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arXiv quant-ph/0104107quant-ph
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未知受控U门的单重态及本征态和本征值的估计

Singlet states and the estimation of eigenstates and eigenvalues of an unknown Controlled-U gate

Mark Hillery, Vladimir Buzek

摘要:

我们考虑几个问题,涉及到找到本征值和生成未知的酉门的本征态。我们首先检查作用于量子位的受控U门,并假设我们知道本征值。然后展示了如何使用单重态在门的本征态中产生量子比特。然后,我们去除了我们知道本征值的假设,并展示了如何找到本征值并在本征态中产生量子比特。最后,我们来看看酉算子作用于qutrits的情况,它的本征值为1和-1,其中本征值1是双退化的。本征态是未知的。我们能够使用单重态来产生对应于-1本征值的本征态中的四重态。

英文摘要:

We consider several problems that involve finding the eigenvalues and generating the eigenstates of unknown unitary gates. We first examine Controlled-U gates that act on qubits, and assume that we know the eigenvalues. It is then shown how to use singlet states to produce qubits in the eigenstates of the gate. We then remove the assumption that we know the eigenvalues and show how to both find the eigenvalues and produce qubits in the eigenstates. Finally, we look at the case where the unitary operator acts on qutrits and has eigenvalues of 1 and -1, where the eigenvalue 1 is doubly degenerate. The eigenstates are unknown. We are able to use a singlet state to produce a qutrit in the eigenstate corresponding to the -1 eigenvalue.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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