Normalization procedure for relaxation studies in NMR quantum information processing

Abstract

NMR quantum information processing studies rely on the reconstruction of the density matrix representing the so-called pseudo-pure states (PPS). An initially pure part of a PPS state undergoes unitary and non-unitary (relaxation) transformations during a computation process, causing a "loss of purity" until the equilibrium is reached. Besides, upon relaxation, the nuclear polarization varies in time, a fact which must be taken into account when comparing density matrices at different instants. Attempting to use time-fixed normalization procedures when relaxation is present, leads to various anomalies on matrices populations. On this paper we propose a method which takes into account the time-dependence of the normalization factor. From a generic form for the deviation density matrix an expression for the relaxing initial pure state is deduced. The method is exemplified with an experiment of relaxation of the concurrence of a pseudo-entangled state, which exhibits the phenomenon of sudden death, and the relaxation of the Wigner function of a pseudo-cat state.

Quantum process tomography with informational incomplete data of twoJ-coupled heterogeneous spins relaxation in a time window much greater thanT1

“…We will be able to quantify, along the time, how much the relaxation process departs from being unital and trace preserving, and we will also characterize how the relaxation process affects the normalization of expectation values. This way we will learn in which time window it is safe to assume the relaxation process is approximated unital or trace preserving, complementing other previous studies [6][7][8]. Thus we hope to shed some light in how one could compensate for the two drawbacks aforementioned, and consequently increase the time window for quantum simulations in liquid state NMR.…”

“…Besides that, we want to follow the quantum process for very long times, much more than the spin-lattice relaxation time T 1 , what raises the problem of how to compare measurements taken in different times, which is what we call the normalization problem. A pedagogical discussion of why the state simulated by a pseudo-pure state evolves nonlienarly under the relaxation process, and an ad hoc phenomenological method to circumvent the normalization problem were presented by Gavini-Viana et al [8]. The basic idea is that a pseudo-pure state, according to Cory et al [5], has the form…”

Experimental protection against evolution of states in a subspace via a super-Zeno scheme on an NMR quantum information processor

“…(6). Renormalization is performed since our focus here is on the quantum state of the spins contributing to the signal and not in the number per se of participating spins [31]. The plots in Fig.…”

Quantum information processing by nuclear magnetic resonance on quadrupolar nuclei

“…As a way to overcome these limitations, we proposed a QST method using only short non-selective RF pulses with a coherence selection scheme [10]. As a result, many studies involving quadrupolar nuclei could benefit from that method, including research on quadrupolar spin decoherence and relaxation [11][12][13][14] and quantum simulation [15]. Section 2 briefly expounds the main concepts regarding PPS and logic gate implementation and QST in high-field NMR of quadrupolar nuclei.…”