Holographic entropy inequalities and the topology of entanglement wedge nesting

We prove two new infinite families of holographic entropy inequalities. A key tool is a graphical arrangement of terms of inequalities that is based on entanglement wedge nesting. It associates the inequalities with tessellations of the torus and the projective plane, which reflect a certain topological aspect of entanglement wedge nesting. The inequalities prove a prior conjecture about the holographic entropy cone. We discuss their relation to black hole physics and differential entropy, and sketch applications to quantum error correction, quantifying randomness of quantum states, and others.