Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Semi-Classical Subspaces, The No Synchronization Law, and More

Samuel Epstein

TL;DR

Theorems which characterize the barrier between the quantum world and the classical realm and the notion of a ``semi-classical subspace'' is introduced, which can be obtained on quantum states in semi-classical subspaces.

Abstract

This paper looks at the intersection of algorithmic information theory and physics, namely quantum mechanics, thermodynamics, and black holes. We discuss theorems which characterize the barrier between the quantum world and the classical realm. The notion of a ``semi-classical subspace'' is introduced. Partial signals and partial information cloning can be obtained on quantum states in semi-classical subspaces. The No Synchronization Law is detailed, which says separate and isolated physical systems evolving over time cannot have algorithmic thermodynamic entropies that are in synch. We look at future work involving the Kolmogorov complexity of black holes.

Semi-Classical Subspaces, The No Synchronization Law, and More

TL;DR

Theorems which characterize the barrier between the quantum world and the classical realm and the notion of a ``semi-classical subspace'' is introduced, which can be obtained on quantum states in semi-classical subspaces.

Abstract

This paper looks at the intersection of algorithmic information theory and physics, namely quantum mechanics, thermodynamics, and black holes. We discuss theorems which characterize the barrier between the quantum world and the classical realm. The notion of a ``semi-classical subspace'' is introduced. Partial signals and partial information cloning can be obtained on quantum states in semi-classical subspaces. The No Synchronization Law is detailed, which says separate and isolated physical systems evolving over time cannot have algorithmic thermodynamic entropies that are in synch. We look at future work involving the Kolmogorov complexity of black holes.
Paper Structure (15 sections, 10 theorems, 18 equations, 1 figure)

This paper contains 15 sections, 10 theorems, 18 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The No Synchronization Law
  3. The Algorithmic Content of Quantum States
  4. Vitányi Complexity
  5. Gács Complexity
  6. Quantum Unitary Complexity
  7. BvL Complexity
  8. Algorithmic Properties of Quantum States
  9. Mutual Information Between Quantum States
  10. Measurements
  11. Decoherence
  12. Predictability Sieve
  13. Semi-Classical Subspaces
  14. No Synchronization Law
  15. Looking Forward: Black Holes

Key Result

Theorem 1

Let $\Lambda$ be the uniform distribution over all $n$ qubit pure states.

Figures (1)

  • Figure 1: Properties of four measures of the algorithmic content of quantum states.

Theorems & Definitions (13)

  • Definition 1
  • Definition 2
  • Theorem 1: EpsteinAPhysics24
  • Theorem 2: EpsteinAPhysics24
  • Theorem 3: EpsteinAPhysics24
  • Theorem 4: EpsteinAPhysics24
  • Theorem 5: EpsteinAPhysics24
  • Theorem 6: EpsteinAPhysics24
  • Definition 3: Algorithmic Predictability Sieve
  • Theorem 7
  • ...and 3 more