Decay of entangled fermion pairs with post-selection

TL;DR

This paper explores how post-selection measurements on one fermion in an entangled pair affect the other, even after decay, with potential experimental tests using muon pairs in high-energy physics.

Contribution

It introduces a novel analysis of post-selection effects on entangled fermion pairs after decay, highlighting a physically equivalent spin projection phenomenon.

Findings

Post-selection influences the state of the surviving fermion.

The effect is experimentally accessible with muon pairs.

Potential applications in quantum information and particle physics experiments.

Abstract

We consider a pair of unstable fermions in a spin-entangled state. After the decay of one fermion, a spin measurement is performed on the surviving partner, with a Stern-Gerlach experiment or similar. The measurement not only projects the spin of the surviving fermion, but is also physically equivalent to a spin projection for the decayed one -- even when it no longer exists. This post-selection effect would be experimentally accessible using muon pairs in a maximally-entangled state, produced either in the decay of a scalar particle, or in $e^+ e^-$ collisions at wide angles.