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arXiv:2609.40080

Universal Entanglement Distillation

Salvatore Tirone, Francesco Anna Mele, Vittorio Giovannetti, Ludovico Lami

quant-phcs.ITSubmitted Sep 30, 2026• Announced Oct 1, 2026• 0 citations
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Abstract

We present a universal entanglement distillation protocol that asymptotically achieves the distillable entanglement of any unknown bipartite state in a fixed finite dimension. That is, its ebit yield attains every rate below the optimum that would be available if the state were known, with vanishing trace-distance error. Our approach combines tomography by local operations and classical communication with an adaptive distillation routine, using a local robustness lemma to control finite-sample estimation errors. We also characterize worst-case distillation from a family of states: the optimal uniform rate is the minimum distillable entanglement on the family's closure. These results show that ignorance of the state need not incur an asymptotic rate penalty.

Comments
33 pages, 1 figure. See also the independent work by Takagi et al., which appeared on the arXiv today

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We present a universal entanglement distillation protocol that asymptotically achieves the distillable entanglement of any unknown bipartite state in a fixed finite dimension. That is, its ebit yield attains every rate below the optimum that would be available if the state were known, with vanishing trace-distance error. Our approach combines tomography by local operations and classical communication with an adaptive distillation routine, using a local robustness lemma to control finite-sample estimation errors. We also characterize worst-case distillation from a family of states: the optimal uniform rate is the minimum distillable entanglement on the family's closure. These results show that ignorance of the state need not incur an asymptotic rate penalty.
Distillable entanglement---the maximum rate of Bell states extractable from the given noisy entangled states via local operations and classical communication (LOCC)---has been a central quantity to characterize the operational value of entangled states. However, this operational meaning had been known to be valid only under a crucial assumption: both parties know the description of the input state and can choose the protocol tailored to it, which does not necessarily reflect the natural operational setting. Here, we show that the distillable entanglement is the fundamental operational quantity even without this assumption. We present a universal LOCC protocol---whose description does not depend on the input state and thus works universally for any input---that achieves the distillable entanglement of an arbitrary unknown input state. Our result therefore lifts the distillable entanglement to a robust notion of an operationally meaningful quantity and clarifies that input-state knowledge is not necessary to achieve the optimal rate of entanglement distillation. Our protocol is based on state merging for compound states, together with the uniform convergence property of the finite-block quantity toward distillable entanglement.
The information-theoretic approach to entanglement typically relies on arbitrarily many input copies and unboundedly complex operations; however, the available resources are constrained in reality. This motivates the study of entanglement theory with limited resources. One of its central questions is which quantities characterize entanglement manipulations, and so far, only the idealized case of pure states has been well explored. In this work, we address entanglement distillation from mixed states and identify the Rényi coherent information as the quantity determining the optimal rate in the worst case under two distinct resource constraints. We first characterize the sample-efficient regime, in which unbounded computational power is allowed. Our universal protocol achieves this rate without knowledge of the input state under certain polynomial rank constraints. This rate is optimal among universal protocols: we construct states whose distillable entanglement is nearly extensive, yet from which no universal sample-efficient protocol attains a rate above their Rényi coherent information. We then push this characterization to the computationally efficient frontier: the same bound holds for any efficient protocol even when the input state is known, and another universal protocol achieves this rate efficiently under additional polynomial constraints on the marginal ranks. Overall, our results give the Rényi coherent information a novel operational meaning in two computational settings: universal distillation with limited copies and efficient distillation even with knowledge of the input state.
We prove continuity of distillable entanglement, the optimal asymptotic rate at which copies of a bipartite state can be converted into maximally entangled pairs by local operations and classical communication (LOCC) with vanishing error. We establish an explicit asymptotic continuity bound that holds for arbitrary bipartite states and depends logarithmically on the system dimension. This bound has the same structure as known continuity bounds for conditional entropy, entanglement cost, and relative entropy of entanglement. Our proof constructs an explicit LOCC protocol that converts either of two arbitrary bipartite states into the other at an ebit cost that vanishes as their trace distance tends to zero.
Entanglement distillation from noisy bipartite states and reliable quantum communication over noisy channels are fundamental tasks in quantum information theory. Yet existing coding schemes typically require prior knowledge of the underlying state or channel, or assume independent or weakly correlated quantum information sources. Here, using Schur-Weyl duality, we establish a universal quantum error-correction principle that overcomes these limitations. We show that the irreducible permutation spaces arising from the local Schur-Weyl decomposition of multiple copies of an unknown bipartite mixed state form maximally entangled quantum code spaces whose error structure is governed entirely by representation theory. Correcting these symmetry-resolved errors yields protocols for entanglement distillation and quantum communication that achieve coherent-information rates with exponentially vanishing error and optimal second-order corrections, even in the case of almost i.i.d. resources. Our approach also provides sharp finite-copy guarantees that are worst-case optimal at every finite block length, including in the sample-efficient regime, where the number of copies scales only polynomially with the number of qubits. Together, these results establish Schur-Weyl duality as a general mechanism for universal, robust, and optimal quantum coding, unifying entanglement distillation, quantum error correction, and quantum communication within a common representation-theoretic framework.
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.
The performance of quantum resource manipulation protocols, including key examples such as distillation of quantum entanglement, is measured in terms of the rate at which desired target states can be produced from a given noisy state. However, to achieve optimal rates, known protocols require precise tailoring to the quantum state in question, demanding a perfect knowledge of the input and allowing no errors in its preparation. Here we show that distillation of quantum resources in the framework of resource non-generating operations can be performed universally: optimal rates of distillation can be achieved with no knowledge of the input state whatsoever, certifying the robustness of quantum resource distillation. The findings apply in particular to the purification of quantum entanglement under non-entangling maps, where the optimal rates are governed by the regularised relative entropy of entanglement. Our result relies on an extension of the generalised quantum Stein's lemma in quantum hypothesis testing to a composite setting where the null hypothesis is no longer a fixed quantum state, but is rather composed of i.i.d. copies of an unknown state. The solution of this asymptotic problem is made possible through new developments in one-shot quantum information and a refinement of the blurring technique from [Lami, arXiv:2408.06410].