Absolutely Maximal Entanglement in Continuous Variables
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866908658243207168 |
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| author | Kwon, James I. Brady, Anthony J. Albert, Victor V. |
| author_facet | Kwon, James I. Brady, Anthony J. Albert, Victor V. |
| contents | We explore absolutely maximal entanglement (AME) and k-uniformity in continuous-variable (CV) quantum systems, and show that-unlike in qudit systems-such entanglement is readily realizable in both Gaussian and non-Gaussian quantum states of multiple modes. We demonstrate that Gaussian CV cluster states are generically AME, rederiving the results of [Phys. Rev. Lett. 103, 070501 (2009)] from a generalized stabilizer formalism, and provide explicit constructions based on Cauchy, Vandermonde, totally positive, and real-block-code generator matrices. We further extend AME properties to a family of non-Gaussian states constructed from discrete Zak basis states that incorporate grid states (a.k.a., Gottesman-Kitaev-Preskill states) as non-Gaussian resources. Realizations of CV AME states enable open-destination multi-party CV teleportation, CV quantum secret sharing, CV majority-agreed key distribution, perfect-tensor networks on arbitrary geometries, and multi-unitary circuits. Our extension to non-Gaussian AME states may further provide robustness to Gaussian noise and benefits to quantum CV information processing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15698 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Absolutely Maximal Entanglement in Continuous Variables Kwon, James I. Brady, Anthony J. Albert, Victor V. Quantum Physics Information Theory We explore absolutely maximal entanglement (AME) and k-uniformity in continuous-variable (CV) quantum systems, and show that-unlike in qudit systems-such entanglement is readily realizable in both Gaussian and non-Gaussian quantum states of multiple modes. We demonstrate that Gaussian CV cluster states are generically AME, rederiving the results of [Phys. Rev. Lett. 103, 070501 (2009)] from a generalized stabilizer formalism, and provide explicit constructions based on Cauchy, Vandermonde, totally positive, and real-block-code generator matrices. We further extend AME properties to a family of non-Gaussian states constructed from discrete Zak basis states that incorporate grid states (a.k.a., Gottesman-Kitaev-Preskill states) as non-Gaussian resources. Realizations of CV AME states enable open-destination multi-party CV teleportation, CV quantum secret sharing, CV majority-agreed key distribution, perfect-tensor networks on arbitrary geometries, and multi-unitary circuits. Our extension to non-Gaussian AME states may further provide robustness to Gaussian noise and benefits to quantum CV information processing. |
| title | Absolutely Maximal Entanglement in Continuous Variables |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2503.15698 |