How to share a continuous-variable quantum secret by optical interferometry

Abstract

We develop the theory of continuous-variable quantum secret sharing and propose its interferometric realization using passive and active optical elements. In the ideal case of infinite squeezing, a fidelity $\mathcal{F}$ of unity can be achieved with respect to reconstructing the quantum secret. We quantify the reduction in fidelity for the (2,3) threshold scheme due to finite squeezing and establish the condition for verifying that genuine quantum secret sharing has occurred.

6 pages, 4 figures, revised version has been extended at places to make the paper clearer. Submitted to PRA

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