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arXiv quant-ph/0608196quant-ph
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宏观不同状态叠加的可视化

Visualization of superposition of macroscopically distinct states

Tomoyuki Morimae, Akira Shimizu

摘要:

我们提出了一种多体纯态中宏观不同态叠加的可视化方法。我们引入了一个可视化函数,这是一个粗粒度的准联合概率密度的两个或两个以上的埃尔米特加法算子。如果一个状态包含宏观上不同状态的叠加,可以通过绘制适当取算子的可视化函数来可视化它们。我们还解释了如何有效地找到合适的运营商为一个给定的状态。作为例子,我们可视化四个国家包含宏观上不同的状态的叠加:基态的XY模型,海森堡反铁磁体,一个国家在肖尔的因式分解算法,并在格罗弗的量子搜索算法的状态。虽然可视化函数可以取负值,但是如果在可视化函数中使用的粗粒度函数的特征宽度足够大,则可视化函数变为非负的(因此变为粗粒度联合概率密度)。

英文摘要:

We propose a method of visualizing superpositions of macroscopically distinct states in many-body pure states. We introduce a visualization function, which is a coarse-grained quasi joint probability density for two or more hermitian additive operators. If a state contains superpositions of macroscopically distinct states, one can visualize them by plotting the visualization function for appropriately taken operators. We also explain how to efficiently find appropriate operators for a given state. As examples, we visualize four states containing superpositions of macroscopically distinct states: the ground state of the XY model, that of the Heisenberg antiferromagnet, a state in Shor's factoring algorithm, and a state in Grover's quantum search algorithm. Although the visualization function can take negative values, it becomes non-negative (hence becomes a coarse-grained joint probability density) if the characteristic width of the coarse-graining function used in the visualization function is sufficiently large.

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