Unitary-projective entanglement dynamics
By Amos Chan, R. Nandkishore, M. Pretko, Graeme Smith. Physical review B, 2018
393 citations recorded by the source corpus.
Starting from a state of low quantum entanglement, local unitary time evolution increases the entanglement of a quantum many-body system. In contrast, local projective measurements disentangle degrees of freedom and decrease entanglement. We study the interplay of these competing tendencies by considering time evolution combining both unitary and projective dynamics. We begin by constructing a toy model of Bell pair dynamics which demonstrates that measurements can keep a system in a state of low (i.e. area law) entanglement, in contrast with the volume law entanglement produced by generic pure unitary time evolution. While the simplest Bell pair model has area law entanglement for any measurement rate, as seen in certain non-interacting systems, we show that more generic models of entanglement can feature an area-to-volume law transition at a critical value of the measurement rate, in agreement with recent numerical investigations. As a concrete example of these ideas, we analytically investigate Clifford evolution in qubit systems which can exhibit an entanglement transition. We are able to identify stabilizer size distributions characterizing the area law, volume law and critical 'fixed points.' We also discuss Floquet random circuits, where the answers depend on the order of limits - one order of limits yields area law entanglement for any non-zero measurement rate, whereas a different order of limits allows for an area law - volume law transition. Finally, we provide a rigorous argument that a system subjected to projective measurements can only exhibit a volume law entanglement entropy if it also features a subleading correction term, which provides a universal signature of projective dynamics in the high-entanglement phase. Note: The results presented here supersede those of all previous versions of this manuscript, which contained some erroneous claims.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/cfb6492d89239e6a4da283bd9f0651fb79712331
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Citations in the corpus
- Engineered dissipation for quantum information science (2022, background): “Deep insight is being developed into the connections between classical and quantum chaos 266 , how information propagates in a quantum system 267 , and the interplay between coherent and incoherent processes in the propagation of entanglement 268,269 .”
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement (2018, background): “—We would like to draw the reader’s attention to two related parallel works—by Chan, Nandkishore, Pretko, and Smith [113]; and by Li, Chen, and Fisher [114]—which appeared recently.”
- Measurement-protected quantum phases (2020, background): “[10] Amos Chan, Rahul M.”
- Random Quantum Circuits (2022, background): “Monitored many-body systems have been the subject of much recent progress (58, 59, 60, 61, 62, 54, 55, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 57, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84).”
- Entanglement Membrane in Chaotic Many-Body Systems (2019, background): “The effective spin model may also be extended to dynamics with measurement, or other types of interaction with an environment, for example to clarify the relationship between different universality classes of measurement-induced criticality [78, 79, 83–93].”