Quantum entangled state, resolution of conifold singularity, and toric variety

TL;DR

This paper explores the geometric and combinatorial structures of multipartite quantum systems using conifold and toric variety concepts, revealing connections between geometric resolutions and quantum entanglement.

Contribution

It establishes a novel link between conifold resolutions, toric varieties, and quantum entangled states, extending the understanding to multi-qubit systems.

Findings

Resolved conifold corresponds to the space of pure two-qubit entangled states

Generalization of conifold-entanglement relation to multi-qubit states

Geometric structures provide insights into quantum entanglement properties

Abstract

We investigate the geometrical and combinatorial structures of multipartite quantum systems based on conifold and toric variety. In particular, we study the relations between resolution of conifold, toric variety, a separable state, and a quantum entangled state for bipartite and multi-qubit states. For example we show that the resolved or deformed conifold is equivalent with the space of a pure entangled two-qubit state. We also generalize this result into multi-qubit states.