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arXiv:1510.05313 · Physical Review A

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

Antonio D’Arrigo, Giuliano Benenti, G. Falci, Chiara Macchiavello

Published Dec 29, 2015• 19 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.92.062342

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•Jan 1, 2013•0 citations
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.
Determining a noisy quantum channel's