Cloning of Quantum Entanglement

Quantum no-cloning, the impossibility of perfectly cloning an arbitrary unknown quantum state, is one of the most fundamental limitations due to the laws of quantum mechanics, which underpin the physical security of quantum key distribution. Quantum physics does allow, however, approximate cloning with either imperfect state fidelity and/or probabilistic success. Whereas approximate quantum cloning of single-particle states has been tested previously, experimental cloning of quantum entanglement—a highly nonclassical correlation—remained unexplored. Based on a multiphoton linear optics platform, we demonstrate quantum cloning of two-photon entangled states for the first time. Remarkably our results show that one maximally entangled photon pair can be broadcast into two entangled pairs, both with state fidelities above 50%. Our results are a key step towards cloning of complex quantum systems, and are likely to provide new insights into quantum entanglement.

Figure 1

Operational principle of our quantum cloning network. (a) A universal single-qubit quantum cloning machine, which generates two approximate clones for an unknown quantum state $|\varphi ⟩$ with the support of two ancilla qubits. (b) Our entanglement cloning network. Charles first prepares his qubits $|0{⟩}_1$ and $|0{⟩}_2$ into an entangled state $|\varphi {⟩}_{12}$ (vertical red line). Next the qubit 1 (2) are fed into a UQCM (gray box) with qubits $|0{⟩}_3$ ($|0{⟩}_5$) and $|0{⟩}_4$ ($|0{⟩}_6$). Charles then simultaneously performs quantum cloning on his two-qubit state by enacting unitary operations ${\widehat{\mathbf{U}}}_1$ and ${\widehat{\mathbf{U}}}_2$ on qubits 1, 3 and qubits 2, 5. Consequently, Bob receives the two-qubit pair (4, 6) while Alice gets her two-qubit pair ($1^{\prime }$, $2^{\prime }$), respectively.

Figure 2

Experimental setup for quantum entanglement cloning. Here two pulsed Ti:sapphire laser beams (with 775 nm central wavelength and 80 MHz repetition rate) are focused on to a 6.3 mm-thick $\beta$-barium-borate crystal (BBO) to produce photon pairs via SPDC. Optical 4f systems of lenses are inserted before each SPDC source for an optimal beam-waist match of $800\mu \mathrm{m}$. The photons in spatial modes 1 and 2 are combined into one path with BDs and HWPs (inset). The HWP in mode 2 is used to prepare a desired initial state. The photon pairs of EPR1 and EPR2 are prepared in singlet states with similar optical arrangements. Polarization states of photons in modes $1^{\prime }$, $2^{\prime }$, 4, and 6 are analyzed by using QWPs, HWPs, and PBSs. All photons are spectrally filtered by 30-nm band-pass filters. Sixfold coincidences are recorded with a multichannel coincidence unit.

Figure 3

Experimental entanglement characterization in three complementary bases. (a) For the linear basis ($|H⟩/|V⟩$), the measured expectation value $⟨{\widehat{\sigma }}_z{\widehat{\sigma }}_z⟩$ is $0.433\pm 0.015$ ($0.372\pm 0.016$) for the local (distant) case. (b) Corresponding to the diagonal basis ($|D⟩/|A⟩=|H⟩\pm |V⟩$), the measured $⟨{\widehat{\sigma }}_x{\widehat{\sigma }}_x⟩$ is $0.420\pm 0.015$ ($0.369\pm 0.016$). (c) For the circular basis ($|L⟩/|R⟩=|H⟩\pm i|V⟩$), the measured $⟨{\widehat{\sigma }}_y{\widehat{\sigma }}_y⟩$ is $-0.423\pm 0.015$ ($-0.347\pm 0.015$). The accumulation time for each setting is 12 h. The expectation values and error bars are calculated with raw counts.

Figure 4

Experimental density matrices reconstruction of the initial and cloned states. (a) [(b)], the real [imaginary] part of the density matrices of the initial input bipartite system. (c) and (d) The real parts of the density matrices are shown for the local and distant two-photon cloned state, respectively. The elements of imaginary parts are small, hence, are not shown. The empty bars illustrate the theoretical values while the solid bars are calculated from experimental raw data.

Figure 5

Fidelities of the cloned two-photon states for various beam splitter reflectivities. The dots represent the fidelities determined from the local measurements for $⟨{\widehat{\sigma }}_k^{\otimes 4}⟩(k=x,y,z)$ on photons $1^{\prime }$, $2^{\prime }$, 4, and 6. Further, the solid curves represent the theoretical fidelity of photon pair ($1^{\prime }$, $2^{\prime }$) (blue) and (4, 6) (orange) with simulated mode-mismatch noise. The error bars represent 1 standard deviation.