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Long-Range Nonstabilizerness and Phases of Matter
David Aram Korbany1, Michael J Gullans2, Lorenzo Piroli1
1INFN, Sezione di Bologna, Università di Bologna, Dipartimento di Fisica e Astronomia, via Irnerio 46, I-40126 Bologna, Italy.
Physical Review Letters
|October 31, 2025
Summary
Long-range nonstabilizerness, a measure of quantum resources, is a common feature in many-body systems. This study identifies a condition in 1D gapped systems for its persistence even after applying local quantum circuits.
Area of Science:
- Quantum Information Theory
- Condensed Matter Physics
- Many-Body Quantum Physics
Background:
- Nonstabilizerness quantifies quantum resources beyond classical capabilities.
- Shallow local quantum circuits are practical for near-term quantum devices.
- Understanding nonstabilizerness is crucial for quantum computation and error correction.
Purpose of the Study:
- To investigate long-range nonstabilizerness in many-body quantum systems.
- To determine conditions under which nonstabilizerness persists against local operations.
- To explore implications for quantum state preparation and error correction.
Main Methods:
- Analysis of long-range nonstabilizerness in generic many-body states.
- Focus on ground states of gapped local Hamiltonians in 1D.
- Rigorous results using translation-invariant matrix product states (MPS) and renormalization-group flow.
Main Results:
- Long-range nonstabilizerness is a generic property of many-body states.
- A sufficient condition for long-range nonstabilizerness in 1D gapped systems was derived.
- This condition depends solely on local MPS tensors and relates to quantized mutual information.
Conclusions:
- The derived condition provides a practical tool for identifying persistent nonstabilizerness.
- Findings have implications for designing robust quantum protocols in 1D systems.
- The study connects fundamental properties of MPS to practical quantum information tasks.
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