Positive maps from the walled Brauer algebra

• URL: http://arxiv.org/abs/2112.12738v3
• Date: Thu, 7 Mar 2024 10:45:14 GMT
• Title: Positive maps from the walled Brauer algebra
• Authors: Maria Balanz\'o-Juand\'o, Micha{\l} Studzi\'nski, Felix Huber
• Abstract summary: We present positive maps and matrix inequalities for variables from the positive cone. Using our formalism, these maps can be obtained in a systematic and clear way.
• Score: 4.4378250612684
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present positive maps and matrix inequalities for variables from the positive cone. These inequalities contain partial transpose and reshuffling operations, and can be understood as positive multilinear maps that are in one-to-one correspondence with elements from the walled Brauer algebra. Using our formalism, these maps can be obtained in a systematic and clear way by manipulating partially transposed permutation operators under a partial trace. Additionally, these maps are reasonably easy in construction by combining an algorithmic approach with graphical calculus.

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