Implications of the Luders Postulate for Quantum Algorithms

On the Evolution of States in a Quantum-Mechanical Model of Experiments

The postulates of von Neumann and Lüders concerning measurements in quantum mechanics are discussed and criticized in the context of a simple model proposed by Gisin. The main purpose of our paper is to analyze some mathematical aspects of that model and to draw some general lessons on the so-called ``measurement problem'' in quantum mechanics pointing towards the need to introduce general principles that determine the law for the stochastic time evolution of states of individual physical systems.

独立性公设对物理学的若干启示

Some Implications of the Independence Postulate for Physics

本文论证多世界理论与构造者理论均同独立性公设冲突：前者经有限电子自旋测量会产生含禁用序列的正概率分支，后者的反事实二元分类则难以描述禁用序列的发现或创造。

Quantum Reality via Late Time Photodetection

We further investigate postulates for realist versions of relativistic quantum theory and quantum field theory in Minkowski space and other background space-times. According to these postulates, quantum theory is supplemented by local variables that depend on possible outcomes of hypothetical measurements on the late time electromagnetic field in spacelike separated regions. We illustrate the implications in simple examples using photon wave mechanics, and discuss possible extensions to quantum field theory.

The Invariant Set Postulate: A New Geometric Framework for the Foundations of Quantum Theory and the Role Played by Gravity

A new law of physics is proposed, defined on the cosmological scale but with significant implications for the microscale. Motivated by nonlinear dynamical systems theory and black-hole thermodynamics, the Invariant Set Postulate proposes that cosmological states of physical reality belong to a non-computable fractal state-space geometry I, invariant under the action of some subordinate deterministic causal dynamics. An exploratory analysis is made of a possible causal realistic framework for quantum physics, based on key properties of I. For example, sparseness is used to relate generic counte…

Algorithmic Pseudorandomness in Quantum Setups

The Church-Turing thesis is one of the pillars of computer science; it postulates that every classical system has equivalent computability power to the so-called Turing machine. While this thesis is crucial for our understanding of computing devices, its implications in other scientific fields have hardly been explored. Here we start this research programme in the context of quantum physics and show that computer science laws have profound implications for some of the most fundamental results of the theory. We first show how they question our knowledge on what a mixed quantum state is, as we i…

Quantum Relativity

Starting with a consideration of the implication of Bell inequalities in quantum mechanics, a new quantum postulate is suggested in order to restore classical locality and causality to quantum physics: only the relative coordinates between detected quantum events are valid observables. This postulate supports the EPR view that quantum mechanics is incomplete, while also staying compatible to the Bohr view that nothing exists beyond the quantum. The new postulate follows from a more general principle of quantum relativity, which states that only correlations between experimental detections of q…

Histories without collapse

This paper is a comparison of two theories of the probability of a history in quantum mechanics. One is derived from Copenhagen quantum mechanics using the projection postulate and is the basis of the "consistent histories" interpretation; the other is based on a proposal by Bell, originally for the "pilot state" theory but here applied to pure unitary quantum mechanics. The first can be used for a wider class of histories but depends on the projection postulate, or "collapse", which is widely held to be an unsatisfactory feature of the theory; the second can be used in a theory of the univers…

Several foundational and information theoretic implications of Bell's theorem

In 1935, Albert Einstein and two colleagues, Boris Podolsky and Nathan Rosen (EPR) developed a thought experiment to demonstrate what they felt was a lack of completeness in quantum mechanics. EPR also postulated the existence of more fundamental theory where physical reality of any system would be completely describe by the variables/states of that fundamental theory. This variable is commonly called hidden variable and the theory is called hidden variable theory (HVT). In 1964, John Bell proposed an empirically verifiable criterion to test for the existence of these HVTs. He derived an inequ…

A New Look at the Position Operator in Quantum Theory

The postulate that coordinate and momentum representations are related to each other by the Fourier transform has been accepted from the beginning of quantum theory by analogy with classical electrodynamics. As a consequence, an inevitable effect in standard theory is the wave packet spreading (WPS) of the photon coordinate wave function in directions perpendicular to the photon momentum. This leads to several paradoxes. The most striking of them is that coordinate wave functions of photons emitted by stars have cosmic sizes and strong arguments indicate that this contradicts observational dat…

量子力学基础与诠释导论

An Introduction to the Foundations and Interpretations of Quantum Mechanics

本文综述量子力学关键概念与诠释发展，从公设到测量、非定域性及经典涌现，分析哥本哈根、德布罗意-玻姆、多世界等诠释如何回应量子理论对物理实在本质的启示。

Invariant Set Theory: Violating Measurement Independence without Fine Tuning, Conspiracy, Constraints on Free Will or Retrocausality

Invariant Set (IS) theory is a locally causal ontic theory of physics based on the Cosmological Invariant Set postulate that the universe $U$ can be considered a deterministic dynamical system evolving precisely on a (suitably constructed) fractal dynamically invariant set in $U$'s state space. IS theory violates the Bell inequalities by violating Measurement Independence. Despite this, IS theory is not fine tuned, is not conspiratorial, does not constrain experimenter free will and does not invoke retrocausality. The reasons behind these claims are discussed in this paper. These arise from pr…

Schroedinger's cat and the clock: Lessons for quantum gravity

I review basic principles of the quantum mechanical measurement process in view of their implications for a quantum theory of general relativity. It turns out that a clock as an external classical device associated with the observer plays an essential role. This leads me to postulate a ``principle of the integrity of the observer''. It essentially requires the observer to be part of a classical domain connected throughout the measurement process. Mathematically this naturally leads to a formulation of quantum mechanics as a kind of topological quantum field theory. Significantly, quantities wi…

论感受质的因果效力：哲学僵尸是精细调谐的，及其对量子测量理论的启示

On the causal efficacy of qualia: Philosophical zombies are fine-tuned, and implications for the quantum measurement theory

该研究提出感受质在量子力学中具有因果效力，作用于可观测量或波函数坍缩而非波函数层面，指出部分量子态与感受质不一致需修改玻恩定则，哲学僵尸依赖初始条件精细调谐，其存在可作为意识测试，解释经典过程无意识的原因。