Superdense coding: Difference between revisions

Revision as of 15:52, 2 September 2021

Revision as of 15:53, 2 September 2021

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==== Example ====

For example, if the resultant entangled state (after the operations performed by Alice) was <math>B_{1001} = \frac{1}{\sqrt{2}}(|1_A0_B\rangle + |0_A1_B\rangle)</math>, then a CNOT with A as control bit and B as target bit will change <math>B_{01}</math> to become <math>B_{10}' = \frac{1}{\sqrt{2}}(|1_A1_B\rangle + |0_A1_B\rangle)</math>. Now, the Hadamard gate is applied only to A, to obtain

<math>B_{1001}'' = \frac{1}{\sqrt{2}} \left({\left(\frac{1}{\sqrt{2}}(|0 \rangle - |1 \rangle) \right) }_A \otimes

|1_B\rangle + {\left(\frac{1}{\sqrt{2}}(|0 \rangle + |1 \rangle) \right) }_A \otimes

|1_B\rangle\right)</math>

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For simplicity, let's get rid of the subscripts, so we have

<math>B_{1001}'' =

\frac{1}{\sqrt{2}}

\left(