^{1}Department of Physics, University of Washington, Seattle, WA 98195-1560, USA^{2}Microsoft Quantum and Microsoft Research, Redmond, WA 98052, USA^{3}Station Q, Microsoft Research, Santa Barbara, CA 93106-6105, USA

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### Abstract

Motivated by recent work showing that a quantum error correcting code can be generated by hybrid dynamics of unitaries and measurements, we study the long time behavior of such systems. We demonstrate that even in the “mixed” phase, a maximally mixed initial density matrix is purified on a time scale equal to the Hilbert space dimension (i.e., exponential in system size), albeit with noisy dynamics at intermediate times which we connect to Dyson Brownian motion. In contrast, we show that free fermion systems $—$ i.e., ones where the unitaries are generated by quadratic Hamiltonians and the measurements are of fermion bilinears $—$ purify in a time quadratic in the system size. In particular, a volume law phase for the entanglement entropy cannot be sustained in a free fermion system.

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### Cited by

[1] Matteo Ippoliti, Michael J. Gullans, Sarang Gopalakrishnan, David A. Huse, and Vedika Khemani, “Entanglement phase transitions in measurement-only dynamics”, arXiv:2004.09560.

[2] Adam Nahum, Sthitadhi Roy, Brian Skinner, and Jonathan Ruhman, “Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory”, arXiv:2009.11311.

[3] Michael J. Gullans, Stefan Krastanov, David A. Huse, Liang Jiang, and Steven T. Flammia, “Quantum coding with low-depth random circuits”, arXiv:2010.09775.

[4] Jason Iaconis, Andrew Lucas, and Xiao Chen, “Measurement-induced phase transitions in quantum automaton circuits”, arXiv:2010.02196.

[5] Ali Lavasani, Yahya Alavirad, and Maissam Barkeshli, “Topological order and criticality in (2+1)D monitored random quantum circuits”, arXiv:2011.06595.

[6] Sarang Gopalakrishnan and Michael J. Gullans, “Entanglement and purification transitions in non-Hermitian quantum mechanics”, arXiv:2012.01435.

[7] Matteo Ippoliti and Vedika Khemani, “Postselection-free entanglement dynamics via spacetime duality”, arXiv:2010.15840.

[8] Oliver Lunt, Marcin Szyniszewski, and Arijeet Pal, “Dimensional hybridity in measurement-induced criticality”, arXiv:2012.03857.

[9] Chao-Ming Jian, Bela Bauer, Anna Keselman, and Andreas W. W. Ludwig, “Criticality and entanglement in non-unitary quantum circuits and tensor networks of non-interacting fermions”, arXiv:2012.04666.

[10] Shengqi Sang, Yaodong Li, Tianci Zhou, Xiao Chen, Timothy H. Hsieh, and Matthew P. A. Fisher, “Entanglement Negativity at Measurement-Induced Criticality”, arXiv:2012.00031.

The above citations are from SAO/NASA ADS (last updated successfully 2021-01-18 07:19:20). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2021-01-18 07:19:18).

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