A partial-trace matrix inequality and Werner-state distillability

• URL: http://arxiv.org/abs/2607.23416v1
• Date: Sun, 26 Jul 2026 02:22:05 GMT
• Title: A partial-trace matrix inequality and Werner-state distillability
• Abstract summary: We prove a bipartite partial-trace inequality for every matrix of rank at most two.<n>We show that two individually one-copy-undistillable Werner states cannot activate each other's one-copyability.
• Score: 6.837240993906597
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Motivated by the equivalent partial-trace formulations of Werner-state distillability [P. Costa Rico, Lett. Math. Phys. 115, 47 (2025); S.-Y. Qi et al., Phys. Rev. A 110, 012406 (2024)], we prove a bipartite partial-trace inequality for every matrix of rank at most two. As applications, we prove the two-copy undistillability of NPT Werner states in arbitrary local dimension, thereby resolving this open problem highlighted in [P. Horodecki et al., PRX Quantum 3, 010101 (2022)]. We further prove a two-parameter extension of the matrix inequality and show that two individually one-copy-undistillable NPT Werner states cannot activate each other's one-copy distillability. We also resolve the singular-value maximization problem associated with the two-ququart case.

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