12 ms·
What do you mean by “unitary evolution is a theory where nothing changes”?
by antidesitter 8y ago
What do you mean by “unitary evolution is a theory where nothing changes”?
- mathgenius 8y agoFor any two state vectors, |u> and |v>, unitary evolution preserves the amplitude <u|v>: <u|U^\dag U|v> = <u|v>.
- monktastic1 8y agoSure, if U operates on both |u> and |v>, their inner product doesn't change. But why does this mean that "nothing ever changes?" |u> can evolve independently of |v>, after all. OTOH, I can understand the argument that nothing ever happens. One reasonable requirement for something to happen is that it should not be able to "unhappen," which is why some are looking for the possibility of irreversible decoherence.
- mathgenius 8y ago" |u> can evolve independently of |v> " This is not unitary. Quantum theory has two parts: unitary evolution, and measurement processes. That's it.
- monktastic1 8y agoEh? If U is a unitary operator that can act on |u>, then U @ I is a unitary operator on the state |u> @ |v>, producing U|u> @ |v>. Can you explain what you mean?
- antidesitter 8y agoDoesn’t that assume |v> evolves the same way |u> does (according to U)?
- mathgenius 8y agoAnything else is not unitary evolution.
- antidesitter 8y agoWhat do you mean? Let u and v be qubits. Apply a Hadamard gate to u while leaving v unchanged. Then they have evolved independently (but unitarily): u according to H, and v according to I.