Abstract
The fully symmetric Gaussian tripartite entangled pure states will not exhibit two-mode Einstein Podolsky-Rosen (EPR)-steering. This means that any two participants cannot share quantum secrets using the security of one-sided device independent quantum key distribution (1SDI-QKD) without involving the third. They are restricted at most to standard quantum key distribution (S-QKD), which is less secure. Here we show that least some asymmetric tripartite systems can exhibit bipartite EPR-steering, so that two of the participants can use 1SDI-QKD without involving the other. This is possible because the promiscuity relations of continuous-variable tripartite entanglement are different from those of discrete-variable systems. We analyse these properties for two different systems, showing that the asymmetric system has an extra degree of flexibility not found in the symmetric one.
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