On Hastings' Counterexamples to the Minimum Output Entropy Additivity Conjecture
On Hastings' Counterexamples to the Minimum Output Entropy Additivity Conjecture
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DOI：
10.1142/s1230161210000047
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发表时间：
2009-07
期刊：
影响因子：
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通讯作者：
F. Brandão;M. Horodecki
中科院分区：
文献类型：
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作者：
F. Brandão;M. Horodecki
黑斯廷斯最近报道了违反最小输出熵可加性猜想的通道的随机构造。在这里，我们重新审视他的论点，提出一个简化的证明。特别是，我们不诉诸于一个随机的二分纯态的施密特系数的精确概率分布，在原来的证明，而是得出必要的大偏差范围内的浓度的措施参数。此外，我们证明了绝大多数的渠道组成的Haar随机等距其次是部分跟踪的环境中，环境尺寸远大于输出尺寸的非加性。这使得黑斯廷斯的原始推理更清晰，并扩展了可加性可以被证明是违反的通道类。
Hastings recently reported a randomized construction of channels violating the minimum output entropy additivity conjecture. Here we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact probability distribution of the Schmidt coefficients of a random bipartite pure state, as in the original proof, but rather derive the necessary large deviation bounds by a concentration of measure argument. Furthermore, we prove non-additivity for the overwhelming majority of channels consisting of a Haar random isometry followed by partial trace over the environment, for an environment dimension much bigger than the output dimension. This makes Hastings' original reasoning clearer and extends the class of channels for which additivity can be shown to be violated.