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  • Letter
  • Open Access

Uncovering measurement-induced entanglement via directional adaptive dynamics and incomplete information

Yu-Xin Wang (王语馨)1,2,*, Alireza Seif1, and Aashish A. Clerk1

  • *Contact author: yxwang@uchicago.edu
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Phys. Rev. A 110, L050602 – Published 19 November, 2024

DOI: https://doi.org/10.1103/PhysRevA.110.L050602

Abstract

The rich entanglement dynamics and transitions exhibited by monitored quantum systems typically only exist in the conditional state, making observation extremely difficult. In this Letter, we construct a general recipe for mimicking the conditional entanglement dynamics of a monitored system in a corresponding measurement-free dissipative system involving directional interactions between the original system and a set of auxiliary register modes. This mirror setup autonomously implements a measurement-feedforward dynamics that effectively retains a coarse-grained measurement record. We illustrate our ideas in a bosonic system featuring a competition between entangling measurements and local unitary dynamics, and also discuss extensions to qubit systems and truly many-body systems.

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References (76)

  1. B. Skinner, J. Ruhman, and A. Nahum, Measurement-induced phase transitions in the dynamics of entanglement, Phys. Rev. X 9, 031009 (2019).
  2. Y. Li, X. Chen, and M. P. A. Fisher, Measurement-driven entanglement transition in hybrid quantum circuits, Phys. Rev. B 100, 134306 (2019).
  3. A. Zabalo, M. J. Gullans, J. H. Wilson, S. Gopalakrishnan, D. A. Huse, and J. H. Pixley, Critical properties of the measurement-induced transition in random quantum circuits, Phys. Rev. B 101, 060301(R) (2020).
  4. Y. Bao, S. Choi, and E. Altman, Theory of the phase transition in random unitary circuits with measurements, Phys. Rev. B 101, 104301 (2020).
  5. S. Choi, Y. Bao, X.-L. Qi, and E. Altman, Quantum error correction in scrambling dynamics and measurement-induced phase transition, Phys. Rev. Lett. 125, 030505 (2020).
  6. A. Lavasani, Y. Alavirad, and M. Barkeshli, Measurement-induced topological entanglement transitions in symmetric random quantum circuits, Nat. Phys. 17, 342 (2021).
  7. X. Turkeshi, A. Biella, R. Fazio, M. Dalmonte, and M. Schiró, Measurement-induced entanglement transitions in the quantum Ising chain: From infinite to zero clicks, Phys. Rev. B 103, 224210 (2021).
  8. M. Van Regemortel, Z.-P. Cian, A. Seif, H. Dehghani, and M. Hafezi, Entanglement entropy scaling transition under competing monitoring protocols, Phys. Rev. Lett. 126, 123604 (2021).
  9. O. Alberton, M. Buchhold, and S. Diehl, Entanglement transition in a monitored free-fermion chain: From extended criticality to area law, Phys. Rev. Lett. 126, 170602 (2021).
  10. T. Botzung, S. Diehl, and M. Müller, Engineered dissipation induced entanglement transition in quantum spin chains: From logarithmic growth to area law, Phys. Rev. B 104, 184422 (2021).
  11. A. Lavasani, Y. Alavirad, and M. Barkeshli, Topological order and criticality in (2+1)D monitored random quantum circuits, Phys. Rev. Lett. 127, 235701 (2021).
  12. P. M. Poggi and M. H. Muñoz-Arias, Measurement-induced multipartite-entanglement regimes in collective spin systems, Quantum 8, 1229 (2024).
  13. Y. Minoguchi, P. Rabl, and M. Buchhold, Continuous Gaussian measurements of the free boson CFT: A model for exactly solvable and detectable measurement-induced dynamics, SciPost Phys. 12, 009 (2022).
