Area and volume as emergent phenomena from entangled qubits

TL;DR

This paper demonstrates how geometric quantities like area and volume can emerge from entangled multi-qubit states, linking quantum information to geometric concepts through explicit state constructions and quantum circuits.

Contribution

It introduces a method to derive geometric measures such as area and volume directly from entangled qubit states, providing a new perspective on emergent geometry in quantum information.

Findings

Area derived from 4-qubit entangled state

Volume derived from 9-qubit entangled state

Quantum circuits implemented using Qiskit

Abstract

Recently, a connection has been shown between certain geometric quantities and quantum information theory. In this paper, we demonstrate that geometric quantities such as area and volume can emerge directly from entangled multi-qubit states. In particular, the area of a two-dimensional parallelogram is derived from a 4-qubit entangled state, the vector area of a three-dimensional parallelogram from three 6-qubit entangled states, and the volume of a three-dimensional parallelepiped from a 9-qubit entangled state. Corresponding quantum circuits are constructed and implemented using Qiskit to generate the required entangled states. Given that parallelograms and parallelepipeds serve as elementary building blocks for more complex geometric structures, these results may offer a pathway toward exploring emergent geometry in quantum information frameworks