Detecting entanglement of random states with an entanglement witness

TL;DR

This paper investigates the challenges of detecting entanglement in high-dimensional random states, showing that complexity hampers witness-based detection and that coarse graining reduces detection probability exponentially.

Contribution

It introduces analysis of entanglement detection difficulty in random states and quantifies how coarse graining affects detection success rates.

Findings

Detection of entanglement is difficult in complex random states.

Coarse graining causes exponential decay in entanglement detection probability.

Results explain the emergence of classicality in quantum chaotic systems.

Abstract

The entanglement content of high-dimensional random pure states is almost maximal, nevertheless, we show that, due to the complexity of such states, the detection of their entanglement using witness operators is rather difficult. We discuss the case of unknown random states, and the case of known random states for which we can optimize the entanglement witness. Moreover, we show that coarse graining, modeled by considering mixtures of m random states instead of pure ones, leads to a decay in the entanglement detection probability exponential with m. Our results also allow to explain the emergence of classicality in coarse grained quantum chaotic dynamics.