Distillation of continuous variable qudits from single photon sources: A cascaded approach

Abstract

Creation of high fidelity photonic quantum states in the continuous variable regime is indispensable for the implementation of quantum technologies universally. However, this is a challenging task as it requires higher nonlinearity or larger Fock states. In this article, we surmount this necessity by using a linear optical setup with a cascaded arrangement of beam splitters that relies solely on single photon sources and single photon detectors to tailor desired single mode nonclassical states. To show the utility of this setup, we demonstrate the generation of displaced higher photon states with unit fidelity and the family of Schrodinger cat states above $98\%$ fidelity. In addition, we manifest the generation of GKP resource states, such as ON states and weak cubic phase states with $99\%$ fidelity. Creating such a variety of important states in this single setup is made feasible by stating the output in the form of displaced qudits. This figure of merit facilitates efficient identification and optimization of input parameters required to generate the target single mode quantum states. We also account for the experimental imperfections by incorporating detector inefficiencies and non-unit single photon sources. This cascaded setup will assist the experimentalists to explore the feasible creation of target states using currently available resources, such as single photon sources and single photon detectors.

Figures (5)

• Figure 1: A coherent state and a single photon state are directed into the input ports of $\hbox{BS}_1$. When a single photon is conditionally measured at one of $\hbox{BS}_1$'s output ports, $\hbox{DQ}_1$ is produced at the other port. This $\hbox{DQ}_1$ is subsequently introduced to $\hbox{BS}_2$, where it undergoes a catalysis operation, yielding $\hbox{DQ}_2$ and so on.
• Figure 2: The Wigner function of the created photon states with unit fidelity. (a), (b), (c) and (d) correspond to $\ket{2}$, $\ket{3}$, $\ket{4}$ and $\ket{5}$ with displacement respectively.
• Figure 3: The Wigner functions for the generated states are depicted as follows: (a) even cat states with $h=0$, (b) odd cat states with $h=1$. For three headed cat states, the Wigner functions are shown in (c) for $h=0$ and (d) for $h=1$. Similarly, the Wigner functions of compass states are illustrated in (e) for $h=0$ and (f) for $h=1$.
• Figure 4: The bar plots portray the comparison of photon probability amplitudes PND between the target states and the cascaded output states. PND of the states between (a) $\ket{03}$ and $\ket{\psi}_3$, (b) $\ket{04}$ and $\ket{\psi}_4$ and (c) $\ket{CPS}$ and $\ket{\psi}_3$ respectively.
• Figure 5: The figures portray the fidelity between the realistic generation and the ideal generation of the created states. Here, detector inefficiency $\eta_d = 0.98$ is fixed and fidelity is taken for various non-unit source efficiency $\eta_s$. (a), (b) and (c) correspond to higher Fock states, optimal squeezed states and LSCS generation respectively.