Quantum Mechanics from Relational Properties, Part II: Measurement and EPR

Abstract

Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the relational probability amplitude matrix is transformed and how mutual information is exchanged during measurement, we derive the formulation that is mathematically equivalent to the traditional quantum measurement theory. More importantly, the formulation results in significant conceptual consequences. We show that for a given quantum system, it is possible to describe its time evolution without explicitly calling out a reference system. However, description of a quantum measurement must be explicitly relative. Traditional quantum mechanics assumes a super observer who can instantaneously know the measurement results from any location. For a composite system consists space-like separated subsystems, the assumption of super observer must be abandoned and the relational formulation of quantum measurement becomes necessary. This is confirmed in the resolution of EPR paradox. Information exchange is relative to a local observer in quantum mechanics. Different local observers can achieve consistent descriptions of a quantum system if they are synchronized on the information regarding outcomes from any measurement performed on the system. It is suggested that the synchronization of measurement results from different observers is a necessary step when combining quantum mechanics with the relativity theory.

arXiv comment19 pages, 1 figure. This version improves the published version (v3) by clarifying the connection with the quantum reference frame theories. Introduction section may have overlap with arXiv:1807.01583, arXiv:1706.01317 as they are parts of a same series

References in corpus (19)

• Quantum entanglement
• Decoherence, einselection, and the quantum origins of the classical
• Decoherence, the measurement problem, and interpretations of quantum mechanics
• Relational Quantum Mechanics
• Open Quantum Systems. An Introduction
• Reference frames, superselection rules, and quantum information
• The resource theory of quantum reference frames: manipulations and monotones
• Quantum Mechanics as Quantum Information (and only a little more)
• Quantum-Bayesian Coherence: The No-Nonsense Version
• Understanding quantum measurement from the solution of dynamical models
• Relational EPR
• Quantum communication using a bounded-size quantum reference frame
• Degradation of a quantum reference frame
• Changing quantum reference frames
• Toy Model for a Relational Formulation of Quantum Theory
• Quantum reference frames and deformed symmetries
• Quantum Mechanics from Relational Properties, Part I: Basic Formulation
• Relational Quantum Mechanics and Probability
• A relational approach to quantum reference frames for spins

Cited by in corpus (6)

• Understanding quantum mechanics: a review and synthesis in precise language
• Switching Quantum Reference Frames for Quantum Measurement
• Consistent Descriptions of Quantum Measurement
• Quantum Mechanics from Relational Properties, Part III: Path Integral Implementation
• Information transfer in generalized probabilistic theories based on weak repeatability
• Quantum Entanglement Induced by Gravitational Potential