31.05.2018 (Thursday)

Perfect probabilistic storing and retrieving of unitary channels

Regular Seminar Michal Sedlak (Slovak Academy of Sciences)

14:00 QMW
room G O Jones 610

Any sequence of quantum gates on a set of qubits defines a multipartite unitary transformation. These sequences may correspond to some parts of a quantum computation or they may be used to encode classical/quantum information (e.g. in private quantum channels). If we have only limited access to such a unitary transformation, we may want to store it into a quantum memory and later perfectly retrieve it. Thus, once we cannot use the unitary transformation directly anymore, we could still apply it to any state with the help of the footprint kept in the quantum memory. This can be useful for speeding up some calculations or as an attack for process based quantum key distribution protocol or a communication scheme. We require the storing and retrieving protocol to perfectly reconstruct the unitary transformation, which implies non unit probability of success. We derive optimal probability of success for a d-dimensional unitary transformation used N-times. The optimal probability of success has a very simple form N/(N-1+d^2). This result implies that reliable storing of d^2 parameters of the unknown unitary transformation requires roughly d^2 uses of the transformation.