Difference Sampling
• Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model
• Stabilizer disentangling of conformal field theories
• Chaos and magic in the dissipative quantum kicked top
• Triply efficient shadow tomography
• Entanglement and Stabilizer entropies of random bipartite pure quantum states
• Quantum Complexity Fluctuations from Nuclear and Hypernuclear Forces
• Stabilizer Testing and Magic Entropy via Quantum Fourier Analysis
• Nonstabilizerness in the unitary and monitored quantum dynamics of XXZ-staggered and SYK models
• Stabilizer Rényi Entropy and Conformal Field Theory
• Nonstabilizerness of a Boundary Time Crystal
• Quantum Complexity and Chaos in Many-Qudit Doped Clifford Circuits
• Nonstabilizerness in open XXZ spin chains: Universal scaling and dynamics
• Zero and Finite Temperature Quantum Simulations Powered by Quantum Magic
• Stability of classical shadows under gate-dependent noise
• Interplay of entanglement structures and stabilizer entropy in spin models
• Emergent symmetry in a two-Higgs-doublet model from quantum information and nonstabiliserness
• The non-stabilizerness of fermionic Gaussian states
• Impact of Clifford operations on non-stabilizing power and quantum chaos
• Stabilizer Rényi Entropy Encodes Fusion Rules of Topological Defects and Boundaries
• Exponential learning advantages with conjugate states and minimal quantum memory
• Single-copy stabilizer testing
• Rise and fall of nonstabilizerness via random measurements
• Highly-entangled, highly-doped states that are efficiently cross-device verifiable
• Quantum Magic in Discrete-Time Quantum Walk

Cited by in corpus (3)

• Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks
• Experimental measurement and a physical interpretation of quantum shadow enumerators
• Adaptively secure unitary designs with constant non-Clifford cost