Building all Time Evolutions with Rotationally Invariant Hamiltonians

Understand

All elementary Hamiltonians in nature are expected to be invariant under rotation.

• Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption whose validity is not obvious.
• We introduce two different schemes by which any arbitrary unitary time evolution and measurement can be implemented with desired accuracy by using rotationally invariant Hamiltonians that act on the given system and two ancillary systems serving as reference frames.
• These frames specify the z and x directions and are independent of the desired time evolution.