# Entanglement detection with scrambled data

## TL;DR

This paper explores entanglement detection when measurement data is scrambled, showing entropy-based methods and invariant witnesses can identify entanglement despite data misassignment, revealing complex non-convex state sets.

## Contribution

It introduces entropy-based entanglement detection methods and scrambling-invariant witnesses for scenarios with scrambled measurement data, advancing understanding of entanglement detection under data uncertainty.

## Key findings

- Tsallis- and Rényi entropies can detect entanglement with scrambled data
- Shannon entropy cannot detect entanglement in this scenario
- The set of non-detectable states is non-convex and complex to characterize

## Abstract

In the usual entanglement detection scenario the possible measurements and the corresponding data are assumed to be fully characterized. We consider the situation where the measurements are known, but the data is scrambled, meaning the assignment of the probabilities to the measurement outcomes is unknown. We investigate in detail the two-qubit scenario with local measurements in two mutually unbiased bases. First, we discuss the use of entropies to detect entanglement from scrambled data, showing that Tsallis- and R\'enyi entropies can detect entanglement in our scenario, while the Shannon entropy cannot. Then, we introduce and discuss scrambling-invariant families of entanglement witnesses. Finally, we show that the set of non-detectable states in our scenario is non-convex and therefore in general hard to characterize.