Karol Zyczkowski, Jagellonian University
A pure quantum state of N subsystems with d levels each is called
k-uniform, if all its reductions to k qudits are maximally mixed.
These states form a natural generalization of N-qudits GHZ states
which belong to the class 1-uniform states.
We establish a link between the combinatorial notion of orthogonal arrays
and k-uniform states and prove the existence of several new
classes of such states for N-qudit systems.
In particular, known Hadamard matrices allow us to explicitly
construct 2-uniform states for an arbitrary number of N>5 qubits.
Additionally, we establish links between existence of k-uniform states,
classical and quantum error correction codes and provide
a novel graph representation for such states.
* joint work with Dardo Goyeneche (Conception, Chile)