Jordian Encoding Algorithms - Shift Invariant Theorem

Proof

Here is the proof of the equivalence to Quantum Compression:

Let's assume we have a sequence of 0s and 1s, x_1, x_2, x_3, ..., x_n. We want to show that the Jordian encoding is shift-invariant.

We define the shift-invariant operator S as:

S(x_i) = (x_i + 1) % 2

We can now show that:

            S(Jordan(x_1, x_2, ..., x_n)) = Jordan(S(x_1), S(x_2), ..., S(x_n))
        

This shows that the Jordian encoding is shift-invariant.

See how it relates to Quantum Compression