From 16555851b6514a736c5c9d8e73de7da7fc9b6288 Mon Sep 17 00:00:00 2001 From: Prefetch Date: Thu, 20 Oct 2022 18:25:31 +0200 Subject: Migrate from 'jekyll-katex' to 'kramdown-math-sskatex' --- source/know/concept/superdense-coding/index.md | 94 +++++++++++++++++--------- 1 file changed, 62 insertions(+), 32 deletions(-) (limited to 'source/know/concept/superdense-coding/index.md') diff --git a/source/know/concept/superdense-coding/index.md b/source/know/concept/superdense-coding/index.md index 5c1e4ca..ba6e898 100644 --- a/source/know/concept/superdense-coding/index.md +++ b/source/know/concept/superdense-coding/index.md @@ -20,48 +20,78 @@ 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. +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 $A$ +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:
$(a_1, a_2)$ | -Operator | -Result | -
---|---|---|
$00$ | -$\hat{I}$ | -$\ket{\Phi^{+}} = \frac{1}{\sqrt{2}} \Big(\Ket{0}_A \Ket{0}_B + \Ket{1}_A \Ket{1}_B \Big)$ | -
$01$ | -$\hat{\sigma}_z$ | -$\ket{\Phi^{-}} = \frac{1}{\sqrt{2}} \Big(\Ket{0}_A \Ket{0}_B - \Ket{1}_A \Ket{1}_B \Big)$ | -
$10$ | -$\hat{\sigma}_x$ | -$\ket{\Psi^{+}} = \frac{1}{\sqrt{2}} \Big(\Ket{0}_A \Ket{1}_B + \Ket{1}_A \Ket{0}_B \Big)$ | -
$11$ | -$\hat{\sigma}_x \hat{\sigma}_z$ | -$\ket{\Psi^{-}} = \frac{1}{\sqrt{2}} \Big(\Ket{0}_A \Ket{1}_B - \Ket{1}_A \Ket{0}_B \Big)$ | -
+ $$(a_1, a_2)$$ + | ++ Operator + | ++ Result + | +
+ $$00$$ + | ++ $$\hat{I}$$ + | ++ $$\displaystyle \ket{\Phi^{+}} = \frac{1}{\sqrt{2}} \Big(\Ket{0}_A \Ket{0}_B + \Ket{1}_A \Ket{1}_B \Big)$$ + | +
+ $$01$$ + | ++ $$\hat{\sigma}_z$$ + | ++ $$\displaystyle \ket{\Phi^{-}} = \frac{1}{\sqrt{2}} \Big(\Ket{0}_A \Ket{0}_B - \Ket{1}_A \Ket{1}_B \Big)$$ + | +
+ $$10$$ + | ++ $$\hat{\sigma}_x$$ + | ++ $$\displaystyle \ket{\Psi^{+}} = \frac{1}{\sqrt{2}} \Big(\Ket{0}_A \Ket{1}_B + \Ket{1}_A \Ket{0}_B \Big)$$ + | +
+ $$11$$ + | ++ $$\hat{\sigma}_x \hat{\sigma}_z$$ + | ++ $$\displaystyle \ket{\Psi^{-}} = \frac{1}{\sqrt{2}} \Big(\Ket{0}_A \Ket{1}_B - \Ket{1}_A \Ket{0}_B \Big)$$ + | +