Generating Non-Decomposable Maps with Differentiable Semidefinite Programming
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910221272612864 |
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| author | Morgillo, Angela Rosy Poderini, Davide Anselmi, Fabio Benatti, Fabio Sacchi, Massimiliano F. Macchiavello, Chiara |
| author_facet | Morgillo, Angela Rosy Poderini, Davide Anselmi, Fabio Benatti, Fabio Sacchi, Massimiliano F. Macchiavello, Chiara |
| contents | Positive maps that are not decomposable are a key resource in entanglement theory because they can detect bound entangled states, yet systematic methods for constructing them remain limited. We introduce an optimization framework based on differentiable semidefinite programming (SDP) for generating positive non-decomposable maps under flexible structural constraints on their Choi matrices. The method combines SDP-based certificates of non-decomposability and positivity with gradient-based optimization, enabling a systematic search over maps with different input and output dimensions. Within this framework, we generate previously unknown numerical examples, identify a parametrized family of maps arising from masked Choi matrices, and construct real non-decomposable maps. We further show that the same approach can be adapted to explore open questions in quantum information theory, including the PPT square conjecture and recently proposed eigenvalue bounds for 2-positive trace-preserving maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14644 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generating Non-Decomposable Maps with Differentiable Semidefinite Programming Morgillo, Angela Rosy Poderini, Davide Anselmi, Fabio Benatti, Fabio Sacchi, Massimiliano F. Macchiavello, Chiara Quantum Physics Positive maps that are not decomposable are a key resource in entanglement theory because they can detect bound entangled states, yet systematic methods for constructing them remain limited. We introduce an optimization framework based on differentiable semidefinite programming (SDP) for generating positive non-decomposable maps under flexible structural constraints on their Choi matrices. The method combines SDP-based certificates of non-decomposability and positivity with gradient-based optimization, enabling a systematic search over maps with different input and output dimensions. Within this framework, we generate previously unknown numerical examples, identify a parametrized family of maps arising from masked Choi matrices, and construct real non-decomposable maps. We further show that the same approach can be adapted to explore open questions in quantum information theory, including the PPT square conjecture and recently proposed eigenvalue bounds for 2-positive trace-preserving maps. |
| title | Generating Non-Decomposable Maps with Differentiable Semidefinite Programming |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.14644 |