An ideal echo restores a recoverable bucket but not irreversible loss. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

An echo separates recoverable and lost dephasing

Before the echo, coherent signal is 6. The recoverable bucket is 4 and irreversible loss is 2.

6+4+2=126+4+2=12
Spin echo refocusThe toy echo refocuses recoverable dephasing but not irreversible loss.coherent 6recoverable 4irreversible 2no echo 6echo 10accepted

The echo cannot recover irreversible loss

Without the echo, visible signal is 6. The ideal echo restores the recoverable 4 and reaches 10; the lost 2 stays lost.

6+4=106+4=10
Spin echo refocusThe toy echo refocuses recoverable dephasing but not irreversible loss.coherent 6recoverable 4irreversible 2no echo 6echo 10accepted