Universal Separability and Entanglement in Identical Particle Systems

TL;DR

This paper investigates the concept of universal separability and entanglement in identical particle systems, revealing that bosonic systems have universally separable states, while fermionic systems do not, and neither system admits universally entangled states.

Contribution

It establishes the existence of universally separable states in bosonic systems and the absence of such states in fermionic systems, clarifying the nature of entanglement in identical particles.

Findings

Bosonic systems have universally separable states: i.i.d. pure states.

Fermionic systems lack universally separable states, with few exceptions.

Neither bosonic nor fermionic systems admit universally entangled states.

Abstract

Entanglement is known to be a relative notion, defined with respect to the choice of physical observables to be measured (i.e., the measurement setup used). This implies that, in general, the same state can be both separable and entangled for different measurement setups, but this does not exclude the existence of states which are separable (or entangled) for all possible setups. We show that for systems of bosonic particles there indeed exist such universally separable states: they are i.i.d. pure states. In contrast, there is no such state for fermionic systems with a few exceptional cases. We also find that none of the fermionic and bosonic systems admits universally entangled states.