Question: Problem 6.Non-cloning theorem.Please provide your answer and a brief explanation. (5 points)(Clone a random bit?) Given one sample of an unknown biased random coin (say,

Problem 6.Non-cloning theorem.Please provide your answer and a brief explanation.

  • (5 points)(Clone a random bit?) Given one sample of an unknown biased random coin (say, 0 with probabilitypand 1 with probability 1pandpunknown), is there a procedure to create two copies of such biased random coin? Namely, this procedure needs to generate two independent random coins with the samep.
  • (5 points)(Clone one certain basis?) Is there a procedure to clone qubits restricted to{|+,|}?
  • (Bonus: 5 points)(Clone with many samples?) If you are given 1000 samples of an unknown biased random coin, is it possible to create 1,000,000 independent copies of the random coin? Here we allow the generated copies can be a little different from the original copy. Note that the precise number 1000 (or 1,000, 000) does not change the answer.

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