Entanglement distillation is a fundamental task in quantum information processing. In this work, we investigate the distillability properties of a class of two-qutrit symmetric NPT states of rank five. We resolve the 1-distillability problem for this class by proving that the previously open interval of the eigenvalue parameter is 1-undistillable. For the 2-distillability, we uncover a structural obstruction showing that no Schmidt-rank-two vector has a negative expectation in the relevant subspace. We also perform numerical investigations to explore the 2-distillability beyond this obstruction.Entanglement distillation is a fundamental task in quantum information processing. In this work, we investigate the distillability properties of a class of two-qutrit symmetric NPT states of rank five. We resolve the 1-distillability problem for this class by proving that the previously open interval of the eigenvalue parameter is 1-undistillable. For the 2-distillability, we uncover a structural obstruction showing that no Schmidt-rank-two vector has a negative expectation in the relevant subspace. We also perform numerical investigations to explore the 2-distillability beyond this obstruction.

quant-pharXiv:2608.03710Aug 5, 20260 citations

Entanglement distillation in terms of a conjectured matrix inequality

Yize Sun, Lin Chen

Entanglement distillation is a basic task in quantum information, and the distillable entanglement of three bipartite reduced density matrices from a tripartite pure state has been studied in [Phys. Rev. A 84, 012325 (2011)]. We extend this result to tripartite mixed states by studying a conjectured matrix inequality, namely $\mathop{\rm rank}(\sum_i R_i \otimes S_i)\leq K \mathop{\rm rank}(\sum_i R_i^T \otimes S_i)$ holds for any bipartite matrix $M=\sum_i R_i \otimes S_i$ and Schmidt rank $K$ . We prove that the conjecture holds for $M$ with $K=3$ and some special $M$ with arbitrary $K$ .Entanglement distillation is a basic task in quantum information, and the distillable entanglement of three bipartite reduced density matrices from a tripartite pure state has been studied in [Phys. Rev. A 84, 012325 (2011)]. We extend this result to tripartite mixed states by studying a conjectured matrix inequality, namely $\mathop{\rm rank}(\sum_i R_i \otimes S_i)\leq K \mathop{\rm rank}(\sum_i R_i^T \otimes S_i)$ holds for any bipartite matrix $M=\sum_i R_i \otimes S_i$ and Schmidt rank $K$. We prove that the conjecture holds for $M$ with $K=3$ and some special $M$ with arbitrary $K$.

arXiv:1909.02748Sep 6, 20190 citations

The distillability of entanglement of bipartite reduced density matrices of a tripartite state

Yize Sun, Lin Chen

Abstract The relation between the distillability of entanglement of three bipartite reduced density matrices from a tripartite pure state has been studied in Hayashi and Chen [2011 Phys. Rev. A 84 012325]. We extend this result to the tripartite mixed state of rank at most three. In particular we show that if the state has two bipartite reduced density operators with rank two, then the third bipartite reduced density operator additionally having non positive partial transpose (non-PPT) is distillable. In contrast, we show that the tripartite PPT state with two reduced density operators of rank two is a three-qubit fully separable state. We obtain these facts by proving a conjectured matrix inequality for the bipartite matrix M with Schmidt rank at most three. This is one of the main results of this paper. We also prove it for some M with arbitrary Schmidt rank.Abstract The relation between the distillability of entanglement of three bipartite reduced density matrices from a tripartite pure state has been studied in Hayashi and Chen [2011 Phys. Rev. A 84 012325]. We extend this result to the tripartite mixed state of rank at most three. In particular we show that if the state has two bipartite reduced density operators with rank two, then the third bipartite reduced density operator additionally having non positive partial transpose (non-PPT) is distillable. In contrast, we show that the tripartite PPT state with two reduced density operators of rank two is a three-qubit fully separable state. We obtain these facts by proving a conjectured matrix inequality for the bipartite matrix M with Schmidt rank at most three. This is one of the main results of this paper. We also prove it for some M with arbitrary Schmidt rank.

Journal of Physics A Mathematical and TheoreticalJun 1, 20204 citations

Noise-robust 1-copy distillation protocol for all distillable Bell-diagonal qutrits

Tobias C. Sutter, Christopher Popp, Beatrix C. Hiesmayr

Entanglement distillation is the process of converting noisy entangled states into maximally entangled pure states via local operations and classical communication. A long-standing, unresolved question is which entangled states are amenable to distillation, known as the distillability problem. We solve this for Bell-diagonal qutrits with Weyl structure, and present a noise-robust scheme for entanglement distillation. In particular, we find that violating the positive partial transposition (PPT) criterion is necessary and sufficient for the 1-distillability of these states. For this, we construct a Schmidt rank 2 eigenvector of the partially transposed density matrix associated with its unique, three-fold degenerate negative eigenvalue. This feature makes the derived entanglement distillation protocol resilient to white-noise effects on the quantum states. Our results thus make noisy entangled qutrit pairs more accessible for future quantum technologies.Entanglement distillation is the process of converting noisy entangled states into maximally entangled pure states via local operations and classical communication. A long-standing, unresolved question is which entangled states are amenable to distillation, known as the distillability problem. We solve this for Bell-diagonal qutrits with Weyl structure, and present a noise-robust scheme for entanglement distillation. In particular, we find that violating the positive partial transposition (PPT) criterion is necessary and sufficient for the 1-distillability of these states. For this, we construct a Schmidt rank 2 eigenvector of the partially transposed density matrix associated with its unique, three-fold degenerate negative eigenvalue. This feature makes the derived entanglement distillation protocol resilient to white-noise effects on the quantum states. Our results thus make noisy entangled qutrit pairs more accessible for future quantum technologies.

quant-pharXiv:2604.24460Physical Review AApr 28, 20260 citations

\mathop{\rm rank}(\sum_i R_i \otimes S_i)\leq K \mathop{\rm rank}(\sum_i R_i^T \otimes S_i)

holds for any bipartite matrix

M=\sum_i R_i \otimes S_i

and Schmidt rank

K

. We prove that the conjecture holds for

M

with

K=3

and some special

M

with arbitrary

K