标题： 关于量子信道的环境辅助容量 显示英文标题

标题： On environment-assisted capacities of quantum channels

摘要： 在Gregoratti和Werner [J. Mod. Optics 50, 913-933, 2003 和 quant-ph/0403092]以及Hayden和King [quant-ph/0409026]的初步工作之后，我们研究了在量子信道中由一个“友好的（信道）环境”辅助下容量问题，这个环境可以进行局部测量并将经典信息传送给接收者。 先前的工作[quant-ph/0505038]已经得出了在这种环境帮助下的量子容量公式。 在这里，我们研究了环境辅助的经典容量问题，这个问题表现出一种更为丰富的结构（至少看起来是更难的问题）。 存在几种，可能不等价的允许的局部操作和经典通信模型：单向、任意、可分性和PPT POVM。 在所有这些模型中，解码消息的任务归结为在一个类的操作下，根据某种局部性约束来区分两个接收器之间的一组可能是纠缠的状态。 在介绍了上述操作容量之后，我们证明了环境辅助的经典容量的一个下界总是输入空间维数的半对数。 然后我们开发了一些技术来证明即使允许PPT解码测量（假设某个超可加性猜想成立），存在达到这个下界到较小数量级的信道。 显示英文摘要

摘要： Following initial work by Gregoratti and Werner [J. Mod. Optics 50, 913-933, 2003 and quant-ph/0403092] and Hayden and King [quant-ph/0409026], we study the problem of the capacity of a quantum channel assisted by a "friendly (channel) environment" that can locally measure and communicate classical messages to the receiver. Previous work [quant-ph/0505038] has yielded a capacity formula for the quantum capacity under this kind of help from the environment. Here we study the problem of the environment-assisted classical capacity, which exhibits a somewhat richer structure (at least, it seems to be the harder problem). There are several, presumably inequivalent, models of the permitted local operations and classical communications between receiver and environment: one-way, arbitrary, separable and PPT POVMs. In all these models, the task of decoding a message amounts to discriminating a set of possibly entangled states between the two receivers, by a class of operations under some sort of locality constraint. After introducing the operational capacities outlined above, we show that a lower bound on the environment-assisted classical capacity is always half the logarithm of the input space dimension. Then we develop a few techniques to prove the existence of channels which meet this lower bound up to terms of much smaller order, even when PPT decoding measurements are allowed (assuming a certain superadditivity conjecture).