Quantum steering

For a shared quantum entanglement resource, one party's choice of measurement can prepare different conditional ensembles for the distant party. Discarding the outcome leaves the same distant reduced density matrix, so steering does not itself permit signalling. Demonstrating steering against a local hidden-state model is stronger than merely observing a change in a postselected description.

For a Bell pair $|{\varphi }_{+}⟩=(|00⟩+|11⟩)/\sqrt{2}$, Alice's basic measurement in the entrywise complex conjugate of any desired Bob orthonormal basis prepares each Bob pure state with probability $1/2$. Indeed, if $|u⟩={\sum }_{j=0}^1{u}_j|j⟩$, then $⟨\overline{u}|j⟩=u_j$, which proves the displayed contraction identity. The undisclosed-outcome density matrix stays $I/2$; quantum steering changes the conditional quantum state ensemble without violating the no-communication theorem.