Quantum Non-Local Nonstabilizerness

TL;DR

This paper introduces quantum non-local nonstabilizerness (NN) as a comprehensive measure of quantum resources combining entanglement and nonstabilizerness, with applications in many-body systems and measurement-induced phenomena.

Contribution

It defines NN for pure and mixed states, relates it to entanglement spectra, and uncovers phenomena like nonstabilizerness swapping, advancing quantification of quantum resources.

Findings

NN can be computed for two-qubit pure states and relates to entanglement spectrum.

In critical many-body states, two-point NN exhibits power-law decay.

Measurement-induced NN decays more slowly, enabling nonstabilizerness swapping.

Abstract

Quantum entanglement and quantum nonstabilizerness are fundamental resources that characterize distinct aspects of a quantum state: entanglement reflects non-local correlations, while nonstabilizerness quantifies the deviation from stabilizer states. A quantum state becomes a valuable resource for applications like universal quantum computation only when both quantities are present. Here, we propose that quantum non-local nonstabilizerness (NN) serves as an effective measure of this combined resource, incorporating both entanglement and nonstabilizerness. We demonstrate that NN can be precisely computed for two-qubit pure states, where it is directly related to the entanglement spectrum. We then extend the definition of NN to mixed states and explore its presence in many-body quantum systems, revealing that the two-point NN decays according to a power law in critical states. Furthermore, we explore measurement-induced NN and uncover an intriguing phenomenon termed "nonstabilizerness swapping", analogous to entanglement swapping, wherein post-measurement NN decays more slowly than any pre-measurement correlations. Our results thus represent a pivotal step towards accurately quantifying the "quantumness" of a state and reveal the potential for manipulating this resource through measurements.