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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?

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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.

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  • $\begingroup$ 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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