Superdense coding: Difference between revisions

Revision as of 15:49, 2 September 2021

Revision as of 15:52, 2 September 2021

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2. If Alice wants to send the classical two-bit string 01 to Bob, then she applies the [[Quantum logic gate|quantum ''NOT'' (or ''bit-flip'') gate]], <math>X = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} </math>, to her qubit, so that the resultant entangled quantum state becomes

:<math>|B_{1001}\rangle = \frac{1}{\sqrt{2}}(|1_A0_B\rangle + |0_A1_B\rangle)</math>

3. If Alice wants to send the classical two-bit string 10 to Bob, then she applies the [[Quantum logic gate|quantum ''phase-flip'' gate]] <math>Z = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}</math> to her qubit, so the resultant entangled state becomes

:<math>|B_{0110}\rangle = \frac{1}{\sqrt{2}}(|0_A0_B\rangle - |1_A1_B\rangle)</math>

4. If, instead, Alice wants to send the classical two-bit string 11 to Bob, then she applies the quantum gate <math>Z*X = iY</math> to her qubit, so that the resultant entangled state becomes