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arXiv:2505.24280 · IEEE International Conference on Quantum Computing and Engineering (QCE)

A Double Selection Entanglement Distillation-Based State Estimator

Joshua Carlo A. Casapao, Ananda G. Maity, Naphan Benchasattabuse, Michal Hajdušek, Akihito Soeda, Rodney Van Meter, David Elkouss

Published Aug 30, 2025• 1 citation
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Abstract

With the advent of practical quantum communication networks drawing closer, there is a growing need for reliable estimation protocols that can efficiently characterize quantum resources with minimum resource overhead requirement. A novel approach to this problem is to integrate an estimator into an existing network task, thereby removing the need for an additional characterization protocol. In this work, we show that the measurement statistics of a double selection distillation protocol alone can be used to efficiently estimate the Bell-diagonal parameters of the undistilled states, as well as the resulting distilled states after additional post-processing. We also demonstrate that this novel estimator outperforms the previously proposed distillation-based estimator in terms of resource complexity.

DOI
10.1109/qce65121.2025.00122

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With the advent of practical quantum communication networks drawing closer, there is a growing need for reliable estimation protocols that can efficiently characterize quantum resources with minimum resource overhead requirement. A novel approach to this problem is to integrate an estimator into an existing network task, thereby removing the need for an additional characterization protocol. In this work, we show that the measurement statistics of a double selection distillation protocol alone can be used to efficiently estimate the Bell-diagonal parameters of the undistilled states, as well as the resulting distilled states after additional post-processing. We also demonstrate that this novel estimator outperforms the previously proposed distillation-based estimator in terms of resource complexity.
Abstract Minimizing both experimental effort and consumption of valuable quantum resources in state estimation is vital in practical quantum information processing. Typically, estimation protocols are independently implemented from other protocols, incurring additional resource cost. Here, we explore the estimation of states as an additional benefit of entanglement distillation protocols. We show that the Bell-diagonal parameters of any undistilled state can be efficiently estimated solely from the measurement statistics of probabilistic distillation protocols. We further introduce the distillation-based state estimator ‘Disti-Mator’ designed for a realistic experimental setting, and exhibit its robustness through numerical simulations. Our results demonstrate that a separate estimation protocol can be circumvented whenever distillation is an indispensable communication-based task.
Estimating noise processes is an essential step for practical quantum information processing. Standard estimation tools require consuming valuable quantum resources. Here we ask the question of whether the noise affecting entangled states can be learned solely from the measurement statistics obtained during a distillation protocol. As a first step, we consider states of the Werner form and find that the Werner parameter can be estimated efficiently from the measurement statistics of an idealized distillation protocol. Our proposed estimation method can find application in scenarios where distillation is an unavoidable step.
Distillation, or purification, is central to the practical use of quantum resources in noisy settings often encountered in quantum communication and computation. Conventionally, distillation requires using some restricted "free" operations to convert a noisy state into one that approximates a desired pure state. Here, we propose to relax this setting by only requiring the approximation of the measurement statistics of a target pure state, which allows for additional classical postprocessing of the measurement outcomes. We show that this extended scenario, which we call "virtual resource distillation," provides considerable advantages over standard notions of distillation, allowing for the purification of noisy states from which no resources can be distilled conventionally. We show that general states can be virtually distilled with a cost (measurement overhead) that is inversely proportional to the amount of existing resource, and we develop methods to efficiently estimate such cost via convex and semidefinite programming, giving several computable bounds. We consider applications to coherence, entanglement, and magic distillation, and an explicit example in quantum teleportation (distributed quantum computing). This work opens a new avenue for investigating generalized ways to manipulate quantum resources.
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.
The quantum internet uses high-quality entanglement distribution to enable long-distance communication. The quality of entanglement is measured by distillable entanglement, which quantifies how many maximally entangled states can be refined from a given ensemble of noisy states. Therefore, identifying highly distillable states is essential for ensuring efficient entanglement distribution. GivenKKKensembles of noisy entangled states, we address the problem of identifying highly distillable states, i.e., states with distillable entanglement exceeding a prespecified threshold. We propose entanglement distillation-based estimation protocols on two copies of bipartite2×22 \times 22×2and2×32 \times 32×3pure states. We characterize their distillable entanglement by estimating statedependent parameters from measurement statistics. We identify a structural connection to the Thresholding Bandit problem (TBP) in classical Multi-Armed Bandits (MAB) literature and use these policies to obtain guarantees on the sample complexity for estimating the state-dependent parameters. We also provide numerical results showcasing the performance of the proposed distillation protocol and TBP policies.
High-fidelity entanglement shared between distant quantum systems is an essential resource for quantum communication and computation. Entanglement distillation addresses this need by converting multiple noisy Bell pairs into fewer higher-fidelity pairs, using only local quantum operations and classical communication. However, this approach typically requires a substantial overhead in the number of qubits. To bypass this hurdle, we propose to leverage the high-dimensional Hilbert space of a single pair of bosonic systems to store a large amount of entanglement, replacing the need for multi-qubit systems. To distill entanglement in such a setup, we devise a new entanglement distillation protocol, tailored for bosonic systems. The protocol converts a highly-entangled noisy state between two bosonic systems into a lower-dimensional but high-fidelity entangled state, using only local bosonic operations. We show that our protocol significantly enhances the fidelity of the entangled state in the presence of naturally occurring loss and dephasing errors. Compared to methods relying on multiple Bell pairs, our scheme offers a more hardware-efficient strategy, providing a practical route toward the realization of entanglement distillation.