Universal uncertainty principle in the measurement operator formalism
Universal uncertainty principle in the measurement operator formalism
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DOI：
10.1088/1464-4266/7/12/033
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发表时间：
2005-12-01
期刊：
影响因子：
--
通讯作者：
Ozawa, M
中科院分区：
文献类型：
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作者：
Ozawa, M
海森伯的不确定性原理被理解为对测量设置了限制;然而，海森伯、肯纳德和罗伯逊建立的长期数学公式不允许这样的解释。最近，人们发现了一个新的关系式，它给出了一般量子测量中噪声和扰动之间普遍有效的关系式，并且已经清楚地表明，这个新关系式起着第一原理的作用，可以在统一的处理中导出各种测量和信息处理的量子极限。本文研究了基于测量算子形式的模型无关方法中噪声扰动不确定性原理的上述发展，该方法被广泛接受用于描述量子信息领域中的一类广义测量。我们得到明确的公式的噪声和干扰的测量算子给出的测量，并表明，投影测量不满足海森堡型噪声干扰关系，这是典型的γ射线显微镜思想实验。我们还表明，在一个泡利算子的投影测量的另一个泡利算子的干扰不断等于根2，并检查如何这种测量违反海森堡型关系，但满足新的噪声干扰关系。
Heisenberg's uncertainty principle has been understood to set a limitation on measurements; however, the long-standing mathematical formulation established by Heisenberg, Kennard, and Robertson does not allow such an interpretation. Recently, a new relation was found to give a universally valid relation between noise and disturbance in general quantum measurements, and it has become clear that the new relation plays a role of the first principle to derive various quantum limits on measurement and information processing in a unified treatment. This paper examines the above development on the noise-disturbance uncertainty principle in the model-independent approach based on the measurement operator formalism, which is widely accepted to describe a class of generalized measurements in the field of quantum information. We obtain explicit formulae for the noise and disturbance of measurements given by measurement operators, and show that projective measurements do not satisfy the Heisenberg-type noise-disturbance relation that is typical in the gamma-ray microscope thought experiments. We also show that the disturbance on a Pauli operator of a projective measurement of another Pauli operator constantly equals root 2, and examine how this measurement violates the Heisenberg-type relation but satisfies the new noise-disturbance relation.