Entanglement and the linearity of quantum mechanics

TL;DR

This paper explores how the linearity of quantum mechanics constrains the structure of optimal universal entanglement processes, revealing that the resulting states are either pure Bell states or mixed, with entropy differences diminishing in large Hilbert spaces.

Contribution

It demonstrates the restrictions imposed by quantum linearity on the structure of optimal entangled states across different Hilbert space dimensions.

Findings

Optimal entanglement processes produce pure Bell states or mixed states.

Linearity constraints limit the structure of entangled states.

Entropy difference approaches one bit in large Hilbert spaces.

Abstract

Optimal universal entanglement processes are discussed which entangle two quantum systems in an optimal way for all possible initial states. It is demonstrated that the linear character of quantum theory which enforces the peaceful coexistence of quantum mechanics and relativity imposes severe restrictions on the structure of the resulting optimally entangled states. Depending on the dimension of the one-particle Hilbert space such a universal process generates either a pure Bell state or mixed entangled states. In the limit of very large dimensions of the one-particle Hilbert space the von-Neumann entropy of the optimally entangled state differs from the one of the maximally mixed two-particle state by one bit only.