Information Invariance and Quantum Probabilities
Information Invariance and Quantum Probabilities
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DOI：
10.1007/s10701-009-9316-7
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发表时间：
2009-07-01
影响因子：
1.5
通讯作者：
Zeilinger, Anton
中科院分区：
文献类型：
--
作者：
Brukner, Caslav;Zeilinger, Anton
我们考虑概率理论，其中最基本的系统（二维系统）包含一位信息。假设该位包含在任何完整的相互补充测量值集中。在相互补充的测量集的连续变化下信息不变性的要求唯一地挑选出概率是二次的信息测量。给出与量子理论中相同的自由度数与维度的缩放比例的假设本质上源自这样的假设：高维系统的所有物理状态都是且仅是那些可以从中后选择二维系统的物理状态的假设。所有可能的后选二维系统中包含不超过一位信息（通过二次测度量化）的要求相当于量子理论中密度算子的正性。
We consider probabilistic theories in which the most elementary system, a two-dimensional system, contains one bit of information. The bit is assumed to be contained in any complete set of mutually complementary measurements. The requirement of invariance of the information under a continuous change of the set of mutually complementary measurements uniquely singles out a measure of information, which is quadratic in probabilities. The assumption which gives the same scaling of the number of degrees of freedom with the dimension as in quantum theory follows essentially from the assumption that all physical states of a higher dimensional system are those and only those from which one can post-select physical states of two-dimensional systems. The requirement that no more than one bit of information (as quantified by the quadratic measure) is contained in all possible post-selected two-dimensional systems is equivalent to the positivity of density operator in quantum theory.