Almost every pure state of three qubits is completely determined by its two-particle reduced density matrices.

In a system of n quantum particles, we define a measure of the degree of irreducible n-way correlation, by which we mean the correlation that cannot be accounted for by looking at the states of n-1 particles. In the case of almost all pure states of three qubits, we show that there is no such correlation: almost every pure state of three qubits is completely determined by its two-particle reduced density matrices.

The parts determine the whole in a generic pure quantum state.

We show that almost every pure state of multiparty quantum systems (each of whose local Hilbert space has the same dimension) is completely determined by the state's reduced density matrices of a fraction of the parties; this fraction is less than about two-thirds of the parties for states of large numbers of parties. In other words, once the reduced states of this fraction of the parties have been specified, there is no further freedom in the state.

Remote state preparation.

Quantum teleportation uses prior entanglement and forward classical communication to transmit one instance of an unknown quantum state. Remote state preparation (RSP) has the same goal, but the sender knows classically what state is to be transmitted. We show that the asymptotic classical communication cost of RSP is one bit per qubit--half that of teleportation--and even less when transmitting part of a known entangled state. We explore the tradeoff between entanglement and classical communication required for RSP, and discuss RSP capacities of general quantum channels.