Forgetting in the Synchronization of Quantum Networks

TL;DR

This paper investigates how quantum networks lose initial information over time due to decoherence, especially when internal and external interactions are incompatible, providing conditions for near-complete decoherence in qubit networks.

Contribution

It establishes a general theorem identifying conditions under which quantum networks experience almost complete decoherence, highlighting the impact of non-commuting Hamiltonian and swapping operators.

Findings

Almost complete decoherence occurs under certain conditions.

Quantum dissipation networks tend to forget initial information.

The theorem clarifies the role of non-commuting interactions in decoherence.

Abstract

In this paper, we study the decoherence property of synchronization master equation for networks of qubits interconnected by swapping operators. The network Hamiltonian is assumed to be diagonal with different entries so that it might not be commutative with the swapping operators. We prove a theorem establishing a general condition under which almost complete decohernece is achieved, i.e., all but two of the off-diagonal entries of the network density operator asymptotically tend to zero. This result explicitly shows that quantum dissipation networks tend to forget the information initially encoded when the internal (induced by network Hamiltonian) and external (induced by swapping operators) qubit interactions do not comply with each other.