Probabilistic coding of quantum states

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

Entanglement-swapping boxes and their communication properties

We pose the fundamental question of communication properties of primitives irrespectively of their implementation. To illustrate the idea we introduce the concept of entanglement-swapping boxes, i.e. we consider any quantum operations which perform entanglement swapping, not necessarily via simple quantum teleportation. We ask a question about the properties of such boxes., i.e. what local operations and how much classical communication are needed to perform them. We also ask if any box which performs entanglement swapping can be used to establish classical communication. We show that each box needs at least two bits of classical communication to perform it. It is also shown that each box can be used for classical communication and, most importantly, that there exist boxes which allow to communicate at most one bit. Surprisingly we find basic irreversibility in the process of entanglement swapping with respect to its communication properties.Comment: Accepted for publication in Phys. Rev. A as a Rapid Communicatio