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.
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.
Entanglement distillation is a fundamental operation in quantum information processing used to obtain higher-fidelity entangled pairs from a supply of less entangled quantum states using local operations aided by classical communication (LOCC). In a physically relevant setting, where states with an initial fidelity of
f0, probabilistically generated over multiple,
m, memory pairs distributed between two parties, Alice and Bob, are pairwise distilled, the optimal policy identifies the system-configuration dependent sequence of entanglement generation and distillation operations that need to be performed in order to minimize the expected time to reach some target fidelity
fT>f0. Here, we formulate and systematically analyze this task as a Markov decision problem and using a value iteration algorithm, obtain optimal deterministic policies that minimize the expected waiting time required to reach a target fidelity. Our results show that the expected waiting time under the optimal policy decreases with increasing generation probability
p and number of quantum memories
m - as expected. In contrast, it exhibits non-monotonic behavior with respect to
f0 for a fixed fidelity gap,
(Δf=fT−f0). While the optimal policy consistently outperforms baseline policies such as the greedy, nested and entanglement pumping policies, its relative advantage is regime-dependent, being determined by the system parameters (
p,f0,fT,m), and exhibits a nontrivial dependence on the fidelity gap
Δf. Our results highlight the value of formulating entanglement distillation as a Markov decision problem, enabling the systematic design of policies that achieve target fidelity thresholds for quantum information tasks in realistic resource-constrained settings.
Quantum state estimation plays a crucial role in ensuring reliable creation of entanglement within quantum networks, yet conventional Quantum State Tomography (QST) methods remain resource-intensive and impractical for scaling. To address these limitations, we experimentally validate Distimation, a novel distillation-based protocol designed for efficient Bell-diagonal state estimation. Using IBM Quantum simulators and hardware, we demonstrate that Distimation accurately estimates Bell parameters under simulated and real-world noise conditions, but also demonstrating limitations with operational noise and number of available shots. Additionally, we simulate an asymmetric-fidelity Bell pair scenario via Measurement-Based Quantum Computation (MBQC) to further validate Distimation under realistic network conditions. Our results establish Distimation as a viable method for scalable, real-time entanglement monitoring in practical quantum networks.
Quantum technologies rely on high-quality resource states, such as maximally entangled or private states, which are indispensable for quantum communication and cryptography. In practice, however, these states are inevitably degraded by noise. Distillation protocols aim to recover high-resource states from multiple imperfect copies, and while stabilizer-based methods have demonstrated high performance in entanglement purification, they have yet to be established for broader tasks such as secret-key distillation. This work introduces a unified framework for stabilizer-based resource distillation in systems of prime local dimension. By formulating stabilizer routines as quantum channels and deriving closed-form expressions for their output, we enable the application of stabilizer operations to general input states and diverse distillation objectives. We identify key invariances in resource measures, such as coherent and private information, and demonstrate how they can be leveraged to significantly reduce the numerical complexity of channel optimization. To illustrate the framework's versatility, we introduce several protocols: gF-IMAX for general fidelity optimization, and (S)CI-IMAX and (S)PI-IMAX for optimizing (smooth) coherent and private information in both asymptotic and one-shot regimes. Our numerical results confirm that these protocols effectively tailor stabilizer channels to specific operational tasks, establishing them as a robust and flexible tool for quantum resource distillation.
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.