论文标题
测试测试的rényi差异
Test-measured Rényi divergences
论文作者
论文摘要
定义两个量子状态的量子rényi$α$ divergence的一种可能性是优化其后计量概率分布的经典rényi$α$ - 差异比所有可能的测量值（测量的rényidivergence）优化了其测量后概率分布，并可能在两个状态的多个副本（可能是常规的）$ nnyi $ nynyi $ nynyi $ nynyi $ nynyi $ nynyi $的副本上。定理的一个关键观察是渐近二进制量子状态歧视的强逆向指数的是，正则测量的rényi$α$ divergence与夹心的rényi$α$ divergence恰逢$α> 1 $。此外，从同一定理中也是如此，为了实现这一目标，考虑到任何数量的副本的$ 2 $ -OUTCOMERMOUCTIONS（测试）（这有点令人惊讶，因为实现了$ n $ $ n $的测量的rényi$α$ -Divergence，这可能需要一定数量的测量值，这些副本可能需要在$ n $ n $ n $ n $ n $ n $ n $ n $ n中脱离）。鉴于此，当$α<1 $ $时，似乎很自然。但是，我们表明事实并非如此。实际上，我们表明，即使对于通勤状态（经典案例），可以使用$ 2 $ -OUTCOME的正规化数量严格地比Rényi$α$ divergence（在经典案例中是独一无二）小。在一般量子案例中，这表明上述“正则测试测试”rényi$α$ divergence甚至在$α<1 $ $α<1 $时，甚至都不是与$α> 1 $ $的情况形成鲜明对比的经典rényi发散的量子。
One possibility of defining a quantum Rényi $α$-divergence of two quantum states is to optimize the classical Rényi $α$-divergence of their post-measurement probability distributions over all possible measurements (measured Rényi divergence), and maybe regularize these quantities over multiple copies of the two states (regularized measured Rényi $α$-divergence). A key observation behind the theorem for the strong converse exponent of asymptotic binary quantum state discrimination is that the regularized measured Rényi $α$-divergence coincides with the sandwiched Rényi $α$-divergence when $α>1$. Moreover, it also follows from the same theorem that to achieve this, it is sufficient to consider $2$-outcome measurements (tests) for any number of copies (this is somewhat surprising, as achieving the measured Rényi $α$-divergence for $n$ copies might require a number of measurement outcomes that diverges in $n$, in general). In view of this, it seems natural to expect the same when $α<1$; however, we show that this is not the case. In fact, we show that even for commuting states (classical case) the regularized quantity attainable using $2$-outcome measurements is in general strictly smaller than the Rényi $α$-divergence (which is unique in the classical case). In the general quantum case this shows that the above "regularized test-measured" Rényi $α$-divergence is not even a quantum extension of the classical Rényi divergence when $α<1$, in sharp contrast to the $α>1$ case.
