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Quantum multipartite entangled states play significant roles in quantum information processing. By using difference schemes and orthogonal partitions, we construct a series of infinite classes of irredundant mixed orthogonal arrays (IrMOAs) and thus provide positive answers to two open problems. The first is the extension of the method for constructing homogeneous systems from orthogonal arrays (OAs) to heterogeneous multipartite systems with different individual levels. The second is the existence of $k$-uniform states in heterogeneous quantum systems. We present explicit constructions of two and three-uniform states for arbitrary heterogeneous multipartite systems with coprime individual levels, and characterize the entangled states in heterogeneous systems consisting of subsystems with nonprime power dimensions as well. Moreover, we obtain infinite classes of $k$-uniform states for heterogeneous multipartite systems for any $kgeq2$. The non-existence of a class of IrMOAs is also proved.
We present a general formalism based on the variational principle for finding the time-optimal quantum evolution of mixed states governed by a master equation, when the Hamiltonian and the Lindblad operators are subject to certain constraints. The pr
Applications of quantum technology often require fidelities to quantify performance. These provide a fundamental yardstick for the comparison of two quantum states. While this is straightforward in the case of pure states, it is much more subtle for
We introduce a new functional to estimate the producibility of mixed quantum states. When applicable, this functional outperforms the quantum Fisher information, and can be operatively exploited to characterize quantum states and phases by multiparti
A set of vertices $Xsubseteq V$ in a simple graph $G(V,E)$ is irredundant if each vertex $xin X$ is either isolated in the induced subgraph $langle Xrangle$ or else has a private neighbor $yin Vsetminus X$ that is adjacent to $x$ and to no other vert
Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal. We develo