Distinguishability of hyperentangled Bell state by linear evolution and local projective measurement

TL;DR

This paper explores the limits of distinguishing hyperentangled Bell states using linear evolution and local measurements, showing that only a subset can be distinguished with one copy, but all can be distinguished with two copies.

Contribution

It generalizes Bell state distinguishability bounds to hyperentangled states in multiple variables and provides optimal schemes for different scenarios.

Findings

Maximum of 2^{n+1}-1 classes distinguishable with one copy

Complete distinguishability achievable with two copies

Extended bounds from single-variable to multi-variable hyperentanglement

Abstract

Measuring an entangled state of two particles is crucial to many quantum communication protocols. Yet Bell state distinguishability using a finite apparatus obeying linear evolution and local measurement is theoretically limited. We extend known bounds for Bell-state distinguishability in one and two variables to the general case of entanglement in $n$ two-state variables. We show that at most $2^{n+1}-1$ classes out of $4^n$ hyper-Bell states can be distinguished with one copy of the input state. With two copies, complete distinguishability is possible. We present optimal schemes in each case.