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Physical Review A

Superdense coding in noisy environments: A quantum trajectory approach

Jin Woo Jun

Published Jun 2, 2006• 6 citations
Publisher

Abstract

Using the theory of quantum trajectories, we study the classical capacity $\mathbf{C}$ of noisy quantum channels in the superdense coding protocol. We apply the two models that generalize single-qubit noisy channels, such as amplitude damping and phase flip, to the many-qubit situation. Our numerical results show that the quantum trajectory approach is suitable for modeling the superdense coding protocol in realistic environments.

DOI
10.1103/physreva.73.064301

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Using the theory of quantum trajectories, we study the classical capacity C\mathbf{C}C of noisy quantum channels in the superdense coding protocol. We apply the two models that generalize single-qubit noisy channels, such as amplitude damping and phase flip, to the many-qubit situation. Our numerical results show that the quantum trajectory approach is suitable for modeling the superdense coding protocol in realistic environments.
The theory of quantum trajectories is applied to simulate the effects of quantum noise sources induced by the environment on quantum information protocols. We study two models that generalize single qubit noise channels like amplitude damping and phase flip to the many-qubit situation. We calculate the fidelity of quantum information transmission through a chaotic channel using the teleportation scheme with different environments. In this example, we analyze the role played by the kind of collective noise suffered by the quantum processor during its operation. We also investigate the stability of a quantum algorithm simulating the quantum dynamics of a paradigmatic model of chaos, the baker's map. Our results demonstrate that, using the quantum trajectories approach, we are able to simulate quantum protocols in the presence of noise and with large system sizes of more than 20 qubits.
We study the fidelity of quantum teleportation for the situation in which quantum logic gates are used to provide the long distance entanglement required in the protocol, and where the effect of a noisy environment is modeled by means of a generalized amplitude damping channel. Our results demonstrate the effectiveness of the quantum trajectories approach, which allows the simulation of open systems with a large number of qubits (up to 24). This shows that the method is suitable for modeling quantum information protocols in realistic environments.
Abstract We introduce an escort-qubit–assisted protocol that restores and stabilizes superdense coding capacity in the presence of amplitude damping channel (ADC) noise. The protocol is analyzed under three fundamental noisy configurations: amplitude damping acting on Alice’s subsystem, on Bob’s subsystem, and on both subsystems covering all practically relevant scenarios. In the absence of protection, we show that ADC effects cause a monotonic degradation of the superdense coding capacity, driving it below the classical limit in the strong decoherence regime and completely erasing the quantum advantage. Our escort-qubit protocol overcomes this limitation by coherently tracking the channel-induced Kraus trajectories during entanglement distribution. Post-selection of the no-flip trajectory, projects the shared state onto a maximally entangled resource state, thereby recovering the optimal superdense coding capacity of two classical bits, independent of the noise strength and noisy configuration. Importantly, when all ADC trajectories are taken into account, the resulting average capacity although inherently suboptimal remains strictly above both the classical limit and the unprotected capacity across the entire decoherence range. These results establish the escort-qubit protocol as a powerful, scalable, and experimentally viable approach for preserving quantum advantage and enhancing information throughput in noisy quantum communication networks.
In a realistic situation, the secret sharing of classical or quantum information will involve the transmission of this information through noisy channels. We consider a three qubit pure state. This state becomes a mixed-state when the qubits are distributed over noisy channels. We focus on a specific noisy channel, the phase-damping channel. We propose a protocol for secret sharing of classical information with this and related noisy channels. This protocol can also be thought of as cooperative superdense coding. We also discuss other noisy channels to examine the possibility of secret sharing of classical information.