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Quantum Communications and Quantum Imaging

Threshold quantum distillation

Shashank Gupta, Carlos Cid, William J. Munro

Published Oct 4, 2024• 0 citations
Publisher

Abstract

Quantum distillation is the task of concentrating quantum correlations present in N imperfect copies using free operations by involving all P the parties sharing the quantum correlation. We present a threshold quantum distillation task where the same objective is achieved but using a lesser number of parties (K<P). In particular, we give exact local filtering operations by the participating parties sharing a high-dimension multipartite entangled state to distil the perfect quantum correlation. Later, we bridge a connection between threshold quantum entanglement distillation and quantum steering distillation.

DOI
10.1117/12.3034544

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Quantum distillation is the task of concentrating quantum correlations present in N imperfect copies using free operations by involving all P the parties sharing the quantum correlation. We present a threshold quantum distillation task where the same objective is achieved but using a lesser number of parties (K<P). In particular, we give exact local filtering operations by the participating parties sharing a high-dimension multipartite entangled state to distil the perfect quantum correlation. Later, we bridge a connection between threshold quantum entanglement distillation and quantum steering distillation.
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.
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.
We study the process of assisted work distillation. This scenario arises when two parties share a bipartite quantum state ρ_{AB} and their task is to locally distill the optimal amount of work when one party is restricted to thermal operations, whereas the other can perform general quantum operations and they are allowed to communicate classically. We demonstrate that this question is intimately related to the distillation of classical and quantum correlations. In particular, we show that the advantage of one party performing global measurements over many copies of ρ_{AB} is related to the nonadditivity of the entanglement of formation. We also show that there may exist work bound in the quantum correlations of the state that is only extractable under the wider class of local Gibbs-preserving operations.
Quantum steering is a critical resource for multiple parties in real networks. Due to its inherent properties, new steerable resources cannot be generated using only free operations, and reallocating Einstein-Podolsky-Rosen steering within networks of certain structures has significant challenges. Therefore, this paper proposes a distillation scheme that selects remaining three-qubit states with bipartite steering components and distills them to yield a state with purer steerability. Based on different construction of communication networks, our protocol combines scenario-specific distillation strategies to obtain high-fidelity steerable states using a low number of copies via distinct measurement operations. The results indicate that our scheme eliminates the need to reallocate new steering states, reduces the steerable resources required for distillation, and remains robust to measurement defects. Furthermore, we introduce a framework for determining the presence of bipartite steerable in three-qubit states.
Entanglement is at the heart of quantum theory and is responsible for various quantum-enabling technologies. In practice, during its preparation, storage, and distribution to the intended recipients, this valuable quantum resource may suffer from noisy interactions that reduce its usefulness for the desired information-processing tasks. Conventional schemes of entanglement distillation aim to alleviate this problem by performing collective operations on multiple copies of these decohered states and sacrificing some of them to recover Bell pairs. However, for this scheme to work, the states to be distilled should already contain a large enough fraction of maximally entangled states before these collective operations. Not all entangled quantum states meet this premise. Here, by using the paradigmatic family of two-qutrit Werner states as an exemplifying example, we experimentally demonstrate how one may use single-copy local filtering operations to meet this requirement and to recover the quantumness hidden in these higher-dimensional states. Among others, our results provide the first proof-of-principle experimental certification of the Bell-nonlocal properties of these intriguing entangled states, the activation of their usefulness for quantum teleportation, dense coding, and an enhancement of their quantum steerability, and hence usefulness for certain discrimination tasks. Our theoretically established lower bounds on the steering robustness of these states, when they admit a symmetric quasiextension or a bosonic symmetric extension, and when they show hidden dense-codability, may also be of independent interest.
We recently proposed an entanglement distillation protocol based on local operations and classical communication that probabilistically and universally distills a maximally entangled Bell pair from multiple copies of an unknown two-qubit state [Phys. Rev. Lett. 135, 260202 (2025)]. Here, we investigate the robustness of this protocol against imperfections in its implementation. We consider several incoherent and coherent gate-error models, as well as measurement readout errors, and determine the regimes in which distillation enhances the fidelity with the target Bell state. We find that the protocol remains effective over substantial error ranges, although its robustness depends strongly on the type of error. We further analyze asymmetric errors between the two parties and identify conditions under which complementary postselection outcomes yield identical distillation dynamics, allowing the success probability to be enhanced.