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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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Universal Spreading of Conditional Mutual Information in Noisy Random Circuits.

Su-Un Lee¹, Changhun Oh^1,2, Yat Wong¹

¹Pritzker School of Molecular Engineering, <a href="https://ror.org/024mw5h28">The University of Chicago</a>, Chicago, Illinois 60637, USA.

Physical Review Letters

|December 3, 2024

Summary

Conditional mutual information (CMI) in noisy quantum circuits spreads superlinearly, diverging beyond the light cone due to local noise and scrambling unitaries. This rapid spread follows a universal scaling law in open quantum systems.

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Area of Science:

Quantum Information Science
Condensed Matter Physics
Statistical Mechanics

Background:

Conditional mutual information (CMI) in noiseless quantum circuits spreads linearly within the light cone.
Open quantum systems are crucial for understanding real-world quantum phenomena.

Purpose of the Study:

Investigate the evolution of CMI in noisy one-dimensional random quantum circuits.
Uncover the mechanisms behind CMI spreading in the presence of local noise.
Identify universal scaling laws for CMI dynamics.

Main Methods:

Analysis of one-dimensional random circuits with local noise.
Introduction of a coarse-graining method for analytical treatment.
Validation through numerical simulations.

Main Results:

Noisy circuits exhibit superlinear CMI propagation, exceeding the light cone.
CMI diverges at a critical depth t_{c}∝p^{-1} dependent on error rate p.
Local noise and scrambling unitaries drive rapid CMI spreading by preserving long-range correlations.

Conclusions:

Local noise and scrambling unitaries fundamentally alter CMI dynamics in quantum circuits.
A universal scaling law governs CMI spreading in these open quantum systems.
The findings offer insights into information propagation in realistic quantum devices.