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. Analytical results for the time evolution of mutual information, classical part of correlations, and quantum part characterized by quantum discord have been obtained within the central-spin model in the high-temperature 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 β I in addition to the electron polarization β S have been calculated. It has been shown that the method of reduction of the density matrix to a two-spin electron-nuclear system provides a qualitatively correct description of pair correlations playing the main role at β S ≈ β I and small times. At large times, such correlations decay and multispin correlations ensuring nonzero mutual information and zero quantum discord become dominant.
The quantum properties of dynamic correlations in a system of an electron spin surrounded by nuclear spins under the conditions of free induction decay (FID) and spin echo have been studied. Analytical results for the time evolution of mutual information, classical part of correlations, and quantum part characterized by quantum discord have been obtained within the central spin model in the high-temperature approximation. The same formulas describe the quantum discord in both the FID and the spin echo although the forms of the dependences are different because of difference in the parameters entering into the formulas. Discord of the spin echo compared with the FID has a strong dependence on time at short times, and it tends to zero with decreasing of the magnetic field, whereas in the case of the FID it reaches a plateau.
In this paper, two conjectures which were proposed in [Phys. Rev. A \textbf{82}, 052122(2010)] on the correlations in a bipartite state
ρAB are studied. If the mutual information $I\Pa{\rho^{AB}}$ between two quantum systems
A and
B before any measurement is considered as the total amount of correlations in the state
ρAB, then it can be separated into two parts: classical correlations and quantum correlations. The so-called classical correlations $C\Pa{\rho^{AB}}$ in the state
ρAB, defined by the maximizing mutual information between two quantum systems
A and
B after von Neumann measurements on system
B, we show that it is upper bounded by the von Neumann entropies of both subsystems
A and
B, this answered the conjecture on the classical correlation. If the quantum correlations $Q\Pa{\rho^{AB}}$ in the state
ρAB is defined by $Q\Pa{\rho^{AB}}= I\Pa{\rho^{AB}} - C\Pa{\rho^{AB}}$, we show also that it is upper bounded by the von Neumann entropy of subsystem
B. It is also obtained that $Q\Pa{\rho^{AB}}$ is upper bounded by the von Neumann entropy of subsystem
A for a class of states.
In this paper, two conjectures which were proposed in Luo et al (2010 Phys. Rev. A 82 052122 ) on the correlations in a bipartite state ρ AB are studied. If the mutual information I (ρ AB ) between two quantum systems A and B before any measurement is considered as the total amount of correlations in the state ρ AB , then it can be separated into two parts: classical correlations and quantum correlations. The so-called classical correlations C (ρ AB ) in the state ρ AB are defined by the maximizing mutual information between two quantum systems A and B after von Neumann measurements on system B . We show that it is upper bounded by the von Neumann entropies of both subsystems A and B , which answered the conjecture on the classical correlation. If the quantum correlations Q (ρ AB ) in the state ρ AB are defined by Q (ρ AB ) = I (ρ AB ) − C (ρ AB ), we also show that it is upper bounded by the von Neumann entropy of subsystem B . It is also found that Q (ρ AB ) is upper bounded by the von Neumann entropy of subsystem A for a class of states.
We study non Markovian quantum systems for communication of quantum information. The quantum capacities of an exactly solvable spin-star system are analytically determined.Our results show that they strongly depend on the bath frequencies and system-bath coupling.The Ising spin-bath becomes noisy as the bath temperature is increased decreasing its capacity to transmit information.For random couplings and bath frequencies, recurrences of coherence are small in amplitude and rapidly die out. However, full periodic recurrences occur for equal coupling and frequencies. For small number of bath spins, the capacities are higher at low temperature.We also study two time-correlated non-unital channels for the transmission of classical and quantum information, provided limited or unlimited entanglement is shared prior to the communication.The noise over two successive uses of the channel is assumed to be time-correlated Markov noise.For amplitude-damping channel, the capacities exhibit strong dependence on channel memory.They decrease as the channel noise increases and reduce to zero when noise is maximum. However, our results show that the capacities are always non-zero, in the presence of channel memory.This is similar to the superactivation phenomenon. For perfect memory channel, the capacities acquire maximum value.Finally, we determine the entanglement-assisted classical capacity of generalized amplitude-damping channel. Our results show that depending on the channel noise and system-reservoir coupling, there exists a memory threshold.Below this threshold, the capacity decreases as channel memory increases.However, the capacity increases with memory beyond this threshold and is maximum for perfect memory channels.