Cite this problem as Problem 38.
Let and be quantum states with positive partial transpose (i.e., they are “PPT-states”), and let be a positive operator decribing a yes/no measurement on the BC-system. Then consider the state on AD, conditional on the result of being `yes’, i.e. , where is a normalization factor. The conjecture  by Matthias Christandl states that all such are separable.
Of course, the problem is to prove or disprove this.
The process for getting is called entanglement swapping, and is a key ingredient of quantum repeaters, which seek to establish secret key over a long distance out of entangled states over smaller distance. While it is possible that PPT states allow the extraction of private key , the conjecture would imply that they cannot be used as a resource in a repeater .
 List of problems in an open problem session in Banff, conducted by M. B. Ruskai in 2012.
 K. Horodecki, M. Horodecki, P. Horodecki, J. Oppenheim: Secure key from bound entanglement, quant-ph/0309110 (2003) and Problem 24.
 M. Christandl and R. Ferrara: Private states, quantum data hiding and the swapping of perfect secrecy, arxiv.org/abs/1609.04696