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Speed of Evolution and Correlations in Multi-Mode Bosonic Systems.

Alexei D Kiselev¹, Ali Ranim², Andrei V Rybin³

¹Laboratory of Quantum Processes and Measurements, ITMO University, Kadetskaya Line 3b, 199034 Saint Petersburg, Russia.

Entropy (Basel, Switzerland)

|December 23, 2022

Summary

This study explores quantum speed limits in open multi-mode bosonic systems using an exact solution of the Lindblad master equation. It reveals how intermode couplings and temperature influence the speed of quantum evolution and system distinguishability.

Keywords:

disentanglement intermode couplings mutual information open continuous variable quantum systems quantum speed limits squeezed states

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Area of Science:

Quantum physics
Open quantum systems
Quantum information theory

Background:

Understanding the dynamics of open quantum systems is crucial for quantum technologies.
Quantum speed limits (QSL) define fundamental bounds on the rate of quantum evolution.
Previous studies often simplified intermode couplings or focused on single-mode systems.

Purpose of the Study:

To investigate the speed of evolution and QSL times in open multi-mode bosonic systems.
To derive explicit expressions for evolution speed and QSL times for Gaussian states.
To analyze the influence of intermode couplings, temperature, and system parameters on quantum dynamics.

Main Methods:

Exact solution of the thermal bath Lindblad master equation.
Analysis of Liouvillian superoperator including dynamic and environment-induced intermode couplings.
Derivation of analytical expressions for evolution speed and QSL times for Gaussian states.
Application to a two-mode system with specific intermode coupling vectors and squeezed states.

Main Results:

Derived time-dependent QSL times based on fidelity and Hilbert-Schmidt distance.
Identified dynamical regimes determined by intermode coupling vectors, squeezing, and temperature.
Found that disentanglement time depends on relaxation vector length and squeezing parameter relative to a critical value.
Characterized long-time asymptotic behavior of QSL times and evaluated asymptotic ratios.

Conclusions:

Intermode couplings significantly impact the speed of evolution and QSL times in multi-mode bosonic systems.
The derived analytical results provide a framework for understanding quantum dynamics in complex open systems.
System parameters like temperature and squeezing critically influence dynamical regimes and disentanglement.
The study offers insights into the fundamental limits of quantum information processing and state evolution.