Existence and construction of a quantum channel with given inputs and outputs

Osamu Hirota

Guo Zhi

We derive that sufficient and necessary conditions for existence of a quantum channel φ and a generalized unitary operation e sending Ai to Bi(1≤ i≤ k) for two given families {Ai}i=1k,{Bi}i=1k of matrices,respectively.As an application,a sufficient and necessary condition for existence of a unitary duality quantum computer with given input-output states is obtained.

Guo Guo, Zhihua, Cao +1 more

我们导出那为一条量隧道和为二个给定的家庭送 i 给 B i (1 i k ) 的概括单一的操作的存在的足够、必要的条件 { i } i=1 k， { B i } 矩阵的 i=1 k 分别地。作为一个应用程序，为有给定的输入产量状态的一台单一的两重性量计算机的存在的一个足够、必要的条件被获得。

Masanori Ohya, Dėnes Petz, Noboru Watanabe

Alexander Semenovich Holevo

Pau Colomer, Christian Deppe, Holger Boche +1 more

Following initial work by JaJa, and Ahlswede and Cai, and inspired by a recent renewed surge in interest in deterministic identification (DI) via noisy channels, we consider the problem in its generality for memoryless channels with finite output, but arbitrary input alphabets. Such a channel is essentially given by (the closure of) the subset of its output distributions in the probability simplex. Our main findings are that the maximum number of messages thus identifiable scales super-exponentially as$2^{Rn\log n}$with the block length$n$, and that the optimal rate$R$is upper and lower bounded in terms of the covering (aka Minkowski, or Kolmogorov, or entropy) dimension$d$of a certain algebraic transformation of the output set:$\frac{1}{4}d\leq R\leq\frac{1}{2}d$, Along the way, we present a Hypothesis Testing Lemma that shows it is sufficient to ensure pairwise reliable distinguishability of the output distributions to construct a DI code. Although we do not know the exact capacity formula, we can conclude that the DI capacity exhibits super-activation: there exist channels whose capacity is zero, but whose product has positive capacity. These results are then generalised to classical-quantum channels with finite-dimensional output quantum system (but arbitrary input alphabet), and in particular to quantum channels on finite-dimensional quantum systems under the constraint that the identification code can only use tensor product inputs.