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Replaced tables with images in superdense-coding due to rendering iss…
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frankharkins committed Jan 31, 2020
1 parent 442e3fe commit b89a54c
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7 changes: 6 additions & 1 deletion content/ch-algorithms/superdense-coding.ipynb
Original file line number Diff line number Diff line change
Expand Up @@ -59,13 +59,15 @@
"Encoding Rules for Superdense Coding (Alice protocol)\n",
"Quantum gates/rules\n",
"\n",
"<!--- Table does not render properly when built to html. This is a problem with nbconvert. Replaced with image\n",
"| Intended Message | Applied Gate | Resulting State ($\\cdot\\sqrt{2}$)|\n",
"|:----------------:|:------------:|:--------------------------------:|\n",
"|00 |$I$ | $|00\\rangle + |11\\rangle$ |\n",
"|01 |$X$ | $|01\\rangle + |10\\rangle$ |\n",
"|10 |$Z$ | $|00\\rangle - |11\\rangle$ |\n",
"|11 |$ZX$ | $|10\\rangle - |01\\rangle$ |\n",
"\n",
"--->\n",
"<img src=\"images/superdense_table1.png\" width=\"330\">\n",
"\n",
"Thus if she wants to send a 00, she does nothing to her qubit (apply the identity ($I$) gate). If she sends a 01, then she applies the $X$ gate. Depending on what she wants to send, she applies the appropriate gate. Alice then sends her qubit to Bob for the final step in the process\n",
"\n",
Expand All @@ -76,13 +78,16 @@
"\n",
"Bob applies a CNOT gate using the first qubit as control and the second as target. Then he applies a Hadamard gate and finally performs a measurement in both qubits to extract the classical bits encoded in Alice's qubit.\n",
"\n",
"<!--- Table does not render properly when built to html. This is a problem with nbconvert. Replaced with image\n",
"| Bob Recieves: | After CNOT-gate: | After H-gate: |\n",
"|:-------------------------:|:-------------------------:|:--------------:|\n",
"| $|00\\rangle + |11\\rangle$ | $|00\\rangle + |01\\rangle$ | $|00\\rangle$ |\n",
"| $|01\\rangle + |10\\rangle$ | $|01\\rangle + |11\\rangle$ | $|01\\rangle$ |\n",
"| $|00\\rangle - |11\\rangle$ | $|00\\rangle - |10\\rangle$ | $|10\\rangle$ |\n",
"| $|10\\rangle - |01\\rangle$ | $|11\\rangle - |01\\rangle$ | $|11\\rangle$ |\n",
"--->\n",
"\n",
"<img src=\"images/superdense_table2.png\" width=\"280\">\n",
"\n",
"When Bob performs the measurements, he ends up with four possible outcomes with probability of 1 each. Note that the last outcome has a negative sign $-|11\\rangle$, writing it as $|11\\rangle$ is also correct because the probability is calculated as the amplitude of squared.\n",
"\n",
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