Continuous majorization in quantum phase space for Wigner-positive states and proposals for Wigner-negative states
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| Format: | Preprint |
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2024
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| _version_ | 1866911218681249792 |
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| author | de Boer, Jan Di Giulio, Giuseppe Keski-Vakkuri, Esko Tonni, Erik |
| author_facet | de Boer, Jan Di Giulio, Giuseppe Keski-Vakkuri, Esko Tonni, Erik |
| contents | In quantum resource theory, one is often interested in identifying which states serve as the best resources for particular quantum tasks. If a relative comparison between quantum states can be made, this gives rise to a partial order, where states are ordered according to their suitability to act as a resource. In the literature, various different partial orders for a variety of quantum resources have been proposed. In discrete variable systems, vector majorization of Wigner functions in discrete phase space provides a natural partial order between quantum states. In the continuous variable case, a natural counterpart would be continuous majorization of Wigner functions in quantum phase space. Indeed, this concept was recently proposed and explored (mostly restricting to the single-mode case) in Van Herstraeten, Jabbour, Cerf, Quantum 7, 1021 (2023). In this work, we develop the theory of continuous majorization in the general $N$-mode case. In addition, we propose extensions to include states with finite Wigner negativity. For the special case of the convex hull of $N$-mode Gaussian states, we prove a conjecture made by Van Herstraeten, Jabbour and Cerf. We also prove a phase space counterpart of Uhlmann's theorem of majorization. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_19698 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Continuous majorization in quantum phase space for Wigner-positive states and proposals for Wigner-negative states de Boer, Jan Di Giulio, Giuseppe Keski-Vakkuri, Esko Tonni, Erik Quantum Physics Statistical Mechanics High Energy Physics - Theory Mathematical Physics In quantum resource theory, one is often interested in identifying which states serve as the best resources for particular quantum tasks. If a relative comparison between quantum states can be made, this gives rise to a partial order, where states are ordered according to their suitability to act as a resource. In the literature, various different partial orders for a variety of quantum resources have been proposed. In discrete variable systems, vector majorization of Wigner functions in discrete phase space provides a natural partial order between quantum states. In the continuous variable case, a natural counterpart would be continuous majorization of Wigner functions in quantum phase space. Indeed, this concept was recently proposed and explored (mostly restricting to the single-mode case) in Van Herstraeten, Jabbour, Cerf, Quantum 7, 1021 (2023). In this work, we develop the theory of continuous majorization in the general $N$-mode case. In addition, we propose extensions to include states with finite Wigner negativity. For the special case of the convex hull of $N$-mode Gaussian states, we prove a conjecture made by Van Herstraeten, Jabbour and Cerf. We also prove a phase space counterpart of Uhlmann's theorem of majorization. |
| title | Continuous majorization in quantum phase space for Wigner-positive states and proposals for Wigner-negative states |
| topic | Quantum Physics Statistical Mechanics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2412.19698 |