**Quantum measurement tradeoffs, from Heisenberg to Aharonov to quantum data compression** - Aephraim Steinberg

Tradeoffs in measurement and information are among the central themes of quantum mechanics.
I will try to summarize in this talk a few of our experiments related to modern views of these topics.
In particular, I will try to give an example or two of the power of "weak measurements," both for
fundamental physics and for possible precision metrology. One example will involve revisiting
the question of Heisenberg's famous principle, and an interpretation which is widespread but
has now been experimentally shown to be incorrect. Then I will also discuss recent work
on a "quantum data compression" protocol which would allow a small-scale quantum memory
to store all the extractable information from a larger ensemble of identically prepared systems.