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.

9 pages, 5 figures, to appear in QIP

References in corpus (8)

• NMR Techniques for Quantum Control and Computation
• Sudden Death of Entanglement
• Heralded Entanglement between Atomic Ensembles: Preparation, Decoherence, and Scaling
• Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment
• Reading entanglement in terms of spin configurations in quantum magnets
• Study of localization in the quantum sawtooth map emulated on a quantum information processor
• Phase space contraction and quantum operations
• Relaxation of Pseudo pure states : The Role of Cross-Correlations

Cited by in corpus (4)

• Experimental construction of a W-superposition state and its equivalence to the GHZ state under local filtration
• Experimental protection against evolution of states in a subspace via a super-Zeno scheme on an NMR quantum information processor
• Quantum process tomography with informational incomplete data of two $J$-coupled heterogeneous spins relaxation in a time window much greater than $T_1$
• True experimental reconstruction of quantum states and processes via convex optimization