Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1503.03316 · Journal of Experimental and Theoretical Physics

NMR dynamics of quantum discord for spin-carrying gas molecules in a closed nanopore

M. A. Yurishchev

Published Nov 1, 2014• 14 citations
arXivHTMLPDF

Abstract

A local orthogonal transformation that transforms any centrosymmetric density matrix of a two-qubit system to the X form has been found. A piecewise-analytic-numerical formula Q = min{Q π/2, Q θ, Q 0}, where Q π/2 and Q 0 are analytical expressions and the branch Q 0 θ 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 quantum-information 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

Related papers

Quantum correlations in a system of nuclears= 1/2 spins in a strong magnetic field

Edward B. Fel’dman, E. I. Kuznetsova, M. A. Yurishchev

Entanglement and quantum discord for a pair of nuclear spins s = 1/2 in a nanopore filled with a gas of spin-carrying molecules (atoms) are studied. The correlation functions describing dynamics of dipolar-coupled spins in a nanopore are found. The dependence of spin-pair entanglement on the temperature and the number of spins is obtained from the reduced density matrix, which is centrosymmetric (CS). An analytic expression for the concurrence is obtained for an arbitrary CS density matrix. It is shown that the quantum discord as a measure of quantum correlations attains a significant value at low temperatures. It is also shown that the discord in the considered model has 'flickering' character and disappears periodically in the course of time evolution of the system. The geometric discord is studied for arbitrary 4 × 4 CS density matrices.

arXiv:1209.4166•Journal of Physics A Mathematical and Theoretical•Nov 8, 2012•25 citations

Quantum discord for general X and CS states: A piecewise-analytic-numerical formula

Mikhail A. Yurischev

Quantum discord is a function of density-matrix elements (and through them, e.~g., of temperature, applied fields, time, and so forth). The domain of such a function in the case of two-qubit system with X or centrosymmetric (CS) density matrix can consist at most of three subdomains: two ones, where the quantum discord is expressed in closed analytical forms (Q_0 and Q_{π/2}), and an intermediate subdomain in which for determining the quantum discord Q_θit is required to solve numerically a one-dimensional minimization problem to find the optimal measurement angle θ\in(0,π/2). Exact equations for determining the boundaries between these subdomains are obtained and solved for a number of models. The Q_θsubdomains are discovered in the anisotropic spin dimers in external field. On the other hand, coinciding boundaries and therefore sudden transitions between optimal measurement angles θ=π/2 and θ=0 are observed in dynamics of spin currying particles in closed nanopore and also in phase flip channels. In latter cases the solutions are entirely analytical.

arXiv:1404.5735•Apr 23, 2014•4 citations

Quantum discord for two-qubit CS states: Analytical solution

M. A. Yurishchev

We found an universal local unitary (orthogonal) transformation which transforms any centrosymmetric (CS) density matrix ρ_{CS} into the X density matrix ρ_X: H\otimes Hρ_{CS}H\otimes H=ρ_X, where H is the Hadamard transformation. Because quantum discord is invariant under the local unitary transformations, this remarkable property allows to get the discord of general two-qubit CS states in the analytical form using the corresponding well-known formulas for the X states. Examples of systems with CS density matrices provided from the recent literature, including XXZ spin model with the Dzyaloshinsky-Moriya interaction, a gas of spin-carrying particles in closed nanopore, and a family of pseudopure states.

arXiv:1302.5239•Feb 21, 2013•3 citations

Evolution of quantum discord and its stability in two-qubit NMR systems

Hemant Katiyar, Soumya S. Roy, T. S. Mahesh +1 more

We investigate evolution of quantum correlations in ensembles of two-qubit nuclear spin systems via nuclear magnetic resonance techniques. We use discord as a measure of quantum correlations and the Werner state as an explicit example. We, first, introduce different ways of measuring discord and geometric discord in two-qubit systems and then describe the following experimental studies: (a) We quantitatively measure discord for Werner-like states prepared using an entangling pulse sequence. An initial thermal state with zero discord is gradually and periodically transformed into a mixed state with maximum discord. The experimental and simulated behavior of rise and fall of discord agree fairly well. (b) We examine the efficiency of dynamical decoupling sequences in preserving quantum correlations. In our experimental setup, the dynamical decoupling sequences preserved the traceless parts of the density matrices at high fidelity. But they could not maintain the purity of the quantum states and so were unable to keep the discord from decaying. (c) We observe the evolution of discord for a singlet-triplet mixed state during a radio-frequency spin-lock. A simple relaxation model describes the evolution of discord, and the accompanying evolution of fidelity of the long-lived singlet state, reasonably well.