  14. K. Yokomizo and Y. Ashida, Measurement-induced phase transition in free bosons, arXiv:2405.19768.
  15. A. C. Potter and R. Vasseur, Entanglement dynamics in hybrid quantum circuits, in Quantum Science and Technology (Springer, Cham, 2022), pp. 211–249.
  16. M. P. Fisher, V. Khemani, A. Nahum, and S. Vijay, Random quantum circuits, Annu. Rev. Condens. Matter Phys. 14, 335 (2023).
  17. J. M. Koh, S.-N. Sun, M. Motta, and A. J. Minnich, Measurement-induced entanglement phase transition on a superconducting quantum processor with mid-circuit readout, Nat. Phys. 19, 1314 (2023).
  18. M. Ippoliti and V. Khemani, Postselection-free entanglement dynamics via spacetime duality, Phys. Rev. Lett. 126, 060501 (2021).
  19. A. G. Moghaddam, K. Pöyhönen, and T. Ojanen, Exponential shortcut to measurement-induced entanglement phase transitions, Phys. Rev. Lett. 131, 020401 (2023).
  20. H. Dehghani, A. Lavasani, M. Hafezi, and M. J. Gullans, Neural-network decoders for measurement induced phase transitions, Nat. Commun. 14, 2918 (2023).
  21. S. J. Garratt and E. Altman, Probing postmeasurement entanglement without postselection, PRX Quantum 5, 030311 (2024).
  22. G. Passarelli, X. Turkeshi, A. Russomanno, P. Lucignano, M. Schiró, and R. Fazio, Many-body dynamics in monitored atomic gases without postselection barrier, Phys. Rev. Lett. 132, 163401 (2024).
  23. T. Iadecola, S. Ganeshan, J. H. Pixley, and J. H. Wilson, Measurement and feedback driven entanglement transition in the probabilistic control of chaos, Phys. Rev. Lett. 131, 060403 (2023).
  24. M. Buchhold, T. Müller, and S. Diehl, Revealing measurement-induced phase transitions by pre-selection, arXiv:2208.10506.
  25. P. Sierant and X. Turkeshi, Controlling entanglement at absorbing state phase transitions in random circuits, Phys. Rev. Lett. 130, 120402 (2023).
  26. N. O'Dea, A. Morningstar, S. Gopalakrishnan, and V. Khemani, Entanglement and absorbing-state transitions in interactive quantum dynamics, Phys. Rev. B 109, L020304 (2024).
  27. P. Sierant and X. Turkeshi, Entanglement and absorbing state transitions in (d+1)-dimensional stabilizer circuits, Acta Phys. Pol., A 144, 474 (2023).
  28. M. J. Gullans and D. A. Huse, Scalable probes of measurement-induced criticality, Phys. Rev. Lett. 125, 070606 (2020).
  29. Y. Li, Y. Zou, P. Glorioso, E. Altman, and M. P. A. Fisher, Cross entropy benchmark for measurement-induced phase transitions, Phys. Rev. Lett. 130, 220404 (2023).
  30. C. Noel, P. Niroula, D. Zhu, A. Risinger, L. Egan, D. Biswas, M. Cetina, A. V. Gorshkov, M. J. Gullans, D. A. Huse, and C. Monroe, Measurement-induced quantum phases realized in a trapped-ion quantum computer, Nat. Phys. 18, 760 (2022).
  31. J. C. Hoke, M. Ippoliti, D. Abanin, R. Acharya, M. Ansmann, F. Arute, K. Arya, A. Asfaw, J. Atalaya, J. C. Bardin et al., Measurement-induced entanglement and teleportation on a noisy quantum processor, Nature (London) 622, 481 (2023).
  32. A. J. Friedman, O. Hart, and R. Nandkishore, Measurement-induced phases of matter require feedback, PRX Quantum 4, 040309 (2023).
  33. L. Piroli, Y. Li, R. Vasseur, and A. Nahum, Triviality of quantum trajectories close to a directed percolation transition, Phys. Rev. B 107, 224303 (2023).
  34. V. Ravindranath, Z.-C. Yang, and X. Chen, Free fermions under adaptive quantum dynamics, arXiv:2306.16595.
