Compressively characterizing high-dimensional entangled states with complementary, random filtering

TL;DR

This paper introduces an efficient method for high-dimensional entangled state characterization using random filtering, reducing measurement complexity and leveraging information theory to witness entanglement without full state reconstruction.

Contribution

The authors present a novel measurement technique that uses local, random filtering to efficiently characterize high-dimensional entangled states with fewer measurements.

Findings

Recovered sharp distributions with fewer than 5,000 measurements

Successfully characterized a 65,536-dimensional state

Witnessed entanglement using entropic inequalities

Abstract

The resources needed to conventionally characterize a quantum system are overwhelmingly large for high- dimensional systems. This obstacle may be overcome by abandoning traditional cornerstones of quantum measurement, such as general quantum states, strong projective measurement, and assumption-free characterization. Following this reasoning, we demonstrate an efficient technique for characterizing high-dimensional, spatial entanglement with one set of measurements. We recover sharp distributions with local, random filtering of the same ensemble in momentum followed by position---something the uncertainty principle forbids for projective measurements. Exploiting the expectation that entangled signals are highly correlated, we use fewer than 5,000 measurements to characterize a 65, 536-dimensional state. Finally, we use entropic inequalities to witness entanglement without a density matrix. Our method represents the sea change unfolding in quantum measurement where methods influenced by the information theory and signal-processing communities replace unscalable, brute-force techniques---a progression previously followed by classical sensing.