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arXiv:2505.11487 · Modern Physics Letters A

Area and volume as emergent phenomena from entangled qubits

Juan M. Romero, Emiliano Montoya-González

Published Oct 13, 2025• 0 citations
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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.

DOI
10.1142/s0217732325501949

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Quantum entanglement, traditionally viewed as a correlation between particles, possesses the potential to manifest within complex geometric structures in higher dimensions. This research explores the possibility that entanglement may form intricate geometric tensors, allowing for precise definition and computation of its properties, potentially unveiling novel quantum information processing algorithms. We introduce a novel quantum entanglement model based on multi-dimensional geometry, leveraging non-local quantum information theory to construct a dynamically evolving geometric tensor, and develop algorithms to precisely analyze entanglement's geometric characteristics. This work represents a significant departure from conventional quantum computation by focusing on the geometric properties of entanglement, offering a new perspective on its potential for manipulation and analysis.
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