### Squeezing the limit: Quantum benchmarks for the teleportation and storage of squeezed states

M. Owari, M. B. Plenio, E. S. Polzik, A. Serafini, M. M. Wolf

New J. Phys. 10, 113014, **, (2008)

DOI: 10.1088/1367-2630/10/11/113014
*arXiv.org*: 0808.2260

Abstract: We derive fidelity benchmarks for the quantum storage and teleportation of squeezed states of continuous variable systems, for input ensembles where the degree of squeezing $s$ is fixed, no information about its orientation in phase space is given, and the distribution of phase space displacements is a Gaussian. In the limit where the latter becomes flat, we prove analytically that the maximal classical achievable fidelity (which is 1/2 without squeezing, for $s=1$) is given by $\sqrt{s}/(1+s)$, vanishing when the degree of squeezing diverges. For mixed states, as well as for general distributions of displacements, we reduce the determination of the benchmarks to the solution of a finite-dimensional semidefinite program, which yields accurate, certifiable bounds thanks to a rigorous analysis of the truncation error. This approach may be easily adapted to more general ensembles of input states.