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Stabilizer R\'enyi entropy
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Stabilizer R\'enyi entropy
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We introduce a novel measure for the quantum property of nonstabilizerness - commonly known as "magic" - by considering the R\'enyi entropy of the probability distribution associated to a pure quantum state given by the square of the expectation value of Pauli strings in that state. We show that this is a good measure of nonstabilizerness from the point of view of resource theory and show bounds with other known measures. The stabilizer R\'enyi entropy has the advantage of being easily computable because it does not need a minimization procedure. We present a protocol for an experimental measurement by randomized measurements. We show that the nonstabilizerness is intimately connected to out-of-time-order correlation functions and that maximal levels of nonstabilizerness are necessary for quantum chaos.
Forward citations
Cited by 25 Pith papers
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Universality of Magic in Local Quantum Field Theory
In any local QFT, vacuum-like states have non-flat entanglement spectra because local algebras are type III₁, so no stabilizer state can flow to them in the continuum: QFT states necessarily carry magic.
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Magic Gate Teleportation: Structure, Useful Resource States, and Simpler Feedforward
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Analytical Landscape of Maximal Magic for Two-Qutrit States and Beyond
Maximal stabilizer Rényi entropy for two-qutrit states is ln(81/17), achieved at 18 degenerate maxima; a general prime-d formula ln[d⁴/(2d²−1)] is conjectured and verified for d=2,3,5.
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In a toy qubit model of quarks, BRST cohomology designates baryons as fortuitous and mesons as monotone, with the former displaying super-exponential complexity and the latter power-law complexity in the Veneziano limit.
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Nonlocal Nonstabilizerness from Holographic Schwinger Pair Production
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Production of Magic States via $Z$ Bosons and Dark Photons
Magic distributions are computed for EW processes (reproducing QED at low energy, new at high energy/Z resonance) and dark-sector scatterings, reaching maximal magic at mass ratios m_f/m_χ → 0 and → 1.83929.
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Quantum Resources and Wigner Symmetry in Nucleon-Nucleon Scattering from Effective Field Theory
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Collective neutrino oscillations: Many-body non-forward effects and non-classicality
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Magic and entanglement in 1+1-dimensional SU(2) lattice gauge theory
Tensor network calculation of magic and entanglement in SU(2) lattice gauge theory ground state shows a crossover from magic-rich to less-magic regime at g_star.
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Fortuity and Complexity in a Simple Quark Model
In a toy qubit model of quarks, baryons are fortuitous with exponential counting and super-exponential complexity while mesons are monotone with polynomial counting and power-law complexity.
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Magic and Non-Clifford Gates in Topological Quantum Field Theory
Non-Clifford gates including Ising, Toffoli, and T arise as exact path integrals in Chern-Simons and Dijkgraaf-Witten topological quantum field theories.
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Taming Trotter Errors with Quantum Resources
Higher entanglement entropy reduces variance of Trotter errors and higher magic reduces kurtosis, making error distributions more robust in quantum simulation.
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Spin Correlation and Quantum Entanglement of Fermion Pairs in Transversely Polarized $e^-e^+$ Collisions
Transverse polarization in e+e- collisions generates maximally entangled fermion pairs in QED processes and boosts entanglement in electroweak and Bhabha scattering.
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Complexity of Quadratic Quantum Chaos
Hard-core boson two-body models with random interactions exhibit chaotic spectral statistics, operator growth, and eigenstate properties approaching those of random matrices and the SYK model.
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Quantum entanglement in electron-nucleus collisions: Role of the linearly polarized gluon distribution
The linearly polarized gluon distribution enhances entanglement of heavy quark pairs in electron-nucleus collisions when total and relative transverse momenta are orthogonal.
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