You are an expert at summarizing long articles. Proceed to summarize the following text: 
the development of experimental and theoretical methods of quantum information processing ( qip ) is an important direction of quantum informatics . nmr methods are the simplest ones among different experimental approaches @xcite . it is well known that the liquid state nmr methods @xcite are widely used for experimental realizations of quantum gates and algorithms on the basis of the pseudo - pure states @xcite . however , the possibilities of qip based on the liquid state nmr are limited because the number of correlated qubits is very small ( about 10 ) @xcite and quantum correlations in such systems are not strong . in particular , entanglement is almost absent @xcite .    at the same time , the potential of the solid state nmr methods @xcite is not exhausted yet . multiple quantum ( mq ) spectroscopy in solids @xcite is an example of such a method . mq nmr not only creates multi - qubit coherent states but also allows the investigation of their relaxation under the action of the correlated spin reservoir . mq nmr @xcite is an important method for the investigation of various problems of quantum information processing such as the transmission of quantum information @xcite and decoherence processes @xcite . one - dimensional mq nmr methods are very suitable for solving problems of quantum informatics . the reason is that a consistent quantum - mechanical theory of mq nmr dynamics has been developed only for one - dimensional systems @xcite . that theory is based on the fact that the non - secular two - spin / two - quantum hamiltonian @xcite , describing mq nmr dynamics , is the xy hamiltonian @xcite , which can be diagonalized exactly for one - dimensional systems in the approximation of the nearest neighbor interactions @xcite . as a result , mq nmr dynamics in such systems can be studied analytically . in particular , only mq nmr coherences of the zeroth and plus / minus second orders arise in a one - dimensional chain initially prepared in a thermodynamic equilibrium state @xcite . the developed theory @xcite is based on the model of an isolated spin chain with the nearest neighbor interactions . such a model is realized in quasi - one - dimensional chains of nuclei in calcium fluorapatite with a hexagonal system of fluorine nuclei . the distance between neighboring chains is about three times larger than the distance between the nearest fluorine nuclei in the same chain . taking into account that the dipole - dipole interaction ( ddi ) of the next nearest spins in the chain is eight times weaker than the nearest neighbor interaction @xcite one can use the model of an isolated spin chain with the nearest neighbor interactions for the interpretation of the experimental data obtained from the mq nmr experiments @xcite . the information resource of mq nmr exceeds the resource of conventional nmr @xcite . however , that resource can be used only if the xy hamiltonian is created with sufficient accuracy @xcite . the xy hamiltonian is obtained as the averaged two - spin / two - quantum hamiltonian @xcite which is the average hamiltonian @xcite in the mq nmr experiments . the corrections to the average hamiltonian @xcite spoil the xy hamiltonian . these corrections are proportional to powers of the parameter @xmath0 ( @xmath1 is the period of the irradiating sequence of the preparation period of the mq nmr experiment and @xmath2 is of the order of the ddi ) . we have designed a special probe @xcite for the generation of high - power ultra - short pulses and decreased the period @xmath1 and the parameter @xmath3 in mq nmr experiments . the results @xcite show high accuracy of creating the xy hamiltonian . it is very important that the xy hamiltonian ( the mq nmr hamiltonian ) is related to the flip - flop one by a simple unitary transformation @xcite for one - dimensional systems in the approximation of the nearest neighbor interactions . that fact allows us to realize the quantum state transfer along a one - dimensional spin chain . it is also significant that the relaxation of the mq nmr coherences can be considered as a model for studying the decoherence processes . the paper is organized as follows . an introduction to mq nmr dynamics is given in section  2 . in section 3 we show that mq nmr can be used for the quantum state transfer in one - dimensional spin chains . relaxation of the mq nmr coherences in one - dimensional spin chains is discussed in section 4 . we briefly summarize our results in section 5 . [ cols="^ " , ] we considered the methods of mq nmr spectroscopy of one - dimensional spin systems and their application for solving problems of quantum informatics . the quantum state transfer in linear spin chains can be realized with high fidelity using mq nmr dynamics . decoherence of many - qubit quantum state created on the preparation period of the mq nmr experiment @xcite can be studied on the evolution period of that experiment . the dipolar relaxation of the mq nmr coherences is considered as a model of the decoherence process . the theory of the dipolar relaxation of the mq nmr coherences is developed . the performed mq nmr experiments on the quasi - one - dimensional system of nuclei in calcium fluorapatite are in a good agreement with the theoretical predictions . braunstein , s.  l. , caves , c.  m. , jozsa , r. , linden , n. , popescu , s. , and schack , r. , `` separability of very noisy mixed states and implications for nmr quantum computing , '' _ phys . lett _  * 83 * , 1054 ( 1999 ) . doronin , s.  i. , vasilev , s.  g. , samoilenko , a.  a. , feldman , e.  b. , and shumm , b.  a. , `` dynamics and relaxation of multiple quantum nmr coherences in a quasi - one - dimensional chain of nuclear spins @xmath4f in calcium fluorapatite , '' _ jetp letters _ * 101 * , 613 ( 2015 ) . bochkin , g.  a. , feldman , e.  b. , and vasilev , s.  g. , `` relaxation of multiple quantum nmr coherences in quasi - one - dimensional spin systems , '' _ zeitschrift fr physikalische chemie international journal of research in physical chemistry chemical physics _ * 230 * ( 2016 ) .
multiple quantum ( mq ) nmr methods @xcite are applied to the analysis of various problems of quantum information processing . 
 it is shown that the two - spin / two - quantum hamiltonian @xcite describing mq nmr dynamics is related to the flip - flop hamiltonian of a one - dimensional spin system in the approximation of the nearest neighbor interactions . as a result , it is possible to organize quantum state transfer along a linear chain . 
 mq nmr experiments are performed on quasi - one - dimensional chains of nuclei in calcium fluorapatite . 
 relaxation of the mq nmr coherences is considered as the simplest model of decoherence processes . 
 a theory of the dipolar relaxation of the mq nmr coherences in one - dimensional systems is developed . 
 a good agreement of the theoretical predictions and the experimental data is obtained .