Flexible manipulation of bipartite and multipartite EPR steerings

TL;DR

This work addresses flexible control of EPR steering in a Gaussian, five-mode system by using a spatially structured pump in a type-II optical parametric oscillator. By decomposing the pump into Hermite-Gaussian components with weights $b$, $c$, and angle $\theta$ controlled by a spatial light modulator, the authors manipulate bipartite and multipartite steerings, quantified via covariance-matrix 기반 criteria and symplectic eigenvalues. They establish concrete criteria for bipartite and multipartite steering, map parameter regions enabling all six (1+1) steering types and a range of (1+2), (2+1), (3+1) steerings up to genuine pentapartite steering, and show that balanced pump proportions optimize genuine pentapartite steering. The proposed scheme is experimentally feasible and offers a versatile resource for quantum networks, communication with role changes, and quantum computation tasks requiring reconfigurable steering among multiple users.

Abstract

Bipartite and multipartite quantum steerings are significant resources for various quantum tasks, such as ultrasecure multi-user quantum network, one-site-trusted quantum communication, high-fidelity quantum computation, etc. A flexible steering manipulation scheme of five down-converted Hermitian Gaussian modes generated from an optical parametric oscillator by using a spatial structured pump is presented. In our scheme, not only the direction and types of the bipartite steering, but also different situations of multipartite steering, can be manipulated effectively, by adjusting the pump proportions with a spatial light modulator. In addition, stricter genuine pentapartite steering (only one site is trusted) can also be achieved by making the pump proportions as balanced as possible. Our scheme is versatile and experimentally feasible and offers new insights into the manipulation of steering, especially multipartite steering, which is valuable in many special quantum tasks.

Figures (8)

• Figure 1: The type-II optical parametric oscillator injected with seed and spatial structured pump beams. Here shows an example of pump beam composed of third-order HG modes $\text{HG}_{30}$, $\text{HG}_{03}$, $\text{HG}_{21}$ and $\text{HG}_{12}$ with weights 0.222, 0.509, 0.582 and 0.593, respectively.
• Figure 2: Parameter regions of the six types of bipartite steering with $t=0.5$. The steering between $\hat{a}_2$ and $\hat{a}_4$ with $\theta=\frac{\pi }{8}$ (a), $\hat{a}_2$ and $\hat{a}_3$ with $\theta=\frac{11\pi }{32}$ (b), $\hat{a}_1$ and $\hat{a}_3$ with $\theta=\frac{\pi }{16}$(c), $\hat{a}_2$ and $\hat{a}_5$ with $\theta=\frac{3\pi }{8}$(d), $\hat{a}_1$ and $\hat{a}_4$ with $\theta=\frac{3\pi }{8}$ (e), $\hat{a}_1$ and $\hat{a}_5$ with $\theta=\frac{5\pi }{16}$ (f). (g): The legend of subgraphs (a) - (f), explaining the different colors used to represent various bipartite steering types. Here A and B parties correspond to the signal and idler modes, respectively.
• Figure 3: Parameter regions of bipartite entanglement and steering with $t=0.5$ (subgraphs (a')-(f') mean photon numbers). In (a) and (a'): $\theta=\frac{\pi }{8}$, $b=0.8$; in (b) and (b'): $\theta=\frac{11\pi }{32}$, $c=0.87$; in (c) and (c'): $\theta=\frac{\pi }{16}$, $b=0.5$; in (d) and (d'): $\theta=\frac{3\pi}{8}$, $c=0.5$; in (e) and (e'): $\theta=\frac{3\pi }{8}$, $b=0.5$; in (f) and (f'): $\theta=\frac{5\pi }{16}$, $c=0.85$.
• Figure 4: The parameter regions of the four possible (1+2)-steerings. Here the steered part is the joint mode $\hat{a}_1\hat{a}_2$ and the steering part is $\hat{a}_3$, $\hat{a}_4$ or $\hat{a}_5$. $t=0.5, \theta=\frac{\pi }{4}$. The legend below explains the different colors used to represent various (1+2)-steering situations.
• Figure 5: The parameter regions of the seven possible (2+1)-steerings. Here $\hat{a}_1$ (a) or $\hat{a}_2$ (b) is chosen to be the single steered part and the joint steering part includes two of modes $\hat{a}_3$, $\hat{a}_4$ or $\hat{a}_5$. $t=0.5$, $\theta=\frac{\pi }{4}$. The legend below explains the different colors used to represent various (2+1)-steering situations.