  35. C. LeMaire, A. A. Allocca, J. H. Pixley, T. Iadecola, and J. H. Wilson, Separate measurement- and feedback-driven entanglement transitions in the stochastic control of chaos, Phys. Rev. B 110, 014310 (2024).
  36. H. M. Wiseman, Quantum theory of continuous feedback, Phys. Rev. A 49, 2133 (1994).
  37. H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control (Cambridge University Press, Cambridge, UK, 2009).
  38. A. Metelmann and A. A. Clerk, Nonreciprocal quantum interactions and devices via autonomous feedforward, Phys. Rev. A 95, 013837 (2017).
  39. In this specific case, as the dynamics is Gaussian, every trajectory has the same entanglement.
  40. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevA.110.L050602 for details on trajectory dynamics due to continuously monitoring x̂+, parametric dependence of conditional entanglement generation and entanglement via the corresponding measurement-free protocol, the recovery protocol, and the reservoir engineering realization of each dissipator in Eq. (3), which includes Refs. [71, 72, 73, 74, 75, 76].
  41. P. Calabrese and J. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech.: Theory Exp. (2004) P06002.
  42. M. Žnidarič, T. Prosen, and P. Prelovšek, Many-body localization in the Heisenberg XXZ magnet in a random field, Phys. Rev. B 77, 064426 (2008).
  43. J. H. Bardarson, F. Pollmann, and J. E. Moore, Unbounded growth of entanglement in models of many-body localization, Phys. Rev. Lett. 109, 017202 (2012).
  44. D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Colloquium: Many-body localization, thermalization, and entanglement, Rev. Mod. Phys. 91, 021001 (2019).
  45. C.-M. Jian, Y.-Z. You, R. Vasseur, and A. W. W. Ludwig, Measurement-induced criticality in random quantum circuits, Phys. Rev. B 101, 104302 (2020).
  46. Y. Li, X. Chen, A. W. W. Ludwig, and M. P. A. Fisher, Conformal invariance and quantum nonlocality in critical hybrid circuits, Phys. Rev. B 104, 104305 (2021).
  47. L. Hackl, E. Bianchi, R. Modak, and M. Rigol, Entanglement production in bosonic systems: Linear and logarithmic growth, Phys. Rev. A 97, 032321 (2018).
  48. G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48, 119 (1976).
  49. V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of N-level systems, J. Math. Phys. 17, 821 (1976).
  50. A. Metelmann and A. A. Clerk, Nonreciprocal photon transmission and amplification via reservoir engineering, Phys. Rev. X 5, 021025 (2015).
  51. M. Tsang and C. M. Caves, Evading quantum mechanics: Engineering a classical subsystem within a quantum environment, Phys. Rev. X 2, 031016 (2012).
  52. C. B. Møller, R. A. Thomas, G. Vasilakis, E. Zeuthen, Y. Tsaturyan, M. Balabas, K. Jensen, A. Schliesser, K. Hammerer, and E. S. Polzik, Quantum back-action-evading measurement of motion in a negative mass reference frame, Nature (London) 547, 191 (2017).
  53. Note that at the QMFS point, we only need two auxiliary register modes to fully capture long-time conditional entanglement generation using a protocol that is similar to Eq. (3) but with different time-modulating functions fj(t;tf).
  54. T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev. 58, 1098 (1940).
  55. J. A. Hines, S. V. Rajagopal, G. L. Moreau, M. D. Wahrman, N. A. Lewis, O. Marković, and M. Schleier-Smith, Spin squeezing by Rydberg dressing in an array of atomic ensembles, Phys. Rev. Lett. 131, 063401 (2023).
  56. E. S. Cooper, P. Kunkel, A. Periwal, and M. Schleier-Smith, Graph states of atomic ensembles engineered by photon-mediated entanglement, Nat. Phys. 20, 770 (2024).
