NMR dynamics of quantum discord for spin-carrying gas molecules in a closed nanopore
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NMR Dynamics of Quantum Discord for SpinCarrying Gas Molecules in a Closed Nanopore M. A. Yurishchev Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432 Russia email: [email protected] Received June 23, 2014
Abstract—A local orthogonal transformation that transforms any centrosymmetric density matrix of a two qubit system to the X form has been found. A piecewiseanalytic–numerical formula Q = min{Qπ/2, Qθ, Q0}, where Qπ/2 and Q0 are analytical expressions and the branch Qθ can be obtained only by numerically searching for the optimal measurement angle θ ∈ (0, π/2), is proposed to calculate the quantum discord Q of a general X state. The developed approaches have been applied for a quantitative description of the recently predicted flickering (periodic disappearance and reappearance) of the quantuminformation pair correlation between nuclear 1/2 spins of atoms or molecules of a gas (for example, 129Xe) in a bounded volume in the presence of a strong magnetic field. DOI: 10.1134/S106377611411020X
1. INTRODUCTION The notion of quantum discord introduced to describe all purely quantum correlations in a system currently occupies a central place in discussing the questions of radically increasing the performance of computers, creating secure data transmission net works, implementing the teleportation of states, detecting quantum phase transitions in condensed matter, etc. The progress achieved in the theory and applications of quantum discord is reflected in the recent reviews [1–3]. The actual calculation of quantum discord and, hence, the investigation of the behavior of quantum correlations in various physical systems is severely lim ited by the necessity of performing the optimization procedure entering into the definition of this quantity: the problem belongs to the complete NP class of com plexity [4]. Even for twoqubit models, where the den sity matrix has sizes of only 4 × 4, the achievements by analytical methods are exhausted by the special cases of X density matrices, the Belldiagonal states (include three independent parameters) [5]. (The term “X state” was introduced in 2007 and means a fourth order density matrix in which only the diagonal and antidiagonal entries can be nonzero [6, 7]; an arbitrary X density matrix contains seven real parameters.) Attempts were also made to find analytical formulas for calculating the quantum discord of more general families of X density matrices [8–11]. However, in [12–14] the cases where the analytical formulas [8– 11] are incorrect were demonstrated with specific examples, and it was concluded that “for general two qubit X states quantum discord cannot be evaluated analytically” [14]. In this paper, we will show that the
general formula for calculating the quantum discord of X density matrices is actually piecewiseanalytic– numerical, i.e., the discord is expressed analytically in some regions of the domain of definition and only numerically in other regions. Let us now turn to the p
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