Nandu45321/QuantumSpeedLimit ? reverse-engineered prompt

Build me a small Jupyter notebook project that explores the quantum speed limit and shows the results with clear plots. I want it to calculate and compare the bound for a few different cases, then visualize how the limit changes as the parameters change. Please make the notebook easy to follow, with short explanations in plain English alongside the math and graphs.

Also include a simple Python script if that makes the plotting easier, and make sure the figures are saved cleanly so I can use them in a report. I’d like the final notebook to feel like a polished internship project, with readable outputs, labeled charts, and a short conclusion on what the results mean. If you need to check current docs or formulas online to make sure the implementation is correct, go ahead and do that.