Quantum Benchmark for Teleportation and Storage of Squeezed States

We provide a quantum benchmark for teleportation and storage of single-mode squeezed states with zero displacement and a completely unknown degree of squeezing along a given direction. For pure squeezed input states, a fidelity higher than 81.5% has to be attained in order to outperform any classical strategy based on an estimation of the unknown squeezing and repreparation of squeezed states. For squeezed thermal input states, we derive an upper and a lower bound on the classical average fidelity which tighten for moderate degree of mixedness. These results enable a critical discussion of recent experiments with squeezed light.

Figure 1

Plot of the average CFT for the transfer of single-mode squeezed thermal states with purity $\mu$. Hollow circles (squares), whose coordinates are reported in the table, provide an upper (lower) bound on the average CFT and admit a polynomial fit by the solid (dashed) line, with equation $\frac{4{\mu }^4}{25}-\frac{11{\mu }^3}{20}+\frac{3{\mu }^2}{4}-\frac{11\mu }{25}+\frac{179}{200}$ ($\frac{21{\mu }^4}{200}-\frac{6{\mu }^3}{25}+\frac{3{\mu }^2}{25}+\frac{11\mu }{100}+\frac{18}{25}$). Solid symbols correspond to the measured fidelities versus the purity of the produced states, achieved in recent demonstrations: The diamond “◆” [$\mu \approx 0.58$, $|r|\approx 5.3\mathrm{dB}$, $\mathcal{F}=(85\pm 5)\%$], referring to Ref. 14, and the star “$\star$” [$\mu \approx 0.51$, $|r|\approx 9.1\mathrm{dB}$, $\mathcal{F}=(83\pm 3)\%$], referring to Ref. 17, correspond to teleportation experiments, while the triangle “▴” [$\mu \approx 0.66$, $|r|\approx 5.4\mathrm{dB}$, $\mathcal{F}=(89\pm 1)\%$] denotes the storage experiment of Ref. 18.