Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1307.5403

Entanglement-assisted capacities of time-correlated amplitude-damping channel

Nigum Arshed, A. H. Toor

Published Jul 20, 2013• 6 citations
arXivHTMLPDF

Abstract

We calculate the information capacities of a time-correlated amplitude-damping channel, provided the sender and receiver share prior entanglement. Our analytical results show that the noisy channel with zero capacity can transmit information if it has finite memory. The capacities increase as the memory increases attaining maximum value for perfect memory channel.

DOI
10.48550/arxiv.1307.5403

Related papers

Entanglement-Assisted Classical Capacity of a Generalized Amplitude Damping Channel

Hou Li-Zhen, Mao-Fa Fang

The entanglement-assisted capacity of a generalized amplitude damping channel is investigated by using the properties of partial symmetry and concavity of mutual information. The numerical and analytical results of the entanglement-assisted capacity are obtained under certain conditions. It is shown that the entanglement-assisted capacity depends on the channel parameters representing the ambient temperature and dissipation, and the prior entanglement between sender and receiver can approximately double the classical capacity of the generalized amplitude damping channel.

Chinese Physics Letters•Aug 23, 2007•6 citations

Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem

C. H. Bennett, Peter W. Shor, John A. Smolin +1 more

The entanglement-assisted classical capacity of a noisy quantum channel (C/sub E/) is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel, assuming that the sender and receiver have access to the resource of shared quantum entanglement, which may be used up by the communication protocol. We show that the capacity C/sub E/ is given by an expression parallel to that for the capacity of a purely classical channel: i.e., the maximum, over channel inputs /spl rho/, of the entropy of the channel input plus the entropy of the channel output minus their joint entropy, the latter being defined as the entropy of an entangled purification of /spl rho/ after half of it has passed through the channel. We calculate entanglement-assisted capacities for two interesting quantum channels, the qubit amplitude damping channel and the bosonic channel with amplification/attenuation and Gaussian noise. We discuss how many independent parameters are required to completely characterize the asymptotic behavior of a general quantum channel, alone or in the presence of ancillary resources such as prior entanglement. In the classical analog of entanglement-assisted communication - communication over a discrete memoryless channel (DMC) between parties who share prior random information - we show that one parameter is sufficient, i.e., that in the presence of prior shared random information, all DMCs of equal capacity can simulate one another with unit asymptotic efficiency.

arXiv:quant-ph/0106052•IEEE Transactions on Information Theory•Oct 1, 2002•698 citations

Information Transmission Over Non Markovian Quantum Channels

Nigum Arshed

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.

•Jan 1, 2013•0 citations

Information transmission over an amplitude damping channel with an arbitrary degree of memory

Antonio D’Arrigo, Giuliano Benenti, G. Falci +1 more

We study the performance of a partially correlated amplitude damping channel acting on two qubits. We derive lower bounds for the single-shot classical capacity by studying two kinds of quantum ensembles, one which allows us to maximize the Holevo quantity for the memoryless channel and the other allowing the same task but for the full-memory channel. In these two cases we also show the amount of entanglement which is involved in achieving the maximum of the Holevo quantity. For the single-shot quantum capacity we discuss both a lower and an upper bound, achieving a good estimate for high values of the channel transmissivity. We finally compute the entanglement-assisted classical channel capacity.

arXiv:1510.05313•Physical Review A•Dec 29, 2015•19 citations

Entanglement-Assisted Classical Capacity of Noisy Quantum Channels

Charles H. Bennett, Peter W. Shor, John A. Smolin +1 more

Prior entanglement between sender and receiver, which exactly doubles the classical capacity of a noiseless quantum channel, can increase the classical capacity of some noisy quantum channels by an arbitrarily large constant factor depending on the channel, relative to the best known classical capacity achievable without entanglement. The enhancement factor is greatest for very noisy channels, with positive classical capacity but zero quantum capacity. We obtain exact expressions for the entanglement-assisted capacity of depolarizing and erasure channels in $d$ dimensions.

arXiv:quant-ph/9904023•Physical Review Letters•Oct 11, 1999•611 citations

Classical and quantum capacities of a fully correlated amplitude damping channel

Antonio D’Arrigo, Giuliano Benenti, G. Falci +1 more

We study information transmission over a fully correlated amplitude damping channel acting on two qubits. We derive the single-shot classical channel capacity and show that entanglement is needed to achieve the channel best performance. We discuss the degradability properties of the channel and evaluate the quantum capacity for any value of the noise parameter. We finally compute the entanglement-assisted classical channel capacity.

arXiv:1309.2219•Physical Review A•Oct 31, 2013•46 citations
We calculate the information capacities of a time-correlated amplitude-damping channel, provided the sender and receiver share prior entanglement. Our analytical results show that the noisy channel with zero capacity can transmit information if it has finite memory. The capacities increase as the memory increases attaining maximum value for perfect memory channel.
The entanglement-assisted capacity of a generalized amplitude damping channel is investigated by using the properties of partial symmetry and concavity of mutual information. The numerical and analytical results of the entanglement-assisted capacity are obtained under certain conditions. It is shown that the entanglement-assisted capacity depends on the channel parameters representing the ambient temperature and dissipation, and the prior entanglement between sender and receiver can approximately double the classical capacity of the generalized amplitude damping channel.
The entanglement-assisted classical capacity of a noisy quantum channel (C/sub E/) is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel, assuming that the sender and receiver have access to the resource of shared quantum entanglement, which may be used up by the communication protocol. We show that the capacity C/sub E/ is given by an expression parallel to that for the capacity of a purely classical channel: i.e., the maximum, over channel inputs /spl rho/, of the entropy of the channel input plus the entropy of the channel output minus their joint entropy, the latter being defined as the entropy of an entangled purification of /spl rho/ after half of it has passed through the channel. We calculate entanglement-assisted capacities for two interesting quantum channels, the qubit amplitude damping channel and the bosonic channel with amplification/attenuation and Gaussian noise. We discuss how many independent parameters are required to completely characterize the asymptotic behavior of a general quantum channel, alone or in the presence of ancillary resources such as prior entanglement. In the classical analog of entanglement-assisted communication - communication over a discrete memoryless channel (DMC) between parties who share prior random information - we show that one parameter is sufficient, i.e., that in the presence of prior shared random information, all DMCs of equal capacity can simulate one another with unit asymptotic efficiency.
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.
We study the performance of a partially correlated amplitude damping channel acting on two qubits. We derive lower bounds for the single-shot classical capacity by studying two kinds of quantum ensembles, one which allows us to maximize the Holevo quantity for the memoryless channel and the other allowing the same task but for the full-memory channel. In these two cases we also show the amount of entanglement which is involved in achieving the maximum of the Holevo quantity. For the single-shot quantum capacity we discuss both a lower and an upper bound, achieving a good estimate for high values of the channel transmissivity. We finally compute the entanglement-assisted classical channel capacity.
Prior entanglement between sender and receiver, which exactly doubles the classical capacity of a noiseless quantum channel, can increase the classical capacity of some noisy quantum channels by an arbitrarily large constant factor depending on the channel, relative to the best known classical capacity achievable without entanglement. The enhancement factor is greatest for very noisy channels, with positive classical capacity but zero quantum capacity. We obtain exact expressions for the entanglement-assisted capacity of depolarizing and erasure channels in ddd dimensions.