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

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.

Quadratic dynamical decoupling with nonuniform error suppression

“…The number of pulses comprising a UDD sequence is N if N is even, or N + 1 if N is odd. Generalizations of UDD for generic system-environment interactions include Concatenated UDD (CUDD) [25], Quadratic Dynamical Decoupling (QDD) [26] and Nested Uhrig Dynamical Decoupling (NUDD) [27] (see also [28]). CUDD removes the restriction of single-axis decoupling and suppresses general (three-axis) decoherence errors on a qubit, but still suffers from the exponential cost of CDD.…”

Uhrig dynamical control of a three-level system via non-Markovian quantum state diffusion

“…The control operator P for a single three-level pure dephasing model may be determined by using these two criteria [20]: P 2 = I and {J z , P } = 0. Therefore, it is easy to check that the following two control operators satisfy the required conditions:…”

“…If quantum systems are coupled to small environments, it is straightforward to use the direct numerical simulations to solve the combined system and environment such that the UDD scheme can be efficiently implemented [20]. When the open system is coupled to a large environment consisting of finite or infinite numbers of degrees of freedom, one has to invoke an efficient quantum approach to deal with the open system dynamics allowing dealing with both non-Markovian and Markov environments.…”

“…[18] constructed two layers of nesting UDD that can protect a single qubit against both dephasing and relaxation. In addition, the multi-layer nesting UDD and continuous DD schemes are designed to not only preserve quantum coherence and the entanglement of two-qubit systems [19][20][21][22][23], but also to protect multi-qubit systems [24] and quantum gates [25]. Studies on higher-order effects have also been done for non-ideal pulses [26,27], as well as optimized pulses under different environment noises [28][29][30].…”

Overview of quantum memory protection and adiabaticity induction by fast signal control

“…The latter investigates the ability of using an external field to store, transfer, and manipulate information in correlated systems. Since it is important to protect quantum information from degradation, quantum storage protocols are naturally and closely related to the decoherence suppression [6,7,8,9,10,11,12,13,14,15,16,17,18] and the enhancement of adiabaticity of quantum states [19,20,21]. Despite its long history, quantum decoherence and adiabaticity still challenge our comprehension, and continue to provoke our curiosity, as they are involved with various processes in quantum mechanics.…”