Any modification of the Born rule leads to a violation of the purification and local tomography principles
Any modification of the Born rule leads to a violation of the purification and local tomography principles
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DOI：
10.22331/q-2018-11-06-104
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发表时间：
2018-01
期刊：
影响因子：
6.4
通讯作者：
Thomas D. Galley;L. Masanes
中科院分区：
文献类型：
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作者：
Thomas D. Galley;L. Masanes
利用现有的量子论测量公设的所有替代分类，研究了这些替代理论中双部系统的性质。我们证明了在所有这些理论中，净化原理都是违反的，这意味着一些混合状态不是一个更大系统中纯状态的还原。这使我们能够从纯态和可逆动力学的结构中推导出量子理论的测量假设，以及净化原理的要求。对净化原则的违背暗示了这些理论中存在着某种不可约的经典性，这似乎是在多世界解释中推导玻恩规则问题的重要线索。我们也证明了在所有这些修正中，具有局部测量的状态层析成像任务是不可能的，并提出了一个简单的玩具理论来显示所有这些奇异的非量子现象。这个玩具模型表明，与之前的说法相反，在不违反无信号原则的情况下修改玻恩规则是可能的。最后，我们认为量子测量假设是所有选择中最非经典的。
Using the existing classification of all alternatives to the measurement postulates of quantum theory we study the properties of bi-partite systems in these alternative theories. We prove that in all these theories the purification principle is violated, meaning that some mixed states are not the reduction of a pure state in a larger system. This allows us to derive the measurement postulates of quantum theory from the structure of pure states and reversible dynamics, and the requirement that the purification principle holds. The violation of the purification principle implies that there is some irreducible classicality in these theories, which appears like an important clue for the problem of deriving the Born rule within the many-worlds interpretation. We also prove that in all such modifications the task of state tomography with local measurements is impossible, and present a simple toy theory displaying all these exotic non-quantum phenomena. This toy model shows that, contrarily to previous claims, it is possible to modify the Born rule without violating the no-signalling principle. Finally, we argue that the quantum measurement postulates are the most non-classical amongst all alternatives.