Qubit channels with small correlations

TL;DR

This paper studies a class of correlated quantum channels acting on qubits, optimizing output purity, and finds a phase transition in the optimal input states from partially entangled to maximally entangled as correlation increases.

Contribution

It introduces a new class of correlated qubit channels and analyzes their optimal input states for output purity, revealing a threshold-driven transition in entanglement.

Findings

Optimal input states transition from partially entangled to maximally entangled at a certain correlation threshold.

The behavior of the optimal states is consistent across different p-norms for measuring output purity.

Numerical and heuristic evidence suggests the results are robust beyond the 2-norm analysis.

Abstract

We introduce a class of quantum channels with correlations acting on pairs of qubits, where the correlation takes the form of a shift operator onto a maximally entangled state. We optimise the output purity and show that below a certain threshold the optimum is achieved by partially entangled states whose degree of entanglement increases monotonically with the correlation parameter. Above this threshold, the optimum is achieved by the maximally entangled state characterizing the shift. Although, a full analysis can only be done for the 2-norm, both numerical and heuristic arguments indicate that this behavior and the optimal inputs are independent of p>1 when the optimal output purity is measured using the p-norm.