哪些图形状态对量子信息处理有用？
Which graph states are useful for quantum information processing?
摘要：
图态是基于测量的量子计算（MBQC）的一种优雅而强大的量子资源。它们也用于许多量子协议（纠错，秘密共享等）。本文的主要目的是提供一种可用于量子信息处理的图形态的结构表征。已知gflow（广义流）的存在是开放图（图，输入集和输出集）执行一致和强确定性计算的要求。我们削弱了gflow条件，定义了两种新的更一般的MBQC：均匀等概率和常数概率。从密码学和信息的角度来看，这些类是有用的，因为即使我们不能进行确定性计算，我们也可以保存信息并将其从输入完美地传输到输出。我们推导出这些类的简单图形特征，并证明了确定性和均匀等概率类崩溃时，输入和输出的基数是相同的。我们还证明了在这种情况下的gflow的可逆性。新的图形特征使我们能够从开放图到一般的图，并考虑这个问题：给定一个没有固定输入或输出的图，哪些顶点可以选择作为量子信息处理的输入和输出？我们提出了一个表征的集合可能的输入和输出的等概率类，这也是有效的确定性计算的输入和输出相同的基数。
英文摘要：
Graph states are an elegant and powerful quantum resource for measurement based quantum computation (MBQC). They are also used for many quantum protocols (error correction, secret sharing, etc.). The main focus of this paper is to provide a structural characterisation of the graph states that can be used for quantum information processing. The existence of a gflow (generalized flow) is known to be a requirement for open graphs (graph, input set and output set) to perform uniformly and strongly deterministic computations. We weaken the gflow conditions to define two new more general kinds of MBQC: uniform equiprobability and constant probability. These classes can be useful from a cryptographic and information point of view because even though we cannot do a deterministic computation in general we can preserve the information and transfer it perfectly from the inputs to the outputs. We derive simple graph characterisations for these classes and prove that the deterministic and uniform equiprobability classes collapse when the cardinalities of inputs and outputs are the same. We also prove the reversibility of gflow in that case. The new graphical characterisations allow us to go from open graphs to graphs in general and to consider this question: given a graph with no inputs or outputs fixed, which vertices can be chosen as input and output for quantum information processing? We present a characterisation of the sets of possible inputs and ouputs for the equiprobability class, which is also valid for deterministic computations with inputs and ouputs of the same cardinality.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
