Local operation on identical particles systems

TL;DR

This paper introduces a framework for describing identical particles using local operations and shows how certain measurements can generate entanglement in systems of indistinguishable particles, such as fermions and bosons.

Contribution

It presents a novel approach to entanglement generation via measurement (EbM) in identical particle systems using non-symmetrized operators.

Findings

Measurement operators can produce entanglement in indistinguishable particles.

Entanglement by measurement (EbM) depends on non-mutually exclusive two-particle events.

The framework applies to both fermionic and bosonic systems.

Abstract

We describe identical particles through their extrinsic physical properties and operationally with an operator of selective measure Mm. The operator Mm is formed through non-symmetrized tensor product of one-particle measurement operators, so that it does not commute with the permutation operator P. This operator of selective measure Mm is a local operation (LO) if it acts on physical systems of distinguishable particles, but when Mm acts on the Hilbert sub-space of a system with a constant number of indistinguishable particles this can generate entanglement in the system. We will call entanglement by measurement (EbM), this way of producing entanglement. In this framework, we show entangle production examples for systems of two fermions (or bosons) when the operator Mm has two-particle events that are not mutually exclusive.