I present a novel tripartite scheme for remotely preparing an arbitrary two-qubit state with two three-qubit entanglements. By using a proper positive operator-valued measure (POVM), it is shown the remote two-qubit preparation can be realized in either distant ministrant's place in a probabilistic manner via their collaboration. I also explore its applications to six special ensembles of state in detail. The extensive investigations shows that the remote preparation can be achieved with higher probability provided that the prepared state belongs to the six special ensembles.
Optimization of the mean efficiency for unambiguous (or error-free) discrimination among
N given linearly independent nonorthogonal states should be realized in a way to keep the probabilistic quantum-mechanical interpretation. This imposes a condition on a certain matrix to be positive semidefinite. We reformulated this condition in such a way that the conditioned optimization problem for the mean efficiency was reduced to finding an unconditioned maximum of a function defined on a unit
N sphere for equiprobable states and on an
N ellipsoid if the states are given with different probabilities. We established that for equiprobable states a point on the sphere with equal values of Cartesian coordinates, which we call symmetric point, plays a special role. Sufficient conditions for a vector set are formulated for which the mean efficiency for equiprobable states takes its maximal value at the symmetric point. This set, in particular, includes previously studied symmetric states. A subset of symmetric states, for which the optimal measurement corresponds to a positive-operator-valued measure (POVM) requiring a one-dimensional ancilla space is constructed. We presented our constructions of a POVM suitable for the ancilla space dimension varying from 1 to
N and the Neumark extension differing from the existing schemes by the property that it is straightforwardly applicable to the case when it is desirable to present the whole space
system+ancilla as the tensor product of a two-dimensional ancilla space and the
N-dimensional system space.
By using a proper positive operator-valued measure (POVM), we present a new scheme for probabilistically implementing quantum state sharing of an arbitrary unknown two-qubit state with two non-maximally entangled three-qubit states. In this paper, the sender Alice averagely partitions its unknown original state with two Bell-state measurements and publishes her measurement results via a classical channel. Then by performing a proper POVM, it is shown that either of the two agents Bob or Charlie can recover the original state in a probabilistic manner provided that he/she gets another one's help. Lastly, we concisely generalize the tripartite scheme to a multi-party case.