arXiv:1203.1756•Physical Review A•Jul 11, 2012•28 citations

Quantum discord for qubit–qudit systems

Sai Vinjanampathy, A. R. P. Rau

Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. It has been discussed so far for small systems with only a few independent parameters. We extend here to a much broader class of states when the second party is of arbitrary dimension d, so long as the first, measured, party is a qubit. We present two formulae to calculate quantum discord, the first relating to the original entropic definition and the second to a recently proposed geometric distance measure which leads to an analytical formulation. The tracing over the qubit in the entropic calculation is reduced to a very simple prescription. And, when the d-dimensional system is a so-called X state, the density matrix having non-zero elements only along the diagonal and anti-diagonal so as to appear visually like the letter X, the entropic calculation can be carried out analytically. Such states of the full bipartite qubit-qudit system may be named "extended X states", whose density matrix is built of four block matrices, each visually appearing as an X. The optimization involved in the entropic calculation is generally over two parameters, reducing to one for many cases, and avoided altogether for an overwhelmingly large set of density matrices as our numerical investigations demonstrate. Our results also apply to states of a N-qubit system, where "extended X states" consist of (2^(N+2) - 1) states, larger in number than the (2^(N+1) - 1) of X states of N qubits. While these are still smaller than the total number (2^(2N) - 1) of states of N qubits, the number of parameters involved is nevertheless large. In the case of N = 2, they encompass the entire 15-dimensional parameter space, that is, the extended X states for N = 2 represent the full qubit-qubit system.

arXiv:1106.4488•Journal of Physics A Mathematical and Theoretical•Feb 20, 2012•112 citations

Multiple quantum NMR dynamics of spin-12 carrying molecules of a gas in nanopores

S. I. Doronin, A. V. Fedorova, Edward B. Fel’dman +1 more

We consider the multiple quantum (MQ) NMR dynamics of a gas of spin carrying molecules in nanocavities. MQ NMR dynamics is determined by the residual dipole-dipole interactions, which are not averaged completely due to the molecular diffusion in nanopores. Since the averaged nonsecular Hamiltonian describing MQ NMR dynamics depends on only one coupling constant, this Hamiltonian commutes with the square of the total spin angular momentum Î2. We use the basis of common eigenstates of Î2 and the projection of I on the external magnetic field for investigation of MQ NMR dynamics. This approach allows us to study MQ NMR dynamics in systems consisting of several hundreds of spins. The analytical approximation of the stationary profile of MQ coherences is obtained. The analytical expressions for MQ NMR coherence intensities of the five-spin system in a nanopore are found. Numerical investigations allow us to find the dependencies of intensities of MQ coherences on their orders (the profiles of MQ coherences) in systems consisting of 600 spins and even more. It is shown that the stationary MQ coherence profile in the considered system is an exponential one.

