Protecting unknown two-qubit entangled states by nesting Uhrig's dynamical decoupling sequences

TL;DR

This paper explores how nested Uhrig's dynamical decoupling sequences can effectively protect unknown two-qubit entangled states from decoherence, with the effectiveness highly dependent on the sequence ordering and extending protection to fully unknown states.

Contribution

It introduces a nested UDD approach for protecting unknown two-qubit states without assumptions on system-environment coupling, and analyzes the importance of sequence ordering for decoherence suppression.

Findings

Decoherence suppression is highly sensitive to UDD layer ordering.

Properly ordered nested UDD sequences can effectively protect unknown entangled states.

Four-layer nested UDD can protect completely unknown two-qubit states.

Abstract

Future quantum technologies rely heavily on good protection of quantum entanglement against environment-induced decoherence. A recent study showed that an extension of Uhrig's dynamical decoupling (UDD) sequence can (in theory) lock an arbitrary but known two-qubit entangled state to the $N$th order using a sequence of $N$ control pulses [Mukhtar et al., Phys. Rev. A 81, 012331 (2010)]. By nesting three layers of explicitly constructed UDD sequences, here we first consider the protection of unknown two-qubit states as superposition of two known basis states, without making assumptions of the system-environment coupling. It is found that the obtained decoherence suppression can be highly sensitive to the ordering of the three UDD layers and can be remarkably effective with the correct ordering. The detailed theoretical results are useful for general understanding of the nature of controlled quantum dynamics under nested UDD. As an extension of our three-layer UDD, it is finally pointed out that a completely unknown two-qubit state can be protected by nesting four layers of UDD sequences. This work indicates that when UDD is applicable (e.g., when environment has a sharp frequency cut-off and when control pulses can be taken as instantaneous pulses), dynamical decoupling using nested UDD sequences is a powerful approach for entanglement protection.