No-signalling-based version of Zurek's derivation of quantum probabilities: A note on "Environment-assisted invariance, entanglement, and probabilities in quantum physics"
Zurek has derived the quantum probabilities for Schmidt basis states of bipartite quantum systems in pure joint states, from the assumption that they should be not be affected by one party's action if the action can be undone by the other party (``envariance of probability'') and an auxiliary assumption. We argue that a natural generalization of the auxiliary assumption is actually strong enough to yield the Born rule itself, but that Zurek's argument and protocol can be adapted to do without this assumption, at the cost of using envariance of probability in both directions. We consider alternative motivations for envariance, one based on the no-signalling constraint that actions on one subsystem of a quantum system not allow signalling to another subsystem entirely distinct from the first, and another which is perhaps strongest in the context of a relative-state interpretation of quantum mechanics. In part because of this, we argue that the relative appeal of our version and the original version of Zurek's argument depends in part upon whether one interprets the quantum formalism in terms of relative states or definite measurement outcomes.
Dissipation-Induced Deviations from Kibble-Zurek Scaling in Non-Hermitian Quantum Annealing
Sharif University of Technology（谢里夫理工大学）；Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高等研究所）；Institute for Research in Fundamental Sciences (IPM)（基本科学研究院）
Derivation of the Born rule based on the minimal set of assumptions
测量结果概率的玻恩规则是从五个假设中推导出来的。这些假设表明：（a）状态矢量完全决定了所有测量结果的概率;（b）在测量之间，任何量子系统都受标准量子力学中不涉及测量的那一部分的支配;（c）测量结果的概率服从经典概率论的规则;（d）没有相互作用，就不可能进行信息传递;（e）如果两个自旋为1/2的粒子处于纠缠态（sqrt（1-λ））|升级>| int max（λ）|下载>| down>），并且其中一个自旋由Stern-Gerlach装置测量，则该测量后另一个自旋的状态将为|上>或|向下>，对应于测量结果。这些假设中没有一个是可以忽略的。推导的方法是基于Zurek的环境辅助不变性的思想[PRL 90，120404（2003）]，虽然采取了相当修改的形式。纠缠在我们的方法中起着至关重要的作用（就像在Zurek的方法中一样），所以首先考虑被测量子系统与某些环境纠缠的情况下的概率。纯态中的概率则是一个特例。本文的方法可以适用于理想和非理想的测量设备，无论其结构和工作原理。
Quantum information theorists have created axiomatic reconstructions of quantum mechanics (QM) that are very successful at identifying precisely what distinguishes quantum probability theory from classical and more general probability theories in terms of information-theoretic principles. Herein, we show how one such principle, Information Invariance & Continuity, at the foundation of those axiomatic reconstructions maps to "no preferred reference frame" (NPRF, aka "the relativity principle") as it pertains to the invariant measurement of Planck's constant h for Stern-Gerlach (SG) spin measure…
