# Difficulty of distinguishing product states locally

## TL;DR

This paper demonstrates that for pure product states, practically feasible local measurement strategies can significantly underperform compared to the theoretical optimum, highlighting challenges in quantum information decoding without entanglement.

## Contribution

It shows that simple, current-technology local measurement strategies can be substantially less effective than optimal strategies, even for pure product states.

## Key findings

- Large performance gap between feasible and optimal strategies
- Local strategies can be far from optimal in quantum information extraction
- Even unentangled states pose decoding challenges without entanglement

## Abstract

Non-locality without entanglement is a rather counter-intuitive phenomenon in which information may be encoded entirely in product (unentangled) states of composite quantum systems in such a way that local measurement of the subsystems is not enough for optimal decoding. For simple examples of pure product states, the gap in performance is known to be rather small when arbitrary local strategies are allowed. Here we restrict to local strategies readily achievable with current technology; those requiring neither a quantum memory nor joint operations. We show that, even for measurements on pure product states there can be a large gap between such strategies and theoretically optimal performance. Thus even in the absence of entanglement physically realizable local strategies can be far from optimal for extracting quantum information.