Experimental linear-optical implementation of a multifunctional optimal qubit cloner

We present the first experimental implementation of a multifunctional device for the optimal cloning of one to two qubits. Previous implementations have always been designed to optimize the cloning procedure with respect to one single type of a priori information about the cloned state. In contrast, our “all-in-one” implementation is optimal for several prominent regimes such as universal cloning, phase-covariant cloning, and also the first ever realized mirror phase-covariant cloning, when the square of the expected value of Pauli's $Z$ operator is known in advance. In all these regimes the experimental device yields clones with almost maximum achievable average fidelity (97.5$\%$ of theoretical limit). Our device has a wide range of possible applications in quantum information processing, especially in quantum communication. For instance, one can use it for incoherent and coherent attacks against a variety of cryptographic protocols, including the Bennett-Brassard 1984 protocol of quantum key distribution through the Pauli damping channels. It can be also applied as a state-dependent photon multiplier in practical quantum networks.

Figure 1

Overview of various distributions on Bloch's sphere describing a priori knowledge of qubits and the corresponding optimal cloning machines which are special cases of our multifunctional cloner: (a) uniform distribution can be cloned by the UC, (b) qubits on the equator of the Bloch sphere can be cloned by the standard PCC, (c) a union of the set of qubits for the generalized PCC and its equator-plane reflection can be cloned by the standard MPCC, and (d) any set of qubits of unknown phase symmetric about any equator plane can be cloned by the generalized MPCC.

Figure 2

(a) Scheme of the experimental setup as described in the text. (b) Detailed scheme of the beam-divider assembly. HWP, half-wave plate; QWP, quarter-wave plate; PDBS, polarization-dependent beam splitter; BDA, beam-divider assembly; F, neutral density filter; PBS, polarizing beam splitter; D, single-photon detector; BD, beam divider.

Figure 3

Experimental fidelity $F_{\mathrm{ex}}$ averaged over phase $\varphi$ for the PCC regime depicted against theoretical prediction $F_{\mathrm{th}}$ (solid curve). The short-dashed curve indicates the fidelity drops to 97.5$\%$ with respect to the corresponding theoretical value. The theoretical fidelity $F_{\mathrm{th}}^{\mathit{UC}}$ for the UC is also depicted (long-dashed curve). For the generalized PCC the hemisphere of the cloned qubit is known (the reverse is true for the MPCC); we choose the ancilla deterministically [18] (horizontal for northern hemisphere and vertical for southern hemisphere), and we set transmittances of filters as for the MPCC tuned for the angle $\theta =\pi /2$.

Figure 4

Same as in Fig. 3, but for the MPCC.

Figure 5

The success probability of the MPCC as a function of polar angle $\theta$. $P_{\mathrm{ex}}$ denotes an experimentally determined value, and $P_{\mathrm{th}}$ denotes our theoretical prediction. Note that sometimes the experimental results surpass the theoretical ones; this happens at the expense of lower fidelity of the cloning process.