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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Entanglement-assisted stabilizer formalism ： ウィキペディア英語版 Entanglement-assisted stabilizer formalism In the theory of quantum communication, the entanglement-assisted stabilizer formalism is a method for protecting quantum information with the help of entanglement shared between a sender and receiver before they transmit quantum data over a quantum communication channel. It extends the standard stabilizer formalism by including shared entanglement (Brun ''et al.'' 2006). The advantage of entanglement-assisted stabilizer codes is that the sender can exploit the error-correcting properties of an arbitrary set of Pauli operators. The sender's Pauli operators do not necessarily have to form an Abelian subgroup of the Pauli group $\backslash Pi^$ over $n$ qubits. The sender can make clever use of her shared ebits so that the global stabilizer is Abelian and thus forms a valid quantum error-correcting code. == Definition == We review the construction of an entanglement-assisted code (Brun ''et al.'' 2006). Suppose that there is a nonabelian subgroup $\backslash mathcal\backslash subset\backslash Pi^$ of size $n-k=2c+s$. Application of the fundamental theorem of symplectic geometry (Lemma 1 in the first external reference) states that there exists a minimal set of independent generators $\backslash left\backslash ,\backslash ldots,\backslash bar\_,\backslash bar\_,\backslash ldots,\backslash bar\_\backslash right\backslash \}$ for $\backslash mathcal$ with the following commutation relations: :$$ \left( \bar_,\bar_\right ) = 0\ \ \ \ \ \forall i,j, :$$ \left( \bar_,\bar_\right ) = 0\ \ \ \ \ \forall i,j, :$$ \left( \bar_,\bar_\right ) = 0\ \ \ \ \ \forall i\neq j, :$\backslash left\backslash ,\backslash bar\_\backslash right\backslash \}\; =\; 0\backslash \; \backslash \; \backslash \; \backslash \; \backslash \; \backslash forall\; i.$ The decomposition of $\backslash mathcal$ into the above minimal generating set determines that the code requires $s$ ancilla qubits and $c$ ebits. The code requires an ebit for every anticommuting pair in the minimal generating set. The simple reason for this requirement is that an ebit is a simultaneous $+1$-eigenstate of the Pauli operators $\backslash left\backslash$. The second qubit in the ebit transforms the anticommuting pair $\backslash left\backslash$ into a commuting pair $\backslash left\backslash$. The above decomposition also minimizes the number of ebits required for the code---it is an optimal decomposition. We can partition the nonabelian group $\backslash mathcal$ into two subgroups: the isotropic subgroup $\backslash mathcal\_$ and the entanglement subgroup $\backslash mathcal\_$. The isotropic subgroup $\backslash mathcal\_$ is a commuting subgroup of $\backslash mathcal$ and thus corresponds to ancilla qubits: :$\backslash mathcal\_=\backslash left\backslash ,\backslash ldots,\backslash bar\_\backslash right\backslash \}$. The elements of the entanglement subgroup $\backslash mathcal\_$ come in anticommuting pairs and thus correspond to ebits: :$\backslash mathcal\_=\backslash left\backslash ,\backslash ldots,\backslash bar\_,\backslash bar\_,\backslash ldots,\backslash bar\_\backslash right\backslash \}$ . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Entanglement-assisted stabilizer formalism」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.