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arXiv:2604.24460 · Physical Review A

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

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

quant-phSubmitted Apr 27, 2026• Announced Apr 28, 2026• 0 citations
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Abstract

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.

Journal reference
Phys. Rev. A 114, 032430 (2026)
DOI
10.1103/bgdw-3bln
Comments
6 pages

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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.
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Entanglement distillation is a key step in quantum information, both theoretically and practically. It has been proven that nonpositive-partial transpose (NPT) entangled states of rank at most four is 1-distillable under local operation and classical communications. In this paper, we investigate the distillation of a more complex family of NPT entangled states, namely, a family of symmetric two-qutrit states [Formula: see text] of rank five with given eigenvectors. We explicitly construct five families of such states by requiring four of the five eigenvalues to be the same. We, respectively, show that some of them are 1-distillable. It turns out that such states may be not 1-distillable for some interval of eigenvalues. We provide some conditions for eigenvalues that allow [Formula: see text] to be 1-distillable or to be 1-undistillable.
Quantum network states are multipartite states built from distributing pairwise entanglement among parties and underpin the paradigm of quantum networks for quantum information processing. In this work we introduce the problem of partial distillability in noisy quantum networks. This corresponds to the possibility of distilling by local operations and classical communication an arbitrary pure state for an arbitrary subset of parties starting from a single copy of a quantum network state of an increasing number of parties that share noisy (i.e. mixed) bipartite entangled states. Here, distillation means that the target state is obtained with fidelity as close to 1 as desired as the size of the network increases when the pairwise entangled links support a constant amount of noise. While we prove an obstruction to multipartite distillation protocols after teleportation with channels with constant noise, we show that partial distillability is indeed possible if certain well-established graph-theoretic parameters that measure the connectivity in the network grow fast enough with its size. We give necessary as well as sufficient conditions for partial distillability in terms of these parameters and we moreover provide explicit constructions of networks with partial distillability and a relatively slow connectivity growth.
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© 1963-2012 IEEE. Entanglement distillation, an essential quantum information processing task, refers to the conversion from multiple copies of noisy entangled states to a smaller number of highly entangled states. In this paper, we study the non-asymptotic fundamental limits for entanglement distillation. We investigate the optimal tradeoff between the distillation rate, the number of prepared states, and the error tolerance. First, we derive the one-shot distillable entanglement under completely positive partial transpose preserving operations as a semidefinite program and demonstrate an exact characterization via the quantum hypothesis testing relative entropy. Second, we establish efficiently computable second-order estimations of the distillation rate for general quantum states. In particular, we provide explicit as well as approximate evaluations for various quantum states of practical interest, including pure states, mixture of Bell states, maximally correlated states, and isotropic states.
Bipartite qubit entanglement distillation is the process of converting noisy ebits into pure ebits using only local operations and classical communication. This is a core operation for quantum repeaters, enabling such crucial tasks as long-distance quantum communication and distributed quantum computing. In this work, we introduce a method for searching for entanglement distillation protocols and, using this technique, distil qubit Werner states at a higher rate than could be achieved using previously discovered protocols. In particular, we demonstrate the advantage of our new distillation strategy by improving the best-known lower bound for the two-way-assisted quantum capacity of the qubit depolarising channel across a wide range of channel parameters, making progress in one of the long-standing problems of quantum information theory.