The distinctive symmetry of Bell states

TL;DR

This paper investigates the symmetries that uniquely define Bell states, introducing the concept of atomic symmetry, which relates to maximal entanglement and could extend to multi-qubit systems.

Contribution

It identifies the atomic symmetry as a key additional constraint needed to determine Bell states, providing new insights into the nature of entanglement.

Findings

Atomic symmetry is essential to uniquely determine Bell states.

Imperfection in atomic symmetry correlates linearly with deviation from maximal entanglement.

Atomic symmetry offers a potential criterion for maximal entanglement in multi-qubit states.

Abstract

The Bell's basis is composed of four maximally entangled states of two qubits, named Bell states. They are usual tools in many theoretical studies and experiments. The aim of this paper is to find out the symmetries that determine a Bell state. For this purpose, starting from a general density matrix, physical constraints and symmetry conditions are added until the elements of the Bell's basis are univocally determined. It is found that the usual physical constraints and symmetry conditions do not suffice to determine a Bell state. The additional restriction needed is named here atomic symmetry. It is a sort of global symmetry of the system, not derived from the action = reaction law. It is also found that the imperfection in fulfilling the atomic symmetry is linearly proportional to the deviation of the Concurrence from its maximum value. The atomic symmetry allows a different insight on the nature of entanglement, and might be useful as a criterion to define the condition of maximal entanglement for states with more than two qubits.