Entanglement distillation in terms of Schmidt rank and matrix rank

• URL: http://arxiv.org/abs/2304.05563v2
• Date: Thu, 6 Jul 2023 05:11:45 GMT
• Title: Entanglement distillation in terms of Schmidt rank and matrix rank
• Authors: Tianyi Ding, Lin Chen
• Abstract summary: We distill non-positive-partial-transpose (NPT) bipartite states of some given Schmidt rank and matrix rank. We show that all bipartite states of Schmidt rank two are locally equivalent to classical-classical states, and all bipartite states of Schmidt rank three are 1-undistillable.
• Score: 7.238541917115604
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Entanglement distillation is a key task in quantum-information processing. In this paper, we distill non-positive-partial-transpose (NPT) bipartite states of some given Schmidt rank and matrix rank. We show that all bipartite states of Schmidt rank two are locally equivalent to classical-classical states, and all bipartite states of Schmidt rank three are 1-undistillable. Subsequently, we show that low-rank B-irreducible NPT states are distillable for large-rank reduced density operators by proving low-rank B-irreducible NPT state whose range contains a product vector is distillable. Eventually, we present an equivalent condition to distill $M\times N$ bipartite states of rank $\max\{M,N\}+1$.

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