Quantum and classical correlations in electron-nuclear spin echo
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Quantum and Classical Correlations in Electron–Nuclear Spin Echo V. E. Zobov Kirensky Institute of Physics, Siberian Branch, Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, 660036 Russia email: [email protected] Received June 5, 2014
Abstract—The quantum properties of dynamic correlations in a system of an electron spin surrounded by nuclear spins under the conditions of free induction decay and electron spin echo have been studied. Analyt ical results for the time evolution of mutual information, classical part of correlations, and quantum part characterized by quantum discord have been obtained within the centralspin model in the hightemperature approximation. The same formulas describe discord in both free induction decay and spin echo although the time and magnetic field dependences are different because of difference in the parameters entering into the formulas. Changes in discord in the presence of the nuclear polarization βI in addition to the electron polar ization βS have been calculated. It has been shown that the method of reduction of the density matrix to a twospin electron–nuclear system provides a qualitatively correct description of pair correlations playing the main role at βS ≈ βI and small times. At large times, such correlations decay and multispin correlations ensur ing nonzero mutual information and zero quantum discord become dominant. DOI: 10.1134/S1063776114110132
1. INTRODUCTION Spin echo discovered by Hahn [1] underlies many applications of magnetic resonance, on one hand, as a method for studying the local properties of solids and fluids [2, 3] and, on the other hand, as an imple mented example of the Loschmidt echo when study ing nonequilibrium processes in multispin systems [4, 5]. Interest in studying quantum information has been recently grown [6–9], primarily in view of its proper ties promising fundamentally new possibilities in the speed of a quantum computer for the development of communication and metrology. Because of technical difficulties, real devices implementing these possibili ties on multiparticle quantum systems have not yet been developed. However, the physical properties of quantum information can be studied on such systems by traditional methods, including the spin echo method. The system of an electron spin surrounded by nuclear spins is practically important and wellstudied by this method. In particular, references to the meth ods used, results obtained, and their analysis can be found in theoretical works [10–14]. Such a system seems to be also promising for the implementation of quantum information processing devices [15]. The system of the electron spin surrounded by nuclear spins is close in structure to quantum systems used to implement the deterministic quantum calcula tion model with one polarized qubit interacting with a system of qubits in a mixed state (DQC1) [16]. It is known that the computer of the DQC1 model can the oretically solve some problems reduced to the calcula tion of the trace of a matrix faster th
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