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 
, 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.
Export citation and abstract BibTeX RIS
GENERAL SCIENTIFIC SUMMARY Introduction and background. The storage and teleportation of quantum states have now been accomplished in a variety of physical systems, an outstanding example being the storage of the travelling state of light in the collective spin of static atomic ensembles. But when are such memories truly quantum mechanical, that is, when do they preserve quantum coherence to an extent which cannot be matched by 'classical' devices that simply measure and re-prepare quantum states? Answering this question and justifying the term 'quantum' in 'quantum memory' and 'quantum teleportation' requires theoretical benchmarks which bound the performance of purely classical schemes. This is what we achieve in this study.
Main results. We consider Gaussian input ensembles with a fixed degree of squeezing but no information about its phase-space orientation. Analytical benchmarks are derived, in the case of completely unknown phase-space translations, for pure states and for states subject to additive thermal noise (see figure). Moreover, for ensembles of mixed squeezed states with general distributions of displacements, we reduce the determination of the benchmarks to the solution of a semi-definite program, yielding accurate, certifiable bounds thanks to a rigorous analysis of the truncation error.
Wider implications. The benchmarks derived here constitute a resource to assess the quantum mechanical character of storage and transmission experiments with squeezed states. Furthermore, we emphasize that beating these benchmarks in quantum memory experiments would also demonstrate the ability of storing entanglement with remote systems. We are currently employing these methods in a concrete experiment run by the group of Eugene Polzik in Copenhagen.
Figure. Fidelity benchmarks 
on ensembles with squeezing s, flatly distributed displacements and random phase space orientations. Here, η quantifies the amount of additive thermal noise (e.g., η = 0 for pure squeezed states).