arXiv 1608.075692016-08quant-ph

近似量子克隆和广播的信息论限制

Information-theoretic limitations on approximate quantum cloning and broadcasting

Marius Lemm, Mark M. Wilde

备注：: 13 pages; new results on approximate cloning between general subspaces, e.g., cloning of fermions
发表信息：: Phys. Rev. A 96, 012304 (2017)
DOI：: 10.1103/PhysRevA.96.012304

摘要：

我们证明了新的定量限制任何近似同时克隆或广播的混合状态。结果是基于信息论（熵）的考虑，推广了著名的无克隆和无广播定理。我们还观察和利用了$n$量子比特的对称子空间上的通用克隆机与对称化的部分迹通道是对偶的这一事实。这种对偶性既表现在量子信道的伴随性的代数意义上，也表现在通用克隆机可以用作对称化部分迹信道的近似恢复信道的操作意义上，反之亦然。对偶扩展到子空间上的广义UQCM的性能控制比对称子空间更一般。这提供了一种方法来量化先验信息在克隆方面的有用性。例如，我们可以控制UQCM的反对称类似物在从$n-k$费米子粒子的损失中恢复的性能。

英文摘要：

We prove new quantitative limitations on any approximate simultaneous cloning or broadcasting of mixed states. The results are based on information-theoretic (entropic) considerations and generalize the well known no-cloning and no-broadcasting theorems. We also observe and exploit the fact that the universal cloning machine on the symmetric subspace of $n$ qudits and symmetrized partial trace channels are dual to each other. This duality manifests itself both in the algebraic sense of adjointness of quantum channels and in the operational sense that a universal cloning machine can be used as an approximate recovery channel for a symmetrized partial trace channel and vice versa. The duality extends to give control on the performance of generalized UQCMs on subspaces more general than the symmetric subspace. This gives a way to quantify the usefulness of a-priori information in the context of cloning. For example, we can control the performance of an antisymmetric analogue of the UQCM in recovering from the loss of $n-k$ fermionic particles.

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