Counterexamples to the Maximal p-Norm Multiplicativity Conjecture for all p > 1
Counterexamples to the Maximal p-Norm Multiplicativity Conjecture for all p > 1
复制标题
DOI：
10.1007/s00220-008-0624-0
复制
发表时间：
2008-11-01
影响因子：
2.4
通讯作者：
Winter, Andreas
中科院分区：
文献类型：
--
作者：
Hayden, Patrick;Winter, Andreas
对于所有p > 1，我们证明了具有非乘法最大输出p-范数的量子信道的存在性。等价地，对于所有p > 1，量子通道的阶数p的最小输出Renyi熵不是可加的。发现的违规很大;在所有情况下，产品通道的p阶最小输出Renyi熵不需要显著大于其单个因子的最小输出熵。由于p = 1对应于冯·诺依曼熵，这些反例表明，如果量子信息理论的可加性猜想是正确的，它不能被证明是任何通道无关的保证最大p范数乘法的结果。我们还表明，一类渠道先前研究的上下文中的近似加密导致所有p > 2的反例。
For all p > 1, we demonstrate the existence of quantum channels with non-multiplicative maximal output p-norms. Equivalently, for all p > 1, the minimum output Renyi entropy of order p of a quantum channel is not additive. The violations found are large; in all cases, the minimum output Renyi entropy of order p for a product channel need not be significantly greater than the minimum output entropy of its individual factors. Since p = 1 corresponds to the von Neumann entropy, these counterexamples demonstrate that if the additivity conjecture of quantum information theory is true, it cannot be proved as a consequence of any channel-independent guarantee of maximal p-norm multiplicativity. We also show that a class of channels previously studied in the context of approximate encryption lead to counterexamples for all p > 2.