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Journal of Physics A Mathematical and Theoretical

Dynamics of super quantum discord and optimal dense coding in quantum channels

Фороузан Мирмасоуди, Sodeif Ahadpour

Published Jun 18, 2018• 24 citations
Publisher

Abstract

Abstract Quantum discord (QD), super quantum discord (SQD) and optimal dense coding at entangled states of three types of quantum channels, are investigated. The used models include: two-qubit spin squeezing, the two-qubit Heisenberg XYZ model with decoherency and the Jaynes–Cummings model. In the first two models the quantum correlations and the optimal dense coding capacity are calculated in terms of channel parameters, system initial conditions and decoherency rate. It has been found that valid dense coding can exist, although there is no trace of entanglement in the quantum channel. In contrast, despite the presence of entanglement states in the system, there may be no dense coding capacity. We investigate the effects of cavity Fock states on quantum correlations and optimal dense coding in the Jaynes–Cummings model. Cavity Fock states are found to be effective for quantum correlations and optimal dense coding. The common result of all three models is that the dynamic properties of SQD on our channel enable us to determine when and under what conditions the system is suitable for dense coding capacity.

DOI
10.1088/1751-8121/aacd29

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Abstract Quantum discord (QD), super quantum discord (SQD) and optimal dense coding at entangled states of three types of quantum channels, are investigated. The used models include: two-qubit spin squeezing, the two-qubit Heisenberg XYZ model with decoherency and the Jaynes–Cummings model. In the first two models the quantum correlations and the optimal dense coding capacity are calculated in terms of channel parameters, system initial conditions and decoherency rate. It has been found that valid dense coding can exist, although there is no trace of entanglement in the quantum channel. In contrast, despite the presence of entanglement states in the system, there may be no dense coding capacity. We investigate the effects of cavity Fock states on quantum correlations and optimal dense coding in the Jaynes–Cummings model. Cavity Fock states are found to be effective for quantum correlations and optimal dense coding. The common result of all three models is that the dynamic properties of SQD on our channel enable us to determine when and under what conditions the system is suitable for dense coding capacity.
The aim of this paper is investigation on dynamics of super quantum discord (SQD) and quantum discord (QD) teleportation in the Jaynes–Cummings model. In order to teleport one and two qubit states, a scheme is proposed for quantum channel where is induced from an atom-field interaction. The initial state of the atom is its excited state while the state of field starts in a coherent one. The model reveals that the dynamics of quantum correlations depends crucially on atom-field initial conditions and the field parameters can be utilized as control parameters for optimal teleportation. Interestingly, we find that QD teleportation and SQD teleportation are not always zero when the entanglement falls to zero for a teleported state. This result clearly illustrates that in some cases we can only get a truly quantum teleportation by QD and SQD if we use a suitable field parameters and initial state, which have no entanglement. The results reveal that QD and SQD for teleported states are much robuster than entanglement in the process of communication. According to the results, the proposed scheme can greatly reduce the cost of quantum communication. We also obtain that the behaviour of the QD and SQD teleportation are similar to average fidelity. So, QD and SQD can be used to analyse teleported state as average fidelity.
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Super-quantum discord (SQD) with weak measurement is regarded as a kind of quantum correlation in quantum information processing. We compare and analyze the dynamical evolutions of SQD, quantum discord (QD), and quantum entanglement (QE) between two qubits in the correlated dephasing environmental model. The results indicate that (i) owing to the much smaller influence of weak measurement on the coherence of the system than that of von Neumann projection measurement, SQD with weak measurement is larger than QD, and (ii) dynamical evolution of QD or QE monotonically goes to zero with time, while SQD monotonically tends to a stable value and a freezing phenomenon occurs. The stable value after freezing mainly depends on the measurement strength and the purity of the initial quantum state.
Quantum communication is at the heart of the quantum information theory. We study two types of quantum communication protocols over noisy transmission channels, i.e. super dense coding and cryptography protocols. In the first part of this thesis, for various scenarios, it is discussed how the super dense coding capacity is influenced by noisy quantum channels. The case of memoryless channels as well as those channels with memory which are modelled by uncorrelated and correlated noise, respectively, are considered. Explicitly Pauli channels over arbitrary dimensions are treated and the super dense coding capacity for some resource states is derived. For the qubit depolarizing channel, when noise is uncorrelated, the super dense coding capacity with respect to the input state is also optimized. This illustrates a threshold value of the noise parameter below which the super dense coding capacity is optimized by a maximally entangled initial state, while above the threshold value the super dense coding capacity is optimized by a product state. For Pauli channels, with correlated noise, the case of non unitary encoding is studied and the super dense coding capacity is derived. The first part of this thesis is concluded with an example for multipartite super dense coding. In the second part of the thesis, the problem of optimal eavesdropping on noisy states in quantum key distribution is investigated. The case of the six state protocol, when the signal states are mixed with white noise, is considered. This situation may arise either when Alice deliberately adds noise to the signal states before they leave her lab, or, in a realistic scenario when the eavesdropper (referred to as Eve) is not assumed to replace the noisy quantum channel by a noiseless one. For individual attacks, we find Eve's optimal mutual information with Alice as a function of the quantum bit error rate. Finally, the results illustrate that adding noise on the quantum level can make quantum key distribution more robust against eavesdropping.
We investigate the quantum correlation between light and matter in bipartite quantum systems, drawing on the Jaynes–Cummings model and the Tavis–Cummings model, which are well-established in cavity quantum electrodynamics. Through the resolution of the quantum master equation, we can derive the dissipative dynamics in open systems. To assess the extent of quantum correlation, several measures are introduced: von Neumann entropy, concurrence and quantum discord. The effects of initial entanglement and dissipation intensity on quantum discord are carefully examined. Furthermore, we examined the dynamics of quantum discord within the O H + model.