An example of a quantum statistical model which cannot be mapped to a less informative one by any trace preserving positive map
An example of a quantum statistical model which cannot be mapped to a less informative one by any trace preserving positive map
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量子统计模型的一个示例，该模型无法通过任何保留踪迹的正映射映射到信息量较少的模型
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发表时间：
2014
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通讯作者：
Keiji Matsumoto
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作者：
Keiji Matsumoto
统计模型（试验）的比较是数理统计学的一个重要分支，它对统计学基础的许多方面都有深刻的见解。到目前为止，这个概念有两个量子版本：相对于经典任务和完全量子任务的比较。在后一个版本中，一个量子统计模型比另一个模型更具信息性，当且仅当一个保迹正映射将前者发送给后者。另一方面，在前一个版本中，存在一个保迹正映射将前者发送到后者是一个有用的充分条件。一个自然的问题是，这是否有必要。我们通过举一个反例来否定地解决这个问题。
Comparison of statistical models (experiments) is an important branch of mathematical statistics, which gives deep insights in many aspects of foundation of statistics. So far, there are two quantum versions of the concept: Comparison with respect to classical tasks and full quantum tasks. In the latter version, a quantum statistical model is more informative than another if and only if a trace preserving positive map sends the former to the latter. On the other hand, in the former version, the existence of a trace preserving positive map sending the former to the latter is a useful sufficient condition. A natural question is whether this is necessary or not. We resolve this question negatively by giving a counter example.