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michael_nielsen's profile
michael_nielsen
michael_nielsen
michael_nielsen
@michael_nielsen

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michael_nielsen

@michael_nielsen

Searching for the numinous. Co-purveyor of https://quantum.country/ 

San Francisco, CA
michaelnielsen.org
Joined July 2008

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    1. michael_nielsen‏ @michael_nielsen May 24
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      Here's the natural analogous quantum circuit, replacing the random pair of bits (r, r) by the analogous quantum state (|00>+|11>)/(sqrt 2):pic.twitter.com/2ARuLIXPrM

      1 reply 1 retweet 11 likes
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    2. michael_nielsen‏ @michael_nielsen May 24
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      Now, you can compute the effect of this circuit mechanically - it's just algebra. I won't go through those details now, though the ideas I described yesterday (https://twitter.com/michael_nielsen/status/1131784174203953153 … ) can be used to verify that if the input is |psi> = a|0>+b|1> then the output is a|00>+b|11>:pic.twitter.com/zomapcwdLS

      1 reply 0 retweets 12 likes
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    3. michael_nielsen‏ @michael_nielsen May 24
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      This seems promising: Alice and Bob now share an entangled quantum state with the amplitudes a and b. Can they do something so Bob ends up with the original state a|0>+b|1>?

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    4. michael_nielsen‏ @michael_nielsen May 24
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      Unfortunately, Alice can't do it by simply applying a quantum gate - the state will remain entangled. But maybe she can make a measurement of some sort?

      1 reply 0 retweets 7 likes
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    5. michael_nielsen‏ @michael_nielsen May 24
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      Suppose Alice measures her remaining qubit in some basis |m>. The resulting conditional state for Bob is, up to normalization: a<m|0> |0> + b <m|1> |1>

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    6. michael_nielsen‏ @michael_nielsen May 24
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      Ahah! This is very promising! If we simply choose the basis |m> to be the equal superposition states |+> = (|0>+|1>)/sqrt 2 and |-> = (|0>-|1>)/sqrt 2 then Bob will get the following conditional states: a|0>+b|1> a|0>-b|1>

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    7. michael_nielsen‏ @michael_nielsen May 24
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      That is, Bob's state is just Z^z|psi>, where z is the outcome of a measurement in the |+>, |-> basis.

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    8. michael_nielsen‏ @michael_nielsen May 24
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      And so the following quantum circuit teleports |psi> from Alice to Bob:pic.twitter.com/AfUe1ncMAa

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    9. michael_nielsen‏ @michael_nielsen May 24
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      This is, in fact, the standard quantum teleportation protocol!

      1 reply 0 retweets 12 likes
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    10. michael_nielsen‏ @michael_nielsen May 24
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      This leaves something to be desired as discovery fiction. Still, it's a lot of fun, and think it's pretty good for Twitter!

      2 replies 0 retweets 4 likes
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      michael_nielsen‏ @michael_nielsen May 24
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      Particularly egregious: it doesn't tell us WHY you might suspect teleportation is possible in the first place. Though I wonder if some quantum person thinking hard about classical one-time pads might have discovered it, largely by following their nose.

      4:39 PM - 24 May 2019
      • 9 Likes
      • ILikeTea Giovane Dias Noah Bilgrien oa Robert Pin LukasDanielKlausner Robin Berjon Daniel Houck Bushra Farooqui
      2 replies 0 retweets 9 likes
        1. michael_nielsen‏ @michael_nielsen May 24
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          Anyway, this kind of discovery fiction can be a lot of fun, and going through this exercise certainly helped me understand teleportation better!

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        1. OneBigOh‏ @OneBigOh May 24
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          Replying to @michael_nielsen

          Interesting. The way you defined teleportation in the beginning made me feel that it should be trivially doable, ie if it’s just about recreating a state. For example classical teleportation is trivial if you don’t care about hiding it?

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