The necessary and sufficient conditions when global and local fidelities are equal

TL;DR

This paper establishes the precise conditions under which the quantum fidelity between a bipartite system and its subsystem are equal, providing explicit state representations for pure states.

Contribution

It derives necessary and sufficient conditions for fidelity equality in bipartite pure states, advancing understanding of quantum state similarity measures.

Findings

Identifies conditions for fidelity equality in bipartite pure states

Provides explicit state representations satisfying fidelity equality

Enhances understanding of quantum state similarity measures

Abstract

In the field of quantum information theory, the concept of quantum fidelity is employed to quantify the similarity between two quantum states. It has been observed that the fidelity between two states describing a bipartite quantum system $A \otimes B$ is always less than or equal to the quantum fidelity between the states in subsystem $A$ alone. While this fidelity inequality is well understood, determining the conditions under which the inequality becomes an equality remains an open question. In this paper, we present the necessary and sufficient conditions for the equality of fidelities between a bipartite system $A \otimes B$ and subsystem $A$, considering pure quantum states. Moreover, we provide explicit representations of quantum states that satisfy the fidelity equality, based on our derived results.