3 ms·

Oh, that's not fair. Answers, please.

• ivan_ah 12y ago
  * ) the eigenvectors are [1,1] and [1,-1], via http://live.sympy.org/?evaluate=X%20%3D%20Matrix(%5B%5B0%2C1%5D%2C%5B1%2C0%5D%5D)%0A%23--%0AX%0A%23--%0AX.eigenvects()%0A%23--%0A http://live.sympy.org/?evaluate=X%20%3D%20Matrix(%5B%5B0%2C1... * ) The standard basis B_s = {[1,0],[0,1]} and the Hadamard basis B_h={[1,1],[1,-1]} are a mutually unbiased bases, which means any basis vector lies exactly "in between" the vectors from the other basis. The use of mutually unbiased bases has applications in quantum crypto: if the same basis is used for encoding and decoding a bit of information the bit will be transmitted faithfully, else if a different basis is used for decoding than the basis used for encoding, the receiver will decode pure noise (i.e. a 50-50% random bit). This "uncertainty about which basis is used to encode the message" is the key idea behind the BB84 protocol.