Experimental verification of multi-copy activation of genuine multipartite entanglement

TL;DR

The paper demonstrates two-copy activation of genuine multipartite entanglement (GME) by preparing two copies of a biseparable three-qubit state on a trapped-ion platform and certifying GME with a fully decomposable witness. It uses a balanced mixture of eight three-qubit components $\tilde{\rho}_{ABC}$, such that two copies become GME across the partition $A_{1}A_{2}|B_{1}B_{2}|C_{1}C_{2}$, as shown by a negative witness mean $\langle W\rangle = (-5.7 \pm 0.5) \times 10^{-3}$. The authors also develop a modified algorithm to prove single-copy biseparability and provide a detailed SDP-based witness decomposition (32 Pauli terms) measured in 17 settings. They discuss scalability challenges for higher-copy activations and outline a path toward deploying GME resources in distributed quantum networks, establishing a practical route to harness multi-copy quantum correlations.

Abstract

A central concept in quantum information processing is genuine multipartite entanglement (GME), a type of correlation beyond biseparability, that is, correlations that cannot be explained by statistical mixtures of partially separable states. GME is relevant for characterizing and benchmarking complex quantum systems, and it is an important resource for applications such as quantum communication. Remarkably, it has been found that GME can be activated from multiple copies of biseparable quantum states, which do not possess GME individually. Here, we experimentally demonstrate unambiguous evidence of such GME activation from two copies of a biseparable three-qubit state in a trapped-ion quantum processor. These results not only challenge notions of quantum resources but also highlight the potential of using multiple copies of quantum states to achieve tasks beyond the capabilities of the individual copies.

Figures (2)

• Figure 1: (a) Illustration of the robust biseparable two-copy GME-activatable state $\rho_{\space\raisebox{0 pt}{\tiny{$A\space BC$}}}$ [Eq. \ref{['eq:ourrho']}]. The dark orange oval regions represent the sets of separable states across bipartitions $A|BC, B|AC$, and $C|AB$. The light orange regions represent the GME-activatable states. The union of the orange regions represents the set of biseparable states, while the light-blue region outside contains the GME states. The orange regions between the dashed lines and the borders between the sets of biseparable and GME states represent the set of biseparable two-copy GME-activatable states. The state $\rho_{\space\raisebox{0 pt}{\tiny{$A\space BC$}}}$ (red dot) is a balanced mixture (illustrated by the dotted line) of states separable across bipartitions $A|BC$ and $B|AC$ (white squares), respectively. (b) Diagrammatic representation of two copies of the state $\rho_{\space\raisebox{0 pt}{\tiny{$A\space BC$}}}$. The oval regions labeled by $jk$ with $j=A_{1}, B_{1}, C_{1}$ and $k=A_{2}, B_{2}, C_{2}$ denote sets of states for which the pair of qubits $j$ and $k$ is separable from the rest of the system. The convex hull of the three oval orange regions indicates the set of biseparable states with respect to the partition $A_{1}A_{2}|B_{1}B_{2}|C_{1}C_{2}$. The two-copy state $\rho_{\space\raisebox{0 pt}{\tiny{$A_{1}A_{2}B_{1}B_{2}C_{1}C_{2}$}}}$ (red dot) is a balanced mixture (illustrated by the dotted lines) of four possible tensor products of states depicted by white squares in panel (a), which belong to the sets $A_{1}A_{2}$, $B_{1}B_{2}$, $A_{1}B_{2}$, and $B_{1}A_{2}$ (white squares), respectively. GME with respect to the partition $A_{1}A_{2}|B_{1}B_{2}|C_{1}C_{2}$ is detected by the witness $W$ (solid black line). (c) Illustration of a linear Paul trap and a $^{40}\mathrm{Ca}^{+}$ level diagram. A Paul trap consisting of four blade electrodes and two tip electrodes confines a linear chain of six $^{40}\mathrm{Ca}^{+}$ ions (white dots). The orange and blue labels illustrate the interleaved qubit assignment of the first and the second copy. We refer to the main text for details on the energy-level diagram.
• Figure A.1: Histogram of two-copy witness value obtained by Monte Carlo resampling of the original tomogram.