Revised Proof of the Uniqueness Theorem for 'No Collapse' Interpretations of Quantum Mechanics

On the uniqueness of the equation for state-vector collapse

The linearity of quantum mechanics leads, under the assumption that the wave function offers a complete description of reality, to grotesque situations famously known as Schroedinger's cat. Ways out are either adding elements of reality or replacing the linear evolution by a nonlinear one. Models of spontaneous wave function collapses took the latter path. The way such models are constructed leaves the question, whether such models are in some sense unique, i.e. whether the nonlinear equations replacing Schroedinger's equation, are uniquely determined as collapse equations. Various people work…

Comment on 'Uniqueness of the Equation for Quantum State Vector Collapse' [arXiv:1303.4284]

A diffusive stochastic Schrödinger equation (SSE) is shown for the first time, such that contributes to a non-completely positive dynamics. This contradicts to a recent Letter [arXiv:1303.4284] claiming that SSEs, under most general conditions, enforce complete-positivity. The general form and parametrization of the SSE in the Letter is different from an alternative simpler result, the difference is shown to be completely redundant because of the gauge-freedom of the state vector's phase.

量子-经典概率可检验证明中的坍缩与量子多项式层级

Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy

本文通过证明量子-经典PCP唯一性不降低能力、QMA在量子建议下的Karp-Lipton型坍缩以及有界纠缠量子多项式层级在第四层以上坍缩，揭示了量子证明系统的结构简化规律。

Counterexample to "Sufficient Conditions for uniqueness of the Weak Value" by J. Dressel and A. N. Jordan, arXiv:1106.1871v1

The abstract of "Contextual Values of Observables in Quantum Measurements" by J. Dressel, S. Agarwal, and A. N. Jordan [Phys. Rev. Lett. 104 240401 (2010)] (called DAJ below), states: "We introduce contextual values as a generalization of the eigenvalues of an observable that takes into account both the system observable and a general measurement procedure. This technique leads to a natural definition of a general conditioned average that converges uniquely to the quantum weak value in the minimal disturbance limit." A counterexample to the claim of the last sentence was presented in Version 1…

Breaking quantum linearity: constraints from human perception and cosmological implications

Resolving the tension between quantum superpositions and the uniqueness of the classical world is a major open problem. One possibility, which is extensively explored both theoretically and experimentally, is that quantum linearity breaks above a given scale. Theoretically, this possibility is predicted by collapse models. They provide quantitative information on where violations of the superposition principle become manifest. Here we show that the lower bound on the collapse parameter lambda, coming from the analysis of the human visual process, is ~ 7 +/- 2 orders of magnitude stronger than …

A quantum approach to the uniqueness of Reality

A brief review is given of the present state of an approach to consistency between basic quantum mechanics and a unique macroscopic reality, with no assumption of branching in the state of the universe. The main new idea consists in the recognition of local properties in the growth and transport of entanglement between a macroscopic measuring quantum system and a microscopic measured one. Moving waves of entanglement from the environment arise then and carry external phases, affecting significantly the state of the measuring device. These "predecoherence" waves perturb randomly the growth of o…