How Dynamical Quantum Memories Forget

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.

arXiv comment24 pages, 2 figures (v3) expanding the proof of Lemma 3

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• Entanglement Transitions from Stochastic Resetting of Non-Hermitian Quasiparticles
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• Fate of measurement-induced phase transition in long-range interactions
• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
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• Cross Entropy Benchmark for Measurement-Induced Phase Transitions
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• Quantum coding with low-depth random circuits
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• Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics
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• Ultrafast Entanglement Dynamics in Monitored Quantum Circuits
• Random-matrix models of monitored quantum circuits
• Chaos and magic in the dissipative quantum kicked top
• Field theory of monitored, interacting fermion dynamics with charge conservation
• The impact of different unravelings in a monitored system of free fermions
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• Dynamics and Phases of Nonunitary Floquet Transverse-Field Ising Model
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• Universal Stochastic Equations of Monitored Quantum Dynamics
• Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
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• Protect Measurement-Induced Phase Transition from Noise
• Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
• Measurement-Induced Phase Transition in State Estimation of Chaotic Systems and the Directed Polymer
• Charge and Spin Sharpening Transitions on Dynamical Quantum Trees
• Topological Modes in Monitored Quantum Dynamics
• Measurement Induced Chirality II: Diffusion and Disorder
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• Rise and fall of nonstabilizerness via random measurements
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• Efficient circular Dyson Brownian motion algorithm
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• Entanglement transition in unitary system-bath dynamics
• Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions
• Symmetry and Topology of Monitored Quantum Dynamics
• Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions
• Controlled Zeno-Induced Localization of Free Fermions in a Quasiperiodic Chain