Quantum Pseudoentanglement

TL;DR

This paper introduces pseudoentanglement, a quantum property where efficiently constructible states mimic maximally entangled states, with applications in quantum complexity, entanglement testing, and holography.

Contribution

It constructs pseudoentangled states with near-maximal entanglement across all cuts, advancing the understanding of quantum pseudorandomness and its applications.

Findings

Constructed pseudoentangled states with entanglement close to log n across every cut.

Achieved a tight exponential separation between computational and information-theoretic pseudorandomness.

Simplified proof and improved construction compared to previous work.

Abstract

Entanglement is a quantum resource, in some ways analogous to randomness in classical computation. Inspired by recent work of Gheorghiu and Hoban, we define the notion of "pseudoentanglement'', a property exhibited by ensembles of efficiently constructible quantum states which are indistinguishable from quantum states with maximal entanglement. Our construction relies on the notion of quantum pseudorandom states -- first defined by Ji, Liu and Song -- which are efficiently constructible states indistinguishable from (maximally entangled) Haar-random states. Specifically, we give a construction of pseudoentangled states with entanglement entropy arbitrarily close to $\log n$ across every cut, a tight bound providing an exponential separation between computational vs information theoretic quantum pseudorandomness. We discuss applications of this result to Matrix Product State testing, entanglement distillation, and the complexity of the AdS/CFT correspondence. As compared with a previous version of this manuscript (arXiv:2211.00747v1) this version introduces a new pseudorandom state construction, has a simpler proof of correctness, and achieves a technically stronger result of low entanglement across all cuts simultaneously.