Figure 1

(a) Scheme for the $|\xi ⟩\to |D_4^{(2)}⟩$ conversion. The spatial qubits experience the Hadamard gates ${\mathsf{H}}_{c,d}$ implemented through a polarization insensitive beam splitter (${\mathrm{BS}}_1$). A controlled-NOT (controlled-PHASE) gate $\mathrm{CX}=|0{⟩}_i⟨0|\otimes {\mathbb{1}}_j+|1{⟩}_i⟨1|\otimes {\widehat{\sigma }}_j^x$ ($\overline{\mathrm{CZ}}=|1{⟩}_i⟨1|\otimes {\mathbb{1}}_j+|0{⟩}_i⟨0|\otimes {\widehat{\sigma }}_j^z$) is realized by a half-wave plate (HWP) with axis at 45° (0°) with respect to the vertical direction ($i=c$, $d$, $j=a$, $b$). The control (target) qubit of such gate is the path (polarization) degree of freedom (DOF). (b) and (c) Displaced Sagnac loop for the realization of the QTC/ODT protocol. Panel (b) [(c)] shows the path followed by the upper [lower] photon $A$ [$B$]. The glass plates ${\varphi }_{A,B,X}$ allow us to vary the relative phase between the different paths within the interferometer. (d) Circuit for $1\to 3$ QTC and ODT. Qubits $\{a,b,c,d\}$ are prepared in $|D_4^{(2)}⟩$ while $X$ should be cloned or teleported. For QTC, the ${\mathrm{CX}}_{Xb}$ gate is complemented by the projection of $X$ ($b$) on the eigenstates of ${\sigma }^x$ (${\sigma }^z$), so as to perform a BM. For QTC (ODT), operation O is a local Pauli gate $\mathsf{P}$ determined by the outcome of the BM according to the given table. For ODT (with, say, receiver qubit $c$), the operations in the dashed boxes should be removed.Reuse & Permissions

Figure 2

Theoretical QTC fidelity and experimental density matrices of the clone (qubit $a$) for various input states. We show the fidelities between the experimental input states and clones (associated uncertainties determined by considering Poissonian fluctuations of the coincidence counts). The dashed line shows the theoretical fidelity for pure input states of the client’s qubit. The dashed area encloses the values of the fidelity achieved for a mixed input state of $X$ and the use of an imperfect Dicke resource compatible with the states generated in our experiment (cf. Supplemental Material [28]).Reuse & Permissions