Probabilistic coding of quantum states

Abstract

We discuss the properties of probabilistic coding of two qubits to one qutrit and generalize the scheme to higher dimensions. We show that the protocol preserves the entanglement between the qubits to be encoded and the environment and can also be applied to mixed states. We present a protocol that enables encoding of $n$ qudits to one qudit of dimension smaller than the Hilbert space of the original system and then allows probabilistic but error-free decoding of any subset of $k$ qudits. We give a formula for the probability of successful decoding.