Universal structure of measurement-induced information in many-body ground states (2312.11615v2)
Abstract: Unlike unitary dynamics, measurements of a subsystem can induce long-range entanglement via quantum teleportation. The amount of measurement-induced entanglement or mutual information depends jointly on the measurement basis and the entanglement structure of the state (before measurement), and has operational significance for whether the state is a resource for measurement-based quantum computing, as well as for the computational complexity of simulating the state using quantum or classical computers. In this work, we examine entropic measures of measurement-induced entanglement (MIE) and information (MII) for the ground-states of quantum many-body systems in one- and two- spatial dimensions. From numerical and analytic analysis of a variety of models encompassing critical points, quantum Hall states, string-net topological orders, and Fermi liquids, we identify universal features of the long-distance structure of MIE and MII that depend only on the underlying phase or critical universality class of the state. We argue that, whereas in $1d$ the leading contributions to long-range MIE and MII are universal, in $2d$, the existence of a teleportation transition for finite-depth circuits implies that trivial $2d$ states can exhibit long-range MIE, and the universal features lie in sub-leading corrections. We introduce modified MIE measures that directly extract these universal contributions. As a corollary, we show that the leading contributions to strange-correlators, used to numerically identify topological phases, are in fact non-universal in two or more dimensions, and explain how our modified constructions enable one to isolate universal components. We discuss the implications of these results for classical- and quantum- computational simulation of quantum materials.
- M. B. Hastings and X.-G. Wen, Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance, Phys. Rev. B 72, 045141 (2005).
- L. Piroli, G. Styliaris, and J. I. Cirac, Quantum circuits assisted by local operations and classical communication: Transformations and phases of matter, Phys. Rev. Lett. 127, 220503 (2021).
- N. Tantivasadakarn, R. Verresen, and A. Vishwanath, Shortest route to non-abelian topological order on a quantum processor, Phys. Rev. Lett. 131, 060405 (2023b).
- R. Raussendorf and H. J. Briegel, A one-way quantum computer, Phys. Rev. Lett. 86, 5188 (2001).
- D. Gross and J. Eisert, Novel schemes for measurement-based quantum computation, Phys. Rev. Lett. 98, 220503 (2007).
- A. C. Doherty and S. D. Bartlett, Identifying phases of quantum many-body systems that are universal for quantum computation, Phys. Rev. Lett. 103, 020506 (2009).
- A. Miyake, Quantum computation on the edge of a symmetry-protected topological order, Phys. Rev. Lett. 105, 040501 (2010).
- F. Verstraete, M. Popp, and J. I. Cirac, Entanglement versus correlations in spin systems, Phys. Rev. Lett. 92, 027901 (2004).
- M. J. Bremner, C. Mora, and A. Winter, Are random pure states useful for quantum computation?, Phys. Rev. Lett. 102, 190502 (2009).
- D. Gross, S. T. Flammia, and J. Eisert, Most quantum states are too entangled to be useful as computational resources, Phys. Rev. Lett. 102, 190501 (2009).
- Y. Li, X. Chen, and M. P. A. Fisher, Quantum Zeno effect and the many-body entanglement transition, Physical Review B 98, 205136 (2018).
- Y. Li, X. Chen, and M. P. A. Fisher, Measurement-driven entanglement transition in hybrid quantum circuits, Phys. Rev. B 100, 134306 (2019).
- B. Skinner, J. Ruhman, and A. Nahum, Measurement-induced phase transitions in the dynamics of entanglement, Phys. Rev. X 9, 031009 (2019).
- M. J. Gullans and D. A. Huse, Dynamical Purification Phase Transition Induced by Quantum Measurements, Physical Review X 10, 041020 (2020).
- Y. Bao, M. Block, and E. Altman, Finite time teleportation phase transition in random quantum circuits (2022), arXiv:2110.06963 [quant-ph] .
- G. Q. AI et al., Measurement-induced entanglement and teleportation on a noisy quantum processor, Nature 622, 481 (2023).
- A. J. Ferris and G. Vidal, Perfect sampling with unitary tensor networks, Phys. Rev. B 85, 165146 (2012).
- Z. Cheng and M. Ippoliti, Efficient sampling of noisy shallow circuits via monitored unraveling, PRX Quantum 4, 040326 (2023).
- W. Berdanier, J. Marino, and E. Altman, Universal dynamics of stochastically driven quantum impurities, Phys. Rev. Lett. 123, 230604 (2019).
- M. A. Rajabpour, Entanglement entropy after a partial projective measurement in 1 + 1 dimensional conformal field theories: exact results, Journal of Statistical Mechanics: Theory and Experiment 2016, 063109 (2016).
- P. Calabrese, J. Cardy, and E. Tonni, Entanglement entropy of two disjoint intervals in conformal field theory, Journal of Statistical Mechanics: Theory and Experiment 2009, P11001 (2009).
- D. S. Fisher, Random antiferromagnetic quantum spin chains, Phys. Rev. B 50, 3799 (1994).
- D. S. Fisher, Critical behavior of random transverse-field ising spin chains, Phys. Rev. B 51, 6411 (1995).
- G. Refael and J. E. Moore, Entanglement entropy of random quantum critical points in one dimension, Phys. Rev. Lett. 93, 260602 (2004).
- P. Ruggiero, V. Alba, and P. Calabrese, Entanglement negativity in random spin chains, Phys. Rev. B 94, 035152 (2016).
- G. Vidal, Class of quantum many-body states that can be efficiently simulated, Phys. Rev. Lett. 101, 110501 (2008).
- G. Evenbly and G. Vidal, Algorithms for entanglement renormalization, Phys. Rev. B 79, 144108 (2009).
- T. Zhou and A. Nahum, Emergent statistical mechanics of entanglement in random unitary circuits, Phys. Rev. B 99, 174205 (2019).
- Y. Bao, S. Choi, and E. Altman, Theory of the phase transition in random unitary circuits with measurements, Phys. Rev. B 101, 104301 (2020).
- A. C. Potter and R. Vasseur, Entanglement Dynamics in Hybrid Quantum Circuits, in Entanglement in Spin Chains: From Theory to Quantum Technology Applications, Quantum Science and Technology, edited by A. Bayat, S. Bose, and H. Johannesson (Cham, 2022) pp. 211–249.
- C. C. Wu, Ising models on hyperbolic graphs, Journal of Statistical Physics 85, 251 (1996).
- N. P. Breuckmann, B. Placke, and A. Roy, Critical properties of the ising model in hyperbolic space, Phys. Rev. E 101, 022124 (2020).
- F. Iglói and I. Peschel, On reduced density matrices for disjoint subsystems, Europhysics Letters 89, 40001 (2010).
- A. Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics 303, 2–30 (2003).
- H. Bombin and M. A. Martin-Delgado, Family of non-abelian kitaev models on a lattice: Topological condensation and confinement, Physical Review B 78, 10.1103/physrevb.78.115421 (2008).
- I. Peschel and V. Eisler, Reduced density matrices and entanglement entropy in free lattice models, Journal of Physics A: Mathematical and Theoretical 42, 504003 (2009).