Detecting maximally entangled states without making the Schmidt decomposition

TL;DR

The paper introduces a basis-independent analytical method to identify maximally entangled states without relying on the Schmidt decomposition, simplifying entanglement detection in complex quantum systems.

Contribution

It presents a new technique for detecting maximal entanglement directly from state coefficients, applicable even when Schmidt coefficients are difficult to compute.

Findings

Derived Bell basis for two qubits using the method

Identified a state that is never maximally entangled

Method works without explicit Schmidt decomposition

Abstract

The bipartite entanglement of a pure quantum state is known to be characterized by its Schmidt decomposition. In particular the state is maximally entangled when all the Schmidt coefficients are equal. We point out a convenient method which always yields a single analytical condition for the state to be maximally entangled, in terms of its expansion coefficients in any basis. The method works even when the Schmidt coefficients cannot be calculated analytically, and does not require their calculation. As an example this technique is used to derive the Bell basis for a system of two qubits. In a second example the technique shows a particular state to \textit{never} be maximally entangled, a general conclusion that cannot be reached using the Schmidt decomposition.