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arXiv quant-ph/0307024quant-phhep-th
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论作为量子态的量子运算

On Quantum Operations as Quantum States

Pablo Arrighi, Christophe Patricot

摘要:

我们将量子态和量子操作之间的对应形式化,并利用其结果。这种对应关系已经隐含在完全保正线性映射的算子和表示的各种证明中;我们进一步证明,所有关于量子运算的重要定理都可以直接从关于量子态的定理导出。当我们这样做的时候,讨论首先提供了一个优雅的和原始的审查量子操作的主要特征。接下来(在论文的后半部分),我们发现更多的结果来自我们的对应关系的制定。因此,我们提供了一个量子操作的因式分解条件,并给出了两个新的两体纯态的Schmidt型分解。通过量子操作的复合律,我们在完全纠缠态的集合上定义了一个群结构。关于这种对应关系是仅仅是数学上的,还是可以给出一种物理解释的问题,贯穿全文:我们提供的公式表明,量子态内在地定义了它们的两个子系统之间的量子运算,而这些公式在量子密码学中有应用。关键词:克劳斯,CP-映射,超算子,极值,保迹,因子分解,三角。

英文摘要:

We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely Positive-preserving linear maps; we go further and show that all of the important theorems concerning quantum operations can be derived directly from those concerning quantum states. As we do so the discussion first provides an elegant and original review of the main features of quantum operations. Next (in the second half of the paper) we find more results stemming from our formulation of the correspondence. Thus we provide a factorizability condition for quantum operations, and give two novel Schmidt-type decompositions of bipartite pure states. By translating the composition law of quantum operations, we define a group structure upon the set of totally entangled states. The question whether the correspondence is merely mathematical or can be given a physical interpretation is addressed throughout the text: we provide formulae which suggest quantum states inherently define a quantum operation between two of their subsystems, and which turn out to have applications in quantum cryptography. Keywords: Kraus, CP-maps, superoperators, extremality, trace-preserving, factorizable, triangular.

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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