diff options
author | Prefetch | 2022-10-14 23:25:28 +0200 |
---|---|---|
committer | Prefetch | 2022-10-14 23:25:28 +0200 |
commit | 6ce0bb9a8f9fd7d169cbb414a9537d68c5290aae (patch) | |
tree | a0abb6b22f77c0e84ed38277d14662412ce14f39 /source/know/concept/superdense-coding |
Initial commit after migration from Hugo
Diffstat (limited to 'source/know/concept/superdense-coding')
-rw-r--r-- | source/know/concept/superdense-coding/index.md | 71 |
1 files changed, 71 insertions, 0 deletions
diff --git a/source/know/concept/superdense-coding/index.md b/source/know/concept/superdense-coding/index.md new file mode 100644 index 0000000..f9ffbc1 --- /dev/null +++ b/source/know/concept/superdense-coding/index.md @@ -0,0 +1,71 @@ +--- +title: "Superdense coding" +date: 2021-03-07 +categories: +- Quantum information +layout: "concept" +--- + +In quantum information, **(super)dense coding** +is a protocol to enhance classical communication. +It uses a quantum communication channel and +[entanglement](/know/concept/quantum-entanglement/) +to send two bits of classical data with just one qubit. +It is conceptually similar to [quantum teleportation](/know/concept/quantum-teleportation/). + +Suppose that Alice wants to send two bits of classical data to Bob, +but she can only communicate with him over a quantum channel. +She could send a qubit, which has a larger state space than a classical bit, +but it can only be measured once, thereby yielding only one bit of data. + +However, they are already sharing an entangled pair of qubits +in the [Bell state](/know/concept/bell-state/) $\ket{\Phi^{+}}_{AB}$, +where $A$ and $B$ are qubits belonging to Alice and Bob, respectively. + +Based on the values of the two classical bits $(a_1, a_2)$, +Alice performs the following operations on her side $A$ +of the Bell state: + +<table style="width:70%;margin:auto;text-align:center;"> + <tr> + <th>$(a_1, a_2)$</th> + <th>Operator</th> + <th>Result</th> + </tr> + <tr> + <td>$00$</td> + <td>$\hat{I}$</td> + <td>$\ket{\Phi^{+}} = \frac{1}{\sqrt{2}} \Big(\Ket{0}_A \Ket{0}_B + \Ket{1}_A \Ket{1}_B \Big)$</td> + </tr> + <tr> + <td>$01$</td> + <td>$\hat{\sigma}_z$</td> + <td>$\ket{\Phi^{-}} = \frac{1}{\sqrt{2}} \Big(\Ket{0}_A \Ket{0}_B - \Ket{1}_A \Ket{1}_B \Big)$</td> + </tr> + <tr> + <td>$10$</td> + <td>$\hat{\sigma}_x$</td> + <td>$\ket{\Psi^{+}} = \frac{1}{\sqrt{2}} \Big(\Ket{0}_A \Ket{1}_B + \Ket{1}_A \Ket{0}_B \Big)$</td> + </tr> + <tr> + <td>$11$</td> + <td>$\hat{\sigma}_x \hat{\sigma}_z$</td> + <td>$\ket{\Psi^{-}} = \frac{1}{\sqrt{2}} \Big(\Ket{0}_A \Ket{1}_B - \Ket{1}_A \Ket{0}_B \Big)$</td> + </tr> +</table> + +Her actions affect the state on Bob's side $B$ due to entanglement. +Alice then sends her qubit $A$ to Bob over the quantum channel, +so he has both sides of the entangled pair. + +Finally, Bob performs a measurement of his pair in the Bell basis, +which will yield a Bell state that he can then look up in the table above +to recover the values of the bits $(a_1, a_2)$. +In the end, Alice only sent a single qubit, +and the rest of the information transfer was via entanglement. + + +## References +1. J.B. Brask, + *Quantum information: lecture notes*, + 2021, unpublished. |