Entanglement Superactivation in Multiphoton Distillation Networks

Abstract

In quantum networks, after passing through noisy channels or information processing, residual states may lack sufficient entanglement for further tasks, yet they may retain hidden quantum resources that can be recycled. Efficiently recycling these states to extract entanglement resources such as genuine multipartite entanglement or Einstein-Podolsky-Rosen pairs is essential for optimizing network performance. Here, we develop a tripartite entanglement distillation scheme using an eight-photon quantum platform, demonstrating entanglement superactivation phenomena which are unique to multipartite systems. We successfully generate a three-photon genuinely entangled state from two bi-separable states via local operations and classical communication, demonstrating superactivation of genuine multipartite entanglement. Furthermore, we extend our scheme to generate a three-photon state capable of extracting an Einstein-Podolsky-Rosen pair from two initial states lacking this capability, revealing a previously unobserved entanglement superactivation phenomenon. Our methods and findings offer not only practical applications for quantum networks, but also lead to a deeper understanding of multipartite entanglement structures.

Figures (3)

• Figure 1: Schematic description of two types of entanglement superactivation in tripartite systems. Red dots represent photons. (a) GME superactivation. GME can be activated by collecting two biseparable tripartite states to form a new tripartite state (orange arrow). One can then perform tripartite distillation (green arrow) to concentrate the resources. (b) SLE superactivation. SLE is the property of some quantum states that bipartite entanglement can be localized between two parties with any SLOCC protocol. For some tripartite states, any localization protocol results in bipartite separable states shared between two subsystems (blue arrow) and the resulting states cannot be used to distill entanglement. When two copies of such tripartite states are collected, SLE can be activated and it becomes possible to create a bipartite entangled state.
• Figure 2: Schematic description of the tripartite distillation scheme and the experimental setup. (a) Schematic of the tripartite entanglement distillation scheme. (b) Schematic of the noisy GHZ state generation procedure and entanglement distillation network. (c) Detailed experimental setup. Each to-be-distilled noisy GHZ state is independently prepared with two EPR sources. Three stepping motors are employed to drive a PBS and two HWPs to prepare different components of the noisy GHZ state. PBS$_3$, PBS$_4$, and PBS$_5$ are employed to realize the distillation operation by overlapping photons from two to-be-distilled states. The QWP-HWP-QWP combination after PBS is used to compensate for phase drift between two photons after interference on PBS. C-BBO: combination of $\beta$-barium borate crystals; SC-YVO$_4$: YVO$_4$ crystal for spatial compensation; TC-YVO$_4$: YVO$_4$ crystal for temporal compensation; HWP: half-wave plate; QWP: quarter-wave plate.
• Figure 3: Experimental results. Blue solid lines are fidelities between ideal noisy GHZ states and $\ket{\mathrm{GHZ}_3}$ state. Red solid lines are fidelities of initial states simulated using the knowledge of noises in state preparation. Blue and red shadowed regions represent ranges of entanglement superactivation. (a) Experimental results of the tripartite GME superactivation. Blue and red dashed lines are calculated in the assumption of perfect distillation. Due to unpredictable noises in the state preparation and distillation, experimental results have certain deviations from simulated lines. GME superactivation is demonstrated by states with $p=0.5$, where the fidelity exceeds the GME threshold after distillation. (b) Experimental results of the tripartite SLE superactivation. Blue and red dash-dotted lines are calculated in the assumption of perfect distillation and localization with Pauli-$X$ measurement. Triangles are fidelities of two-photon states extracted by individually localizing two initial states. Diamonds are fidelities of two-photon states extracted by tripartite distillation followed by localization. For two-photon states after the localization operation, their $y$-coordinate values represent fidelities with the EPR pair. States with $p=0.5$ show that the localization operation can extract EPR pairs from noisy states without GME. States with $p=0.4$ and $p=0.36$ show the existence of states that can be used to extract EPR pairs only with the assistance of tripartite distillation.

Theorems & Definitions (1)

• Definition 1: Stochastic Localizable Entanglement