On quantum non-signalling boxes

A classical non-signalling (or causal) box is an operation on classical bipartite input with classical bipartite output such that no signal can be sent from a party to the other through the use of the box. The quantum counterpart of such boxes, i.e. completely positive trace-preserving maps on bipartite states, though studied in literature, have been investigated less intensively than classical boxes. We present here some results and remarks about such maps. In particular, we analyze: the relations among properties as causality, non-locality and entanglement; the connection between causal and entanglement breaking maps; the characterization of causal maps in terms of the classification of states with fixed reductions. We also provide new proofs of the fact that every non-product unitary transformation is not causal, as well as for the equivalence of the so-called semicausality and semilocalizability properties.Comment: 18 pages, 7 figures, revtex

Unconditional privacy over channels which cannot convey quantum information

By sending systems in specially prepared quantum states, two parties can communicate without an eavesdropper being able to listen. The technique, called quantum cryptography, enables one to verify that the state of the quantum system has not been tampered with, and thus one can obtain privacy regardless of the power of the eavesdropper. All previous protocols relied on the ability to faithfully send quantum states. In fact, until recently, they could all be reduced to a single protocol where security is ensured though sharing maximally entangled states. Here we show this need not be the case -- one can obtain verifiable privacy even through some channels which cannot be used to reliably send quantum states.Comment: Related to quant-ph/0608195 and for a more general audienc