My goal is to think of a creative way to clone quantum data, specifically, forensically examine a quantum hard drive or memory of the future.

No, I don't think I can violate the No Cloning Theorem or bypass the Measurement issue. But I was wondering if a creative addition, such as using quantum teleportation or something like that could be used?

For example, what if with every qubit of data (X) on a quantum hard drive, we also required a separate, "assigned" Bell pair (A=B). So every time we create X we also entangle it with A (A=X=B). Could B, outside the hard drive be used to read X? Or am I begging the question...because it would be impossible to entangle X without changing X from it's original state or something like that? Could some mechanism like redundant probability "reads" be used...like something borrowed from quantum error correction ideas?


So the no cloning theorem doesn't preclude you from creating the state $$\alpha|0\rangle + \beta|1\rangle \rightarrow \alpha|00\rangle + \beta|11\rangle,$$ it just says you cant create $$\alpha|0\rangle + \beta|1\rangle \rightarrow (\alpha|0\rangle + \beta|1\rangle)(\alpha|0\rangle + \beta|1\rangle).$$

So yeah, you could do something like create a state like the first state, and then you would have "cloned" the measurement statistics in one basis. That is, if you were only interested in the Z basis measurement statistics of the qubit, and you apply a CNOT to it to create the state $\alpha|00\rangle + \beta|11\rangle$, you would have two qubits which you could measure and sample from that distribution. But only one of them could be measured before the wavefunction collapses, and only the Z basis distribution would be preserved. This is because in the X basis, the state would not be of the form $\gamma|++\rangle + \delta|--\rangle$.

That's the closest I can think of.

  • $\begingroup$ I don't completely understand your answer...a little above my limited understanding of the notation and quantum logic gates. I'm trying to determine in what order entanglement must happen to measure X as stored in memory unchanged? Must I entangle A and X first, before X is stored, or A and X and B before X is stored? $\endgroup$ Jun 27 '20 at 14:49
  • $\begingroup$ So what you're trying to do is the thing that the no-cloning theorem prevents. You can't take a state, 'store' it while making a copy, and then measure your copy to get any information about the stored case. $\endgroup$ Jun 27 '20 at 23:04
  • $\begingroup$ But can I make an entanglement ahead of time, or a three-way entanglement, A=B=X, then do the storage or computation (so that all three have the same value) and measure B? Sort of like teleportation with the three-way entanglement made up ahead of time before X becomes some stored value? $\endgroup$ Jun 28 '20 at 12:32
  • $\begingroup$ so creating A=B=X is the step that violates the no-cloning theorem. It is impossible to create a quantum state that is "equal" to another state by copying it. You can replicate the same steps to get there (IE if your state A is the result of applying some gate to $|0\rangle$, you can get another $|0\rangle$ state and apply the gate again) but if I hand you a qubit in some state, there is no way to copy that state onto a qubit of your own and then return my qubit without its state untouched. $\endgroup$ Jun 28 '20 at 17:54
  • $\begingroup$ How is that we can communicate information using quantum teleportation then? Aren't two Bell pairs (A=B and A=X) being used to communicate X between A & B along with an classical channel? So, to be a pain, but I think you helped me to see that my confusion lies between the difference between the No Cloning Theorem and Quantum Teleportation. $\endgroup$ Jun 29 '20 at 12:08

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