# Probabilistic foundations of quantum mechanics and quantum information

**Authors:** Andrei Khrennikov  
**arXiv:** [quant-ph/0309066](https://arxiv.org/abs/quant-ph/0309066)  
**Date:** 2003-09-08  
**Summary page:** https://www.summarizepaper.com/en/paper/quant-ph--0309066v1/

## Key points

- Superposition: particles can exist in multiple states simultaneously, allowing for potential encoding and processing of vast amounts of information
- Principle of complementarity: certain properties or measurements cannot be observed simultaneously with precision, highlighting limitations in understanding and measurement capabilities within the quantum realm
- Locality: physical interactions between particles are limited by a finite speed, preventing instantaneous communication or influence over long distances
- Hidden variables: hypothetical properties that could potentially explain the probabilistic nature of quantum phenomena, but various interpretations argue against their existence
- Quantum information theory: explores how information can be encoded, transmitted, and processed using principles from quantum mechanics; leverages unique properties such as entanglement and superposition to develop novel algorithms for computation and secure communication

## Summary

In the paper titled "Probabilistic Foundations of Quantum Mechanics and Quantum Information" by Andrei Khrennikov, the author explores the fundamental concepts of quantum mechanics and their relationship to quantum information theory. The paper delves into various interpretations of quantum mechanics, including superposition, the principle of complementarity, locality, and hidden variables. Superposition is a key concept in quantum mechanics where particles can exist in multiple states simultaneously. This phenomenon allows for potential encoding and processing of vast amounts of information in quantum systems. The principle of complementarity states that certain properties or measurements cannot be observed simultaneously with precision, highlighting the inherent limitations in our understanding and measurement capabilities within the quantum realm. Locality refers to the idea that physical interactions between particles are limited by a finite speed, preventing instantaneous communication or influence over long distances. This concept has profound implications for secure communication protocols such as quantum cryptography. Hidden variables are hypothetical properties that could potentially explain the probabilistic nature of quantum phenomena; however, various interpretations argue against their existence and suggest that uncertainty is an intrinsic feature of quantum systems. Quantum information theory is a field that explores how information can be encoded, transmitted, and processed using principles from quantum mechanics. It leverages unique properties such as entanglement and superposition to develop novel algorithms for computation and secure communication. Overall, this paper provides a comprehensive overview of the foundations of quantum mechanics and its connection to quantum information theory. By examining different interpretations and concepts like superposition, complementarity, locality, and hidden variables it sheds light on the underlying principles governing this fascinating field.