New Phase Transitions in Optimal States for Memory Channels

TL;DR

This paper explores phase transitions in optimal input states for memory channels, revealing a complex phase diagram with transitions from separable to entangled states influenced by noise correlations.

Contribution

It introduces a class of correlated Pauli channels and analytically characterizes their phase diagram, including a novel intermediate phase with mixed optimal states.

Findings

Identifies three distinct phases in the two-qubit channel model.

Shows correlation strength influences the transition from separable to entangled states.

Provides a concrete model simulating the channel behavior with random rotations.

Abstract

We investigate the question of optimal input ensembles for memory channels and construct a rather large class of Pauli channels with correlated noise which can be studied analytically with regard to the entanglement of their optimal input ensembles. In a more detailed study of a subclass of these channels, the complete phase diagram of the two-qubit channel, which shows three distinct phases is obtained. While increasing the correlation generally changes the optimal state from separable to maximally entangled states, this is done via an intermediate region where both separable and maximally entangled states are optimal. A more concrete model, based on random rotations of the error operators which mimic the behavior of this subclass of channels is also presented.