Relaxation of pseudo pure states: the role of cross-correlations

Abstract

In Quantum Information Processing by NMR one of the major challenges is relaxation or decoherence. Often it is found that the equilibrium mixed state of a spin system is not suitable as an initial state for computation and a definite initial state is required to be prepared prior to the computation. As these preferred initial states are non-equilibrium states, they are not stationary and are destroyed with time as the spin system relaxes toward its equilibrium, introducing error in computation. Since it is not possible to cut off the relaxation processes completely, attempts are going on to develop alternate strategies like Quantum Error Correction Codes or Noiseless Subsystems. Here we study the relaxation behavior of various Pseudo Pure States and analyze the role of Cross terms between different relaxation processes, known as Cross-correlation. It is found that while cross-correlations accelerate the relaxation of certain pseudo pure states, they retard that of others.

Using a Lindbladian approach to model decoherence in two coupled nuclear spins via correlated phase-damping and amplitude damping noise channels

“…While standard schemes for pseudopure state preparation involve a large number of experiments and lead to reduced signal, recently a few schemes have been proposed that use only one ancilla spin and fewer number of experiments [52,53]. The relaxation behavior of twospin pseudopure states have been investigated and it was noted that cross-correlated spin relaxation plays an important role in accelerating or retarding the lifetimes of such states [54]. The relaxation of pseudopure states in an oriented spin-3/2 system has been described using Redfield theory and reduced spectral densities [55].…”

Quantum information processing through nuclear magnetic resonance

“…Therefore, it is important to investigate relaxation in the context of NMR quantum computing. References [26] and [27] reports a spinlattice relaxation study of various NMR quantum computing coherent states.…”

Normalization procedure for relaxation studies in NMR quantum information processing

“…Besides, NMR coherences vanish in a time T 2 , the transverse relaxation time. Regarding relaxation studies of pseudo-pure states in the context of NMR quantum information processing, one can point out the studies reported on references [11,12,13,18]. In those studies, relaxation behavior of various pseudopure states have been investigated in different NMR systems.…”

“…In Ref. [12] it was found that whereas cross-correlations accelerate the relaxation of certain pseudo-pure states, they delay that of others. On the other hand, a robust method for quantum process tomography provided a set of Lindblad operators that optimally fit the density matrices measured at a sequence of time points [13].…”