Universal entanglement-inspired correlations

TL;DR

This paper introduces a universal framework for quantum correlations inspired by entanglement, linking general product-based correlations to tensor products and establishing a resource theory applicable to multipartite systems.

Contribution

It formulates a generalized correlation notion via arbitrary products, connects it to entanglement, and extends the resource theory to multipartite and non-standard systems.

Findings

Unified framework for correlations beyond tensor products

Resource theory applicable to multipartite and non-standard systems

Applications to fermionic, photonic states, and prime number interpretation

Abstract

Quantum correlations, crucial for the advantage and advancement of quantum science and technology, arise from the impossibility of expressing a quantum state as a tensor product over a given set of parties. In this work, a generalized notion of correlations via arbitrary products is formulated. Remarkably, as a universal property, the connection between such general products and tensor products is established, allowing one to relate generic non-product states to the common notion of entangled states. We construct the set of free operations for general types of products by extending the local-operation-and-classical-communication paradigm, familiar from standard entanglement theory, thereby establishing a resource theory of correlations for general products. A generalization is provided beyond two factors that can be universally related to multipartite entanglement. Applications that highlight the usefulness of the approach are discussed, such as the factorization of fermionic states, the non-local factorization of multi-photon states into single-photon states, and the interesting possibility of understanding prime numbers as a form of single-party entanglement.