# For multi-tape Turing machines, can we assume that each tape can be in its own state independently of the other tapes?

When we consider multi-tape Turing machines, we can assume that each tape is accessed with a separate head and each head can move independently of the other heads. But can we assume that each tape can be in its own state independently of the other tapes (for example, tape 1 in state A, tape 2 in state F, tape 3 in state X simultaneously)?

Then, for example, the table of instructions for some three-tape two-symbol ("0" and "1") machine can look like this:

    | 000         | 001         | ...
----------------------------------
AAA | 011/BXZ/LRL | 010/XYB/RRR | ...
----------------------------------
AAB | 001/TSH/LLR | 110/AET/LLL | ...
----------------------------------
...


For your example, you can encode state "AAA" into state 1, state "AAB" into state 2, and so on (so there are in total $26^3$ states). Now it becomes a normal multi-tape Turing machine.