Lesson 3 — Preserving the State
What Should Transport Preserve?
Transport can be smooth and still distort a state. QM2 requires transport to preserve the state's underlying relational structure.
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✓ Relationship Preserved
The states move, but their relationship remains the same.
Transport moves the states without changing their structure.
State Lengths Unchanged
Angle Between States Unchanged
ASSUMED HERE
QM2 Assumption D2
QM2 assumes that transport preserves the Hermitian inner product.
In simple terms, the states may move, but their lengths and relationships must remain unchanged.
Why Transport Must Be Unitary
DERIVEDThe geometry established in QM1 must be preserved during transport. That requirement forces the transport transformations to be unitary.
Which Motion Preserves the State?
Select every example that preserves the state relationship.