Quantum Information Theory

最近证明，在某些情况下，称为纠缠的量子现象可以增加用于传输经典信息的量子信道的容量。 这样的通道被称为非加性的;然而，没有明确的例子是已知的。 甚至最近，人们观察到，与泡利不相容原理相关的反对称可以用来给出一个通道的例子，当p 2时，该通道对于相关量是非加性的，称为最小输出Renyi熵。 这笔赠款旨在构建更多的非加性通道的例子，并澄清我们对这一现象的理解。 与此相关，PI将仔细研究置换对称性在量子信息理论中的作用。 PI还将研究熵不等式和复合系统的熵向量锥。 这项高度跨学科的工作将澄清泡利不相容原理的作用，该原理在量子信息理论中经常被抑制。 它也会引起量子化学家和凝聚态物理学家的兴趣，特别是那些使用约化密度矩阵的物理学家。 这项工作应该有助于确定量子系统在通信和计算方面优于经典系统的情况。

It is was recently proved that there are situations in which the quantum phenomenon called entanglement can increase the capacity of a quantum channel used to transmit classical information. Such channels are called non-additive; however, no explicit examples are known. Even more recently, it was observed that the anti-symmetry associated with the Pauli exclusion principle can be used to give an example of a channel which is non-additive for a related quantity, called the minimal output Renyi entropy, when p 2. This grant is intended to construct more examples of non-additive channels and clarify our understanding of this phenomenon. In connection with this, the PI will closely examine the role of permutational symmetry in quantum information theory. The PI will also study entropy inequalities and cones of entropy vectors for composite systems. This highly interdisciplinary work will clarify the role of the Pauli exclusion principle, which is often suppressed in quantum information theory. It will also be of interest to quantum chemists and condensed matter physicists, particularly those who used reduced density matrices. The work should help identify situations in which quantum systems have advantages over classical ones for communication, as well as computation.