Remote state preparation of single-partite high-dimensional states in complex Hilbert spaces

Abstract

High-dimensional quantum systems offer a new playground for quantum information applications due to their remarkable advantages such as higher capacity and noise resistance. We propose potentially practical schemes for remotely preparing four- and eight-level equatorial states in complex Hilbert spaces exactly by identifying a set of orthogonal measurement bases. In these minimal-resource-consuming schemes, both pre-shared maximally and non-maximally entangled states are taken into account. The three-, five-, six-, and seven-level equatorial states in complex Hilbert spaces can also be obtained by adjusting the parameters of the desired states. The evaluations indicate that our high-dimensional RSP schemes might be possible with current technology. The collection operations, necessary for our high-dimensional RSP schemes via partially entangled channels, can be avoided by encoding the computational basis in the spatial modes of single-photon systems.

Figures (3)

• Figure 1: (a) Schematic setup to implement $\mathcal{T}_4$ with $c_0=c_1=c_2=c_3=\frac{1}{2}$. The phase shifts 0, $\pi$, $\pi$, $\pi$ are taken for PS$_{0}$, PS$_{1}$, PS$_{2}$, PS$_{3}$, respectively. (b) Schematic setup to implement block $T(\phi,\theta)$BS1994. Phase shifter $\text{PS}(\theta)=e^{\text{i}\theta}$. BS is a 50:50 beam splitter.
• Figure 2: Quantum circuit for concentrating $|\Psi\rangle_{AB} = \frac{1}{2}(|00\rangle + |11\rangle + |22\rangle + |33\rangle)_{AB}$ from $|\tilde{\Psi}\rangle_{AB} = (a_0|00\rangle + a_1|11\rangle + a_2|22\rangle + a_3|33\rangle)_{AB}$. VBS is a variable reflectivity beam splitter and it can be completed by Fig. \ref{['Figure1']}(b). $D$ is a single-photon detector.
• Figure 3: Average fidelity of $\tilde{T}(\phi,\theta)$. $\delta\theta=\delta\phi$, $\theta=\pi/3$, and $\phi=0$ are taken.