Nonstandard protocols for joint remote preparation of a general quantum state and hybrid entanglement of any dimension

Abstract

Joint remote state preparation (JRSP) is a useful way to securely transfer quantum information encoded in quantum states between distant places without physically sending the states themselves. In this paper we study JRSP of the most general D-dimensional quantum state called quDit state, with arbitrary integer D. We first show that, by standard procedures, i.e., by exploiting projective measurements on the Hilbert space of the systems of concern, this task can be completed for the dimensions 2, 4, or 8 only. We then propose a nonstandard protocol by means of a positive operator-valued measurement (POVM), which we suitably design so that our protocol works deterministically for any dimension. We also propose a nonstandard protocol for deterministic JRSP of arbitrary hybrid quDit-quNit entanglement with another POVM. Moreover, we construct quantum circuits to realize the two POVMs in the two nonstandard JRSP protocols mentioned above. Our results may be of interest not only from a theoretical point of view but also from an experimental one.