A quantum state is like a fragile snowflake: touch it, and it's already different. To find out how unpredictable it is, physicists measure entropy. For that, they need copies of the state — like several identical snowflakes to examine under a magnifying glass. But each copy is destroyed after measurement.

Now the chasm has nearly disappeared. The scientists devised an algorithm that requires exactly as many copies as the lower bound dictates. It's as if you found a way to measure temperature without breaking the thermometer after each use.

The secret lies in combining two techniques. First, from a few copies, they make a rough sketch of the state — like a portrait sketch. Then, they refine this sketch with a clever trick: they represent the state as part of a larger pure state. This allows extracting more information from each copy.

Previously, it was unclear whether the lower bound could be achieved at all. Now it's clear: it can. And if someone proposes a method with fewer copies, it would contradict quantum mechanics.