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arXiv 1805.04045quant-ph
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利用和重用相干性实现量子过程

Using and reusing coherence to realize quantum processes

María García Díaz, Kun Fang, Xin Wang, Matteo Rosati, Michalis Skotiniotis, John Calsamiglia, Andreas Winter

摘要:

相干叠加是量子力学的一个关键特征,它是量子技术优于经典技术的基础。最近,一致性被重新塑造为一种资源理论,试图以一种操作上明确界定的方式来确定和量化它。在这里,我们研究了如何在一个国家的相干性可以用来实现一个量子信道通过非相干操作,反过来,以评估其相干程度。我们引入了量子信道相干性的鲁棒性--当在恒定输出信道上计算时,它简化为状态的同名度量--并证明:i)它量化了实现该信道所需的最大相干态的最小秩; ii)如果在输出处恢复一些相干性,其对数量化了实现该信道的摊销成本; iii)其对数还量化了实现信道的许多独立副本的零误差渐近成本。我们还考虑了广义的问题,不完美的实现与任意资源状态。利用相干性的鲁棒性,我们发现在一般情况下,一个量子信道可以实现不采用最大相干的资源状态。事实上,我们证明了\textit{every}纯相干态的维数大于$2$,但弱,原来是一个有价值的资源,实现\textit{some}相干酉信道。我们说明了我们的研究结果的情况下,单量子比特酉通道。

英文摘要:

Coherent superposition is a key feature of quantum mechanics that underlies the advantage of quantum technologies over their classical counterparts. Recently, coherence has been recast as a resource theory in an attempt to identify and quantify it in an operationally well-defined manner. Here we study how the coherence present in a state can be used to implement a quantum channel via incoherent operations and, in turn, to assess its degree of coherence. We introduce the robustness of coherence of a quantum channel---which reduces to the homonymous measure for states when computed on constant-output channels---and prove that: i) it quantifies the minimal rank of a maximally coherent state required to implement the channel; ii) its logarithm quantifies the amortized cost of implementing the channel provided some coherence is recovered at the output; iii) its logarithm also quantifies the zero-error asymptotic cost of implementation of many independent copies of a channel. We also consider the generalized problem of imperfect implementation with arbitrary resource states. Using the robustness of coherence, we find that in general a quantum channel can be implemented without employing a maximally coherent resource state. In fact, we prove that \textit{every} pure coherent state in dimension larger than $2$, however weakly so, turns out to be a valuable resource to implement \textit{some} coherent unitary channel. We illustrate our findings for the case of single-qubit unitary channels.

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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