arXiv:0906.1413•The Journal of Chemical Physics•Sep 14, 2009•35 citations
A local orthogonal transformation that transforms any centrosymmetric density matrix of a two-qubit system to the X form has been found. A piecewise-analytic-numerical formula Q = min{Q π/2, Q θ, Q 0}, where Q π/2 and Q 0 are analytical expressions and the branch Q 0 θ 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 quantum-information 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.
Entanglement and quantum discord for a pair of nuclear spins s = 1/2 in a nanopore filled with a gas of spin-carrying molecules (atoms) are studied. The correlation functions describing dynamics of dipolar-coupled spins in a nanopore are found. The dependence of spin-pair entanglement on the temperature and the number of spins is obtained from the reduced density matrix, which is centrosymmetric (CS). An analytic expression for the concurrence is obtained for an arbitrary CS density matrix. It is shown that the quantum discord as a measure of quantum correlations attains a significant value at low temperatures. It is also shown that the discord in the considered model has 'flickering' character and disappears periodically in the course of time evolution of the system. The geometric discord is studied for arbitrary 4 × 4 CS density matrices.
Quantum discord is a function of density-matrix elements (and through them, e.~g., of temperature, applied fields, time, and so forth). The domain of such a function in the case of two-qubit system with X or centrosymmetric (CS) density matrix can consist at most of three subdomains: two ones, where the quantum discord is expressed in closed analytical forms (Q_0 and Q_{π/2}), and an intermediate subdomain in which for determining the quantum discord Q_θit is required to solve numerically a one-dimensional minimization problem to find the optimal measurement angle θ\in(0,π/2). Exact equations for determining the boundaries between these subdomains are obtained and solved for a number of models. The Q_θsubdomains are discovered in the anisotropic spin dimers in external field. On the other hand, coinciding boundaries and therefore sudden transitions between optimal measurement angles θ=π/2 and θ=0 are observed in dynamics of spin currying particles in closed nanopore and also in phase flip channels. In latter cases the solutions are entirely analytical.
We found an universal local unitary (orthogonal) transformation which transforms any centrosymmetric (CS) density matrix ρ_{CS} into the X density matrix ρ_X: H\otimes Hρ_{CS}H\otimes H=ρ_X, where H is the Hadamard transformation. Because quantum discord is invariant under the local unitary transformations, this remarkable property allows to get the discord of general two-qubit CS states in the analytical form using the corresponding well-known formulas for the X states. Examples of systems with CS density matrices provided from the recent literature, including XXZ spin model with the Dzyaloshinsky-Moriya interaction, a gas of spin-carrying particles in closed nanopore, and a family of pseudopure states.
We investigate evolution of quantum correlations in ensembles of two-qubit nuclear spin systems via nuclear magnetic resonance techniques. We use discord as a measure of quantum correlations and the Werner state as an explicit example. We, first, introduce different ways of measuring discord and geometric discord in two-qubit systems and then describe the following experimental studies: (a) We quantitatively measure discord for Werner-like states prepared using an entangling pulse sequence. An initial thermal state with zero discord is gradually and periodically transformed into a mixed state with maximum discord. The experimental and simulated behavior of rise and fall of discord agree fairly well. (b) We examine the efficiency of dynamical decoupling sequences in preserving quantum correlations. In our experimental setup, the dynamical decoupling sequences preserved the traceless parts of the density matrices at high fidelity. But they could not maintain the purity of the quantum states and so were unable to keep the discord from decaying. (c) We observe the evolution of discord for a singlet-triplet mixed state during a radio-frequency spin-lock. A simple relaxation model describes the evolution of discord, and the accompanying evolution of fidelity of the long-lived singlet state, reasonably well.
Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. It has been discussed so far for small systems with only a few independent parameters. We extend here to a much broader class of states when the second party is of arbitrary dimension d, so long as the first, measured, party is a qubit. We present two formulae to calculate quantum discord, the first relating to the original entropic definition and the second to a recently proposed geometric distance measure which leads to an analytical formulation. The tracing over the qubit in the entropic calculation is reduced to a very simple prescription. And, when the d-dimensional system is a so-called X state, the density matrix having non-zero elements only along the diagonal and anti-diagonal so as to appear visually like the letter X, the entropic calculation can be carried out analytically. Such states of the full bipartite qubit-qudit system may be named "extended X states", whose density matrix is built of four block matrices, each visually appearing as an X. The optimization involved in the entropic calculation is generally over two parameters, reducing to one for many cases, and avoided altogether for an overwhelmingly large set of density matrices as our numerical investigations demonstrate. Our results also apply to states of a N-qubit system, where "extended X states" consist of (2^(N+2) - 1) states, larger in number than the (2^(N+1) - 1) of X states of N qubits. While these are still smaller than the total number (2^(2N) - 1) of states of N qubits, the number of parameters involved is nevertheless large. In the case of N = 2, they encompass the entire 15-dimensional parameter space, that is, the extended X states for N = 2 represent the full qubit-qubit system.
We consider the multiple quantum (MQ) NMR dynamics of a gas of spin carrying molecules in nanocavities. MQ NMR dynamics is determined by the residual dipole-dipole interactions, which are not averaged completely due to the molecular diffusion in nanopores. Since the averaged nonsecular Hamiltonian describing MQ NMR dynamics depends on only one coupling constant, this Hamiltonian commutes with the square of the total spin angular momentum Î2. We use the basis of common eigenstates of Î2 and the projection of I on the external magnetic field for investigation of MQ NMR dynamics. This approach allows us to study MQ NMR dynamics in systems consisting of several hundreds of spins. The analytical approximation of the stationary profile of MQ coherences is obtained. The analytical expressions for MQ NMR coherence intensities of the five-spin system in a nanopore are found. Numerical investigations allow us to find the dependencies of intensities of MQ coherences on their orders (the profiles of MQ coherences) in systems consisting of 600 spins and even more. It is shown that the stationary MQ coherence profile in the considered system is an exponential one.