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Pseudomagic Quantum States
Andi Gu1, Lorenzo Leone2,3, Soumik Ghosh4
1Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA.
Physical Review Letters
|June 10, 2024
Summary
We introduce pseudomagic quantum states that appear computationally simple but are complex. These states reveal that quantum magic is a hidden property, not always apparent to observers with limited computational power.
Area of Science:
- Quantum Information Science
- Quantum Computing Theory
Background:
- Nonstabilizerness quantifies the nonclassical nature of quantum states, crucial for quantum advantage.
- Low nonstabilizerness in quantum states limits potential quantum computational advantage.
Purpose of the Study:
- Introduce "pseudomagic" ensembles of quantum states.
- Investigate the relationship between pseudomagic and pseudoentanglement.
- Explore applications in quantum scrambling, state synthesis, property testing, and cryptography.
Main Methods:
- Define and analyze pseudomagic ensembles.
- Compare pseudomagic with pseudoentanglement.
- Examine computational indistinguishability from the perspective of bounded observers.
Main Results:
- Pseudomagic states are computationally indistinguishable from high nonstabilizerness states despite having low nonstabilizerness.
- Pseudomagic does not follow from nor imply pseudoentanglement.
- Identified states from nonscrambling unitaries that are indistinguishable from scrambled states.
Conclusions:
- Nonstabilizerness is a "hide-able" characteristic of quantum states.
- Findings offer new insights into quantum scrambling and computational complexity.
- Demonstrate the physical significance of quantities measurable by computationally bounded observers.
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