Distributed quantum resources in practical multi-user quantum networks are inevitably degraded by environmental noise, channel loss, and device-induced imperfections. To address these issues, quantum resource distillation offers a fundamental approach to recovering stronger resources from imperfect states. However, conventional implementations often require additional copies, dedicated physical filtering elements, or restrict to bipartite systems, posing challenges for scalable multipartite networks. Here, we introduce the method of quantum resource distillation based on the local measurement program (LMP), which transfers completely positive maps into programmable measurement processes. We experimentally demonstrate the performance of resource distillation through LMP in both bipartite and tripartite photonic systems, including the activation and enhancement of multipartite steering configurations. To demonstrate the flexibility and extensibility of the LMP framework, we also show that virtual resource distillation can be naturally reformulated within it. Our results establish a programmable and experimentally economical approach for distilling quantum resources in multipartite and higher-dimensional systems, thereby providing a practical route toward scalable quantum networks.
Distributed quantum resources in practical multi-user quantum networks are inevitably degraded by environmental noise, channel loss, and device-induced imperfections. To address these issues, quantum resource distillation offers a fundamental approach to recovering stronger resources from imperfect states. However, conventional implementations often require additional copies, dedicated physical filtering elements, or restrict to bipartite systems, posing challenges for scalable multipartite networks. Here, we introduce the method of quantum resource distillation based on the local measurement program (LMP), which transfers completely positive maps into programmable measurement processes. We experimentally demonstrate the performance of resource distillation through LMP in both bipartite and tripartite photonic systems, including the activation and enhancement of multipartite steering configurations. To demonstrate the flexibility and extensibility of the LMP framework, we also show that virtual resource distillation can be naturally reformulated within it. Our results establish a programmable and experimentally economical approach for distilling quantum resources in multipartite and higher-dimensional systems, thereby providing a practical route toward scalable quantum networks.
Noise is, in general, inevitable and detrimental to practical and useful quantum communication and computation. Under the resource theory framework, resource distillation serves as a generic tool to overcome the effect of noise. Yet, conventional resource distillation protocols generally require operations on multiple copies of resource states, and strong limitations exist that restrict their practical utilities. Recently, by relaxing the setting of resource distillation to only approximating the measurement statistics instead of the quantum state, a resource-frugal protocol, "virtual resource distillation," is proposed, which allows more effective distillation of noisy resources. Here, we report its experimental implementation on a photonic quantum system for the distillation of quantum coherence (up to dimension four) and bipartite entanglement. We show the virtual distillation of the maximal superposed state of dimension four from the state of dimension two, an impossible task in conventional coherence distillation. Furthermore, we demonstrate the virtual distillation of entanglement with operations acting only on a single copy of the noisy Einstein-Podolsky-Rosen (EPR) pair and showcase the quantum teleportation task using the virtually distilled EPR pair with a significantly improved fidelity of the teleported state. These results illustrate the feasibility of the virtual resource distillation method and pave the way for accurate manipulation of quantum resources with noisy quantum hardware.
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.
High-dimensional hyperentangled states, serving as crucial physical resources in quantum communication, have attracted significant attention due to their exceptional properties (e.g., higher information density) compared to conventional two-dimensional single-degree-of-freedom entanglement. However, practical quantum entanglement systems inevitably suffer from environmental interactions, resulting in their degradation into partially entangled pure states or even mixed states, thereby significantly compromising the efficiency and security of quantum communication. Consequently, improving entanglement preservation in noisy systems emerges as a pivotal challenge in realizing fault-tolerant quantum networks. We propose two universal distillation schemes based on local positive-operator-valued measures (POVMs) for single-copy $(2\ifmmode\times\else\texttimes\fi{}4\ifmmode\times\else\texttimes\fi{}4)$-dimensional hyperentangled photons. These schemes effectively suppress photon vacuum errors induced by transmission losses and are constructed using spatial-mode and polarization-based POVM measurements, respectively. Our results demonstrate that the spatial-mode-based scheme outperforms its polarization-based counterpart in terms of fidelity and success probability. Remarkably, we discover that with appropriate POVM parameters, the fidelity range of amplitude-damped noisy states can be expanded to cover almost all parameter spaces. Due to the universal applicability of POVM measurements, which require neither auxiliary entanglement nor complex detectors and operate on single copies of imperfect states in each purification round, our scheme provides an experimentally feasible solution for distilling high-dimensional hyperentangled photonic states.
Virtual distillation is a promising error-mitigation technique that exploits multiple copies of a noisy quantum state to estimate observables as if measured on a purified state. Although originally introduced in the context of bosonic many-body systems under the name of virtual cooling, its development and applications have largely focused on qubit-based quantum computation. Here, we establish a framework for virtual distillation in bosonic quantum information processing and continuous-variable quantum computing. Building on a diagonalization of cyclic shift operators implemented with passive linear-optical interferometers, we derive experimentally accessible protocols for estimating virtually distilled expectation values of observables relevant to bosonic architectures. In particular, we show how to recover noise-mitigated expectation values of number operators, phase-shift operators, and arbitrary quadratures from multi-copy measurements. For number operators, we further demonstrate the estimation of virtually distilled correlators of arbitrary order through the characteristic function of the photon-number distribution. We apply the framework to states affected by photon loss and dephasing, two of the dominant noise mechanisms in bosonic quantum computation, and quantify the resulting suppression of noise contributions. Our results extend virtual distillation beyond its original setting and provide a practical route toward error-mitigated measurements in bosonic quantum processors using experimentally available linear-optical resources.
We introduce a threshold quantum distillation protocol that enables the extraction of perfect quantum correlations from multiple imperfect copies of a multipartite quantum state using only a subset of the parties ( Q < P ) in the network. In particular, we show that for high-dimensional Greenberger–Horne–Zeilinger states, entanglement can be distilled by local filtering operations applied by just a single party, independent of the total number of parties in the network. In contrast, for the W states, at least P − 1 parties are required for successful distillation, highlighting a strong connection between distillability and separability. We provide explicit protocols for threshold entanglement distillation and threshold steering distillation (TSD), and establish a direct link between the two: Any assemblage that can be distilled via TSD necessarily corresponds to a distillable entangled state. Our framework introduces a scalable and experimentally viable approach to distillation in quantum networks, with potential applications in distributed quantum computing, communication, and cryptography.