近似虚拟量子广播
Approximate virtual quantum broadcasting
AI总结：
本文提出通过引入系统偏差来实现近似虚拟广播，提供有效SDP确定样本大小与误差阈值的关系，证明了在合理误差下，近似虚拟广播比简单分样本更高效。
摘要：
量子信息的广播定理指出，无法将未知量子态同时广播给两个或更多接收者。近期研究探索了通过'虚拟'实现非物理过程的方式来绕过这一限制，利用测量和数据处理对未知输入的统计样本进行操作。然而，这种数据的统计波动使虚拟副本严重退化，导致协议实际上消耗而非增加样本量，从而使其效果不如简单的样本分割方法。本文通过允许广播数据中引入少量系统偏差，实现了近似虚拟副本。我们提供了高效的半正定规划（SDP）来确定保持近似误差低于设定阈值所需的最小样本量，以及反之亦然。对于合理小的误差值，我们发现近似虚拟广播在样本量上比朴素的样本分割方法更具可行性。在此过程中，我们证明了几种基于对称性的简化，使得最优的近似广播可以以简单类别的去极化通道来表征。
英文摘要：
The no-broadcasting theorem, a fundamental limitation on the communication of quantum information, holds that a physical process cannot broadcast copies of an unknown quantum state to two or more receivers. Recent work has explored ways of circumventing this limitation using "virtual" implementations of non-physical processes using measurement and data-processing on statistical samples of the unknown input. However, the statistical fluctuations of this data degrades the virtual copies so much that the protocol effectively depletes, rather than proliferate, the sample size -- thereby rendering it worse than the "naive" approach of splitting the given sample and sending a subsample to each receiver. In this work, we circumvent this flaw by allowing a small amount of systematic bias in the broadcast data, resulting in approximate virtual copies. We provide efficient semidefinite programs (SDP's) to determine the minimum sample size required to keep the approximation error below a desired threshold and vice versa. For reasonably small error values, we find approximate virtual broadcasting to be viable with sample sizes smaller than naive sample-splitting would demand. Along the way, we prove several symmetry-based simplifications to the problem, allowing optimal approximate broadcasting to be characterized in terms of the simple class of depolarizing channels.
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