Part (b) Now suppose that, instead of 1 bit, your memory con…

Questions

Pаrt (b) Nоw suppоse thаt, insteаd оf 1 bit, your memory contains 1 qubit. Whenever a new bit arrives from the stream, you can act on your qubit by any unitary transformation you want, but can make no other records. Once the stream is finished, you can then measure your qubit to answer a question.   Describe a quantum strategy to guess whether the number of '1' bits in the stream is divisible by 3 and succeeds with probability greater than 1/2. Note that there is no guarantee on the probability of the number of '1' bits. The parity is not necessarily uniformly distributed. Maybe the number is always divisible by 3, maybe the number is not divisible 95% of the time, etc. Explicitly give any unitary transformations and measurements you perform. Briefly justify that your strategy works. A few sentences should be enough.

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