  57. This is similar to the situation of going from Clifford to non-Clifford circuits.
  58. J. Rieser, M. A. Ciampini, H. Rudolph, N. Kiesel, K. Hornberger, B. A. Stickler, M. Aspelmeyer, and U. Delić, Tunable light-induced dipole-dipole interaction between optically levitated nanoparticles, Science 377, 987 (2022).
  59. J. F. Poyatos, J. I. Cirac, and P. Zoller, Quantum reservoir engineering with laser cooled trapped ions, Phys. Rev. Lett. 77, 4728 (1996).
  60. P. M. Harrington, E. J. Mueller, and K. W. Murch, Engineered dissipation for quantum information science, Nat. Rev. Phys. 4, 660 (2022).
  61. H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, Entanglement generated by dissipation and steady state entanglement of two macroscopic objects, Phys. Rev. Lett. 107, 080503 (2011).
  62. D. Kienzler, H.-Y. Lo, B. Keitch, L. de Clercq, F. Leupold, F. Lindenfelser, M. Marinelli, V. Negnevitsky, and J. P. Home, Quantum harmonic oscillator state synthesis by reservoir engineering, Science 347, 53 (2015).
  63. C. Flühmann, T. L. Nguyen, M. Marinelli, V. Negnevitsky, K. Mehta, and J. P. Home, Encoding a qubit in a trapped-ion mechanical oscillator, Nature (London) 566, 513 (2019).
  64. E. E. Wollman, C. U. Lei, A. J. Weinstein, J. Suh, A. Kronwald, F. Marquardt, A. A. Clerk, and K. C. Schwab, Quantum squeezing of motion in a mechanical resonator, Science 349, 952 (2015).
  65. J.-M. Pirkkalainen, E. Damskägg, M. Brandt, F. Massel, and M. A. Sillanpää, Squeezing of quantum noise of motion in a micromechanical resonator, Phys. Rev. Lett. 115, 243601 (2015).
  66. C. U. Lei, A. J. Weinstein, J. Suh, E. E. Wollman, A. Kronwald, F. Marquardt, A. A. Clerk, and K. C. Schwab, Quantum nondemolition measurement of a quantum squeezed state beyond the 3 dB limit, Phys. Rev. Lett. 117, 100801 (2016).
  67. 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).
  68. N. Tantivasadakarn, A. Vishwanath, and R. Verresen, Hierarchy of topological order from finite-depth unitaries, measurement, and feedforward, PRX Quantum 4, 020339 (2023).
  69. E. Bäumer, V. Tripathi, D. S. Wang, P. Rall, E. H. Chen, S. Majumder, A. Seif, and Z. K. Minev, Efficient long-range entanglement using dynamic circuits, PRX Quantum 5, 030339 (2024).
  70. A. Seif, Y.-X. Wang, and A. A. Clerk, Distinguishing between quantum and classical markovian dephasing dissipation, Phys. Rev. Lett. 128, 070402 (2022).
  71. K. Jacobs and D. A. Steck, A straightforward introduction to continuous quantum measurement, Contemp. Phys. 47, 279 (2006).
  72. J. Eisert, S. Scheel, and M. B. Plenio, Distilling Gaussian states with Gaussian operations is impossible, Phys. Rev. Lett. 89, 137903 (2002).
  73. J. Fiurášek and L. Mišta, Gaussian localizable entanglement, Phys. Rev. A 75, 060302(R) (2007).
  74. C. A. Regal, J. D. Teufel, and K. W. Lehnert, Measuring nanomechanical motion with a microwave cavity interferometer, Nat. Phys. 4, 555 (2008).
  75. N. C. Menicucci, S. T. Flammia, and P. van Loock, Graphical calculus for Gaussian pure states, Phys. Rev. A 83, 042335 (2011).
  76. J. T. Barreiro, M. Müller, P. Schindler, D. Nigg, T. Monz, M. Chwalla, M. Hennrich, C. F. Roos, P. Zoller, and R. Blatt, An open-system quantum simulator with trapped ions, Nature (London) 470, 486 (2011).

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Phys. Rev. A 110, L050602– Published 19 November, 2024
  • Received 17 October 2023
  • Revised 19 August 2024
  • Accepted 29 October 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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