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arXiv:1007.1446 · Journal of Physics A Mathematical and Theoretical

Quantum dense coding and dynamics of information over Bloch channels

NASSER METWALLY

Published Jan 4, 2011• 26 citations
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Abstract

Dynamics of coded information over Bloch channels is investigated for different values of the channel's parameters. We show that, the suppressing of the travelling coded information over Bloch channel can be increased by decreasing the equilibrium absolute value of information carrier and consequently decreasing the distilled information by eavesdropper. The amount of decoded information can be improved by increasing the equilibrium values of the two qubits and decreasing the ratio between longitudinal and transverse relaxation times. The robustness of coded information in maximum and partial entangled states is discussed. It is shown that the maximum entangled states are more robust than the partial entangled state over this type of channels.

DOI
10.1088/1751-8113/44/5/055305

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Dynamics of coded information over Bloch channels is investigated for different values of the channel's parameters. We show that, the suppressing of the travelling coded information over Bloch channel can be increased by decreasing the equilibrium absolute value of information carrier and consequently decreasing the distilled information by eavesdropper. The amount of decoded information can be improved by increasing the equilibrium values of the two qubits and decreasing the ratio between longitudinal and transverse relaxation times. The robustness of coded information in maximum and partial entangled states is discussed. It is shown that the maximum entangled states are more robust than the partial entangled state over this type of channels.
Decoherence of entanglement of qubits is investigated which is caused by the phenomenological quantum channel (the Bloch channel) equivalent to the Bloch equations. It is shown how the decoherence of entanglement depends on the longitudinal and transverse relaxation times and the equilibrium value of the qubit. The quantum dense coding system under the influence of the Bloch channel is also investigated. The Shannon mutual information obtained by the Bell measurement and the Holevo capacity is calculated. Furthermore, the microscopic system-reservoir model which yields the Bloch equations is considered. The result shows that the temperature of the thermal reservoir significantly affects the decoherence of entanglement.
The original dense coding protocol is achieved via a quantum channel generated between a single Cooper pair and a cavity. The dynamics of the coded and decoded information is investigated for different values of the channel’s parameters. It is shown that these two types of information increase as the detuning parameter increases or the number of photons inside the cavity decreases. The coded and decoded information increases as the ratio of the capacities between the box and the gate decrease. The dynamics of information is investigated in the presence of imperfect operation during the coding process. It is found that, for the phase flip error, the upper bound of the coded and decoded information is much smaller than that depicted for the bit flip errors.
We investigate the dynamics of two qubits state through the Bloch channel. It is found that the degradation and sudden-death of the entanglement depend on the channel's parameters and the structure of the input state. Starting from partially entangled states as input state, the output states are more robust compared with those obtained from initial maximally entangled states. Also the survivability of entanglement increased as the absolute equilibrium values of the channel increased or the ratio between the longitudinal and transverse relaxation times gets smaller. Ability of using the output states as quantum channels to perform quantum teleportation is investigated. The idea that the useful output states are used to achieve the original quantum teleportation protocol is discussed.
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.
Abstract Quantum entanglement is a special nonlocal association between quantum systems. It is a fundamental feature of the difference between quantum and classical. At the same time, it acts as a very important resource in quantum informatics. Therefore, entanglement plays a noble role in quantum information and quantum computing. Quantum dense coding, as an application of quantum entanglement in practice, is a quantum communication protocol characterized by security and secrecy, which plays a very important role in quantum informatics and cryptography. This paper is mainly in the Non-Markovian environment of Heisenberg Spin chain system, using the quantum dense coding scheme proposed by Bennett et al. to study The dynamics of quantum dense coding channel capacity evolution with time and the entanglement dynamics of the system are discussed in detail.Based on the theoretical knowledge of open quantum systems and the maximum entangled state ∣ψAB⟩=12(∣11⟩+∣00⟩)\left| {{{\mathbf{\psi }}_{{\mathbf{AB}}}}} \right\rangle =\frac{1}{{\sqrt 2 }}\left( {\left| {11} \right\rangle +\left| {00} \right\rangle } \right)∣ψAB​⟩=2​1​(∣11⟩+∣00⟩) as the initial state, the density matrix of the system evolution over time is obtained by quantum state diffusion method,and the evolution of channel capacity and entanglement over time of Heisenberg spin chains is simulated accurately. The results show that: the capacity and entanglement of dense coded channel oscillate with time and reach different stable values. Environmental correlation coefficientγ\gammaγand coupling strengthη\etaηand a play an important role in dense coding and quantum entanglement of quantum systems.Proper selection of parameters can keep the system good entanglement characteristics and increase the channel capacityχ\chiχof the system, thus ensuring the effective transmission and processing of quantum information in practice. It lays a solid foundation for quantum computing
Quantum dense coding enables the transmission of two classical bits of information through the exchange of a single qubit, provided that an entangled state is shared between the communicating parties. While this protocol achieves a fundamental increase in channel capacity, its practical realization is strongly influenced by the presence of noise in realistic quantum channels. This work presents a simulation-based study of dense coding performance under two representative noise models: the depolarizing channel and the amplitude damping channel. Using Qiskit Aer, the bit error rate (BER), frame error rate (FER), and effective channel capacity are evaluated across a range of noise parameters. In addition, a classical threefold repetition strategy is examined as a lightweight error-mitigation technique. Results indicate that depolarizing noise produces more rapid degradation in both BER and channel capacity compared to amplitude damping, while repetition coding provides partial improvement in reliability at the expense of resource overhead. These findings highlight the trade-offs between efficiency and robustness in noisy implementations of dense coding and motivate further exploration of more advanced quantum error correction methods.