Triorthogonal uniqueness theorem and its relevance to the interpretation of quantum mechanics.
Triorthogonal uniqueness theorem and its relevance to the interpretation of quantum mechanics.
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三正交唯一性定理及其与量子力学解释的相关性。
DOI：
10.1103/physreva.49.4213
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
Bub
中科院分区：
文献类型：
--
作者：
Elby;Bub
Many-world, decoherence, and modal interpretations of quantum mechanics suffer from a ``basis degeneracy problem'' arising from the nonuniqueness of some biorthogonal decompositions. We prove that when a quantum state can be written in the triorthogonal form \ensuremath{\Psi}=${\mathit{tsum}}_{\mathit{i}}$${\mathit{c}}_{\mathit{i}}$\ensuremath{\Vert}${\mathit{A}}_{\mathit{i}}$〉\ensuremath{\bigotimes}\ensuremath{\Vert}${\mathit{B}}_{\mathit{i}}$〉\ensuremath{\bigotimes}\ensuremath{\Vert}${\mathit{C}}_{\mathit{i}}$〉, then, even if some of the ${\mathit{c}}_{\mathit{i}}$'s are equal, no alternative bases exist such that \ensuremath{\Psi} can be rewritten ${\mathit{tsum}}_{\mathit{i}}$${\mathit{d}}_{\mathit{i}}$\ensuremath{\Vert}${\mathit{A}}_{\mathit{i}}$'〉\ensuremath{\bigotimes}\ensuremath{\Vert} ${\mathit{B}}_{\mathit{i}}$'〉\ensuremath{\bigotimes}\ensuremath{\Vert}${\mathit{C}}_{\mathit{i}}$'〉. Therefore the triorthogonal decomposition picks out a ``special'' basis. We can use this preferred basis to address the basis degeneracy problem.
Many-world, decoherence, and modal interpretations of quantum mechanics suffer from a ``basis degeneracy problem'' arising from the nonuniqueness of some biorthogonal decompositions. We prove that when a quantum state can be written in the triorthogonal form \ensuremath{\Psi}=${\mathit{tsum}}_{\mathit{i}}$${\mathit{c}}_{\mathit{i}}$\ensuremath{\Vert}${\mathit{A}}_{\mathit{i}}$〉\ensuremath{\bigotimes}\ensuremath{\Vert}${\mathit{B}}_{\mathit{i}}$〉\ensuremath{\bigotimes}\ensuremath{\Vert}${\mathit{C}}_{\mathit{i}}$〉, then, even if some of the ${\mathit{c}}_{\mathit{i}}$'s are equal, no alternative bases exist such that \ensuremath{\Psi} can be rewritten ${\mathit{tsum}}_{\mathit{i}}$${\mathit{d}}_{\mathit{i}}$\ensuremath{\Vert}${\mathit{A}}_{\mathit{i}}$'〉\ensuremath{\bigotimes}\ensuremath{\Vert} ${\mathit{B}}_{\mathit{i}}$'〉\ensuremath{\bigotimes}\ensuremath{\Vert}${\mathit{C}}_{\mathit{i}}$'〉. Therefore the triorthogonal decomposition picks out a ``special'' basis. We can use this preferred basis to address the basis degeneracy problem.