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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2502.06393 |
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| _version_ | 1866916762435452928 |
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| author | Qian, Dongheng Wang, Jing |
| author_facet | Qian, Dongheng Wang, Jing |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06393 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Non-Local Nonstabilizerness Qian, Dongheng Wang, Jing Quantum Physics 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. |
| title | Quantum Non-Local Nonstabilizerness |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2502.06393 |