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arXiv:2408.10842 · Journal of Physics A Mathematical and Theoretical

Optimal superdense coding capacity in the non-Markovian regime

Y. Aiache, Saif M. Al-Kuwari, K. El Anouz, Abderrahim El Allati

Published Apr 19, 2024• 4 citations
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Abstract

Abstract Superdense coding (SDC) is a significant technique widely used in quantum information processing. Indeed, it consists of sending two bits of classical information using a single qubit, leading to faster and more efficient quantum communication. In this paper, we propose a model to evaluate the effect of backflow information in a SDC protocol through a non-Markovian dynamics. The model considers a qubit interacting with a structured Markovian environment. In order to generate a non-Markovian dynamic, an auxiliary qubit contacts a Markovian reservoir in such a way that the non-Markovian regime can be induced. By varying the coupling strength between the central qubit and the auxiliary qubit, the two dynamical regimes can be switched interchangeably. An enhancement in non-Markovian effects corresponds to an increase in this coupling strength. Furthermore, we conduct an examination of various parameters, namely temperature weight, and decoherence parameters in order to explore the behaviors of SDC, quantum fisher information (QFI), and local quantum uncertainty using an exact calculation. The obtained results show a significant relationship between non-classical correlations and QFI since they behave similarly, allowing them to detect what is beyond entanglement. In addition, the presence of non-classical correlations enables us to detect the optimal SDC capacity in a non-Markovian regime.

DOI
10.1088/1751-8121/ad40e0

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Abstract Superdense coding (SDC) is a significant technique widely used in quantum information processing. Indeed, it consists of sending two bits of classical information using a single qubit, leading to faster and more efficient quantum communication. In this paper, we propose a model to evaluate the effect of backflow information in a SDC protocol through a non-Markovian dynamics. The model considers a qubit interacting with a structured Markovian environment. In order to generate a non-Markovian dynamic, an auxiliary qubit contacts a Markovian reservoir in such a way that the non-Markovian regime can be induced. By varying the coupling strength between the central qubit and the auxiliary qubit, the two dynamical regimes can be switched interchangeably. An enhancement in non-Markovian effects corresponds to an increase in this coupling strength. Furthermore, we conduct an examination of various parameters, namely temperature weight, and decoherence parameters in order to explore the behaviors of SDC, quantum fisher information (QFI), and local quantum uncertainty using an exact calculation. The obtained results show a significant relationship between non-classical correlations and QFI since they behave similarly, allowing them to detect what is beyond entanglement. In addition, the presence of non-classical correlations enables us to detect the optimal SDC capacity in a non-Markovian regime.
The complementarity of two observables is often captured in uncertainty relations, which quantify an inevitable trade-off in knowledge. Here we study complementarity in the context of an information-processing task: we link the complementarity of two observables to their usefulness for superdense coding (SDC). In SDC, Alice sends two classical dits of information to Bob by sending a single qudit. However, we show that encoding with commuting unitaries prevents Alice from sending more than one dit per qudit, implying that complementarity is necessary for SDC to be advantageous over a classical strategy for information transmission. When Alice encodes with products of Pauli operators for the XXX and ZZZ bases, we quantify the complementarity of these encodings in terms of the overlap of the XXX and ZZZ basis elements. Our main result explicitly solves for the SDC capacity as a function of the complementarity, showing that the entropy of the overlap matrix gives the capacity, when the preshared state is maximally entangled. We generalize this equation to resources with symmetric noise such as a preshared Werner state. In the most general case of arbitrary noisy resources, we obtain an analogous lower bound on the SDC capacity. Our results shed light on the role of complementarity in determining the quantum advantage in SDC and also seem fundamentally interesting since they bear a striking resemblance to uncertainty relations.
We study the performance of two measures of non-Markovianity in detecting memory effects in two-qubit dephasing channels. By combining independent Markovian and non-Markovian noise on the qubits, our results show that the trace distance measure is able to detect the memory effects when at least one of the local channels displays non-Markovianity. A measure based on channel capacity, in turn, becomes nonzero when the global two-qubit dynamics shows memory effects. We apply these schemes to a well-known superdense coding protocol and demonstrate an optimal noise configuration to maximize the information transmission with independent local noises.
The complementarity of two observables is often captured in uncertainty relations, which quantify an inevitable tradeoff in knowledge. Here we study complementarity in the context of an information processing task: we link the complementarity of two observables to their usefulness for superdense coding (SDC). In SDC, Alice sends two classical dits of information to Bob by sending a single qudit. However, we show that encoding with commuting unitaries prevents Alice from sending more than one dit per qudit, implying that complementarity is necessary for SDC to be advantagous over a classical strategy for information transmission. When Alice encodes with products of Pauli operators for the XXX and ZZZ bases, we quantify the complementarity of these encodings in terms of the overlap of the XXX and ZZZ basis elements. Our main result explicitly solves for the SDC capacity as a function of the complementarity, showing that the entropy of the overlap matrix gives the capacity, when the preshared state is maximally entangled. We generalise this equation to resources with symmetric noise such as a preshared Werner state. In the most general case of arbitrary noisy resources, we obtain an analogous lower bound on the SDC capacity. Our results shed light on the role of complementarity in determining the quantum advantage in SDC and also seem fundamentally interesting since they bear a striking resemblance to uncertainty relations.
Abstract In this work, we investigate the effect of a parity-time ( PT ) symmetric operation on the dynamic behavior of quantum dense coding for a two-qubit system in non-Markovian environments. First, we derive the explicit expressions of quantum dense coding for an exactly solving model consisting of two qubits interacting with an independent structured reservoir. Then, we give two cases, i.e. resonant and off-resonant regimes, to demonstrate the performance of the PT symmetric operation on quantum dense coding dynamics. By investigation, we find that the capacity of quantum dense coding can be obviously enhanced with the assistance of the PT symmetric operation in different regimes. In addition, we show that the optimal local PT symmetric operation can completely protect quantum dense coding. The obtained results imply that the PT symmetric operation method may have potential applications in quantum decoherence control.
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.
It is shown that superdense coding (SDC) experiments by means of nuclear magnetic resonance (NMR) can show non-classical efficiency gain over classical communication only for nuclear spin polarization beyond a certain threshold, and this threshold coincides with that for non-separability of the density matrix. It is also claimed that transfer of two-bit information mediated by a single qubit in the previous NMR SDC experiments with low nuclear spin polarization is not ascribed to the non-classical effect induced by entanglement, but merely to a statistical effect in an ensemble system having a large number of molecules. Towards experimental detection of entanglement, a new class of entanglement witnesses is proposed, which is based on the measurement of nuclear spin magnetizations in the Bell basis and is suitable for actual NMR experiments.