arXiv subjects

G. A. Bochkin

Publications and source records attributed to G. A. Bochkin.

10 recordsLinked to original sources

arXiv2026

Influence of environment on quantum correlations in two-spin systems with dipole-dipole interactions

An influence of environment on quantum correlations (entanglement and quantum discord) is studied in a two-spin-1/2 system with dipole-dipole interactions on the basis of Lindblad equation. We consider the simplest case when the environment causes only dephasing of system spins. The dependencies of entanglement and the quantum discord on the relaxation rate are obtained. We compare the influence of the environment on entanglement and quantum discord.

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arXiv2022

Transfer of 0-order coherence matrix along spin-1/2 chain

In this work, we study transfer of coherence matrices along spin-1/2 chains of various length. Unlike higher order coherence matrices, 0-order coherence matrix can be perfectly transferred if its elements are properly fixed. In certain cases, to provide the perfect transfer, an extended receiver together with optimized its unitary transformation has to be included into the protocol. In this work, the asymptotic perfectly transferable 0-order coherence matrix for an infinitely long chain is considered and deviation of a perfectly transferred state from this asymptotic state is studied as a function of the chain length for various sizes of the extended receiver. The problem of arbitrary parameter transfer via the nondiagonal elements of the 0-order coherence matrix is also considered and optimized using the unitary transformation of the extended receiver.

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arXiv2020

Calculation of $π$ on the IBM quantum computer and the accuracy of one-qubit operations

A quantum algorithm for the calculation of $π$ is proposed and implemented on the five-qubit IBM quantum computer with superconducting qubits. We find $π=3.157\pm0.017$. The error is due to the noise of quantum one-qubit operations and measurements. The results can be used for estimating the errors of the quantum computer and suggest that the errors are purely random.

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arXiv2019

The exact solution for the free induction decay in a quasi-one-dimensional system in a multi-pulse NMR experiment

The exact solution for the free induction decay in a one-dimensional system in the multi-pulse experiment is obtained at both high and low temperatures in the approximation of nearest neighbor interactions. The experimental investigation is performed on a quasi-one-dimensional system of $^{19}$F nuclear spins in a single crystal of fluorapatite. The theoretical results are in a good agreement with the obtained experimental data.

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arXiv2019

Entanglement in block-scalable and block-scaled states

There is a special class of so-called block-scalable initial states of the sender whose transfer to the receiver through the spin chain results in multiplying {their} MQ-coherence matrices by scalar factors (block-scaled receiver's states). We study the entanglement in block-scalable and block-scaled states and show that, generically, the entanglement in block scaled states is less than the entanglement in the corresponding block-scalable states, although the balance between these entanglements depends on particular values of parameters characterizing these states. Using the perturbations of the sender's block-scalable initial states we show that generically the entanglement in the block-scalable states is bigger, while the entanglement in the block-scaled states is less than the entanglements in the appropriate states from their neighborhoods. A short chain of 6 and a long chain of 42 spin-1/2 particles are considered as examples.}

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arXiv2018

Transfer of scaled multiple quantum coherence matrices

Multiple quantum (MQ) NMR coherence spectra, which can be obtained experimentally in MQ NMR, can be transferred from the sender to the remote receiver without mixing the MQ-coherences of different orders and distortions. The only effect of such transfer is scaling of the certain blocks of sender's density matrix (matrices of MQ-coherences of different order). Such a block-scaled transfer is an alternative to the perfect state transfer. In particular, equal scaling of higher order MQ-coherences matrices is possible. Moreover, there are states which can be transferred to the receiver preserving their zero-order coherence matrix. The examples of block-scaled transfer in spin-1/2 communication lines of 6 and 42 nodes with two-qubit sender and receiver are presented.

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arXiv2017

Experimental and theoretical investigations of quantum state transfer and decoherence processes in quasi-one-dimensional systems in multiple-quantum NMR experiments

Multiple quantum (MQ) NMR methods \cite{Baum} are applied to the analysis of various problems of quantum information processing. It is shown that the two-spin/two-quantum Hamiltonian \cite{Baum} 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 \BPChem{\^{19}F} nuclei in calcium fluorapatite \BPChem{Ca\_5(PO\_4)\_3F}. 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.

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arXiv2016

Optimization of remote one- and two-qubit state creation via multi-qubit unitary transformations at sender and receiver sides

We study the optimization problem for remote one- and two-qubit state creation via a homogeneous spin-1/2 communication line using the local unitary transformations of the multi-qubit sender and extended receiver. We show that the maximal length of a communication line used for the needed state creation (the critical length) increases with an increase in the dimensionality of the sender and extended receiver. The model with the sender and extended receiver consisting of up to 10 nodes is used for the one-qubit state creation and we consider two particular states: the almost pure state and the maximally mixed one. Regarding the two-qubit state creation, we numerically study the dependence of the critical length on a particular triad of independent eigenvalues to be created, the model with four-qubit sender without an extended receiver is used for this purpose.

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arXiv2015

Extension of the remotely creatable region via the local unitary transformation on the receiver side

We consider the remote state creation via the homogeneous spin-1/2 chain and show that the significant extension of the creatable region can be achieved using the local unitary transformation of the so-called extended receiver (i.e. receiver joined with the nearest node(s)). This transformation is { most} effective in the models with all-node interactions. We consider the model with the two-qubit sender, one-qubit receiver and two-qubit extended receiver.

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arXiv2015

Remote one-qubit state control by pure initial state of two-qubit sender. Selective-region- and eigenvalue-creation

We study the problem of remote one-qubit mixed state creation using a pure initial state of two-qubit sender and spin-1/2 chain as a connecting line. We express the parameters of creatable states in terms of transition amplitudes. We show that the creation of complete receiver's state-space can be achieved only in the chain engineered for the one-qubit perfect state transfer (PST) (for instance, in the fully engineered Ekert chain), the chain can be arbitrarily long in this case. As for the homogeneous chain, the creatable receiver's state region decreases quickly with the chain length. Both homogeneous chains and chains engineered for PST can be used for the purpose of selective state creation, when only the restricted part of the whole receiver's state space is of interest. Among the parameters of the receiver's state, the eigenvalue is the most hard creatable one and therefore deserves the special study. Regarding the homogeneous spin chain, an arbitrary eigenvalue can be created only if the chain is of no more then 34 nodes. Alternating chain allows us to increase this length up to 68 nodes.

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