Pseudomagic Quantum States

TL;DR

This paper introduces pseudomagic quantum states that appear nonmagical to computationally limited observers but are indistinguishable from truly magical states, revealing new insights into quantum scrambling and cryptography.

Contribution

It defines pseudomagic ensembles, demonstrating they are distinct from pseudoentanglement, and explores their implications for quantum scrambling, state synthesis, and cryptography.

Findings

Pseudomagic states are computationally indistinguishable from high nonstabilizerness states.

Pseudomagic does not imply pseudoentanglement, nor vice versa.

Pseudomagic states can originate from non-scrambling unitaries yet appear scrambled.

Abstract

Notions of nonstabilizerness, or "magic", quantify how non-classical quantum states are in a precise sense: states exhibiting low nonstabilizerness preclude quantum advantage. We introduce 'pseudomagic' ensembles of quantum states that, despite low nonstabilizerness, are computationally indistinguishable from those with high nonstabilizerness. Previously, such computational indistinguishability has been studied with respect to entanglement, introducing the concept of pseudoentanglement. However, we demonstrate that pseudomagic neither follows from pseudoentanglement nor implies it. In terms of applications, the study of pseudomagic offers fresh insights into the theory of quantum scrambling: it uncovers states that, even though they originate from non-scrambling unitaries, remain indistinguishable from scrambled states to any physical observer. Additional applications include new lower bounds on state synthesis problems, property testing protocols, and implications for quantum cryptography. Our work is driven by the observation that only quantities measurable by a computationally bounded observer - intrinsically limited by finite-time computational constraints - hold physical significance. Ultimately, our findings suggest that nonstabilizerness is a 'hide-able' characteristic of quantum states: some states are much more magical than is apparent to a computationally bounded observer.