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arXiv quant-ph/0407117quant-ph
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部分量子态

Parts of Quantum States

Nick S. Jones, Noah Linden

摘要:

结果表明,一般N方纯量子态(具有等维子系统)是由它们的略多于一半的约化态唯一确定的,换句话说,几乎所有N方纯态的所有信息都在略多于一半的约化态集合中.对于N偶数,在少于N/2方的约化状态被证明是几乎所有状态的不充分描述(当N是奇数时,类似的结果成立)。值得注意的是,实代数几何是任何量子态部分分析的自然框架:两个简单的多项式,一个二次多项式和一个三次多项式,包含它们的所有结构。描述了可为简化状态集属于纯态或混合态提供条件的数学技术。

英文摘要:

It is shown that generic N-party pure quantum states (with equidimensional subsystems) are uniquely determined by their reduced states of just over half the parties; in other words, all the information in almost all N-party pure states is in the set of reduced states of just over half the parties. For N even, the reduced states in fewer than N/2 parties are shown to be an insufficient description of almost all states (similar results hold when N is odd). It is noted that Real Algebraic Geometry is a natural framework for any analysis of parts of quantum states: two simple polynomials, a quadratic and a cubic, contain all of their structure. Algorithmic techniques are described which can provide conditions for sets of reduced states to belong to pure or mixed states.

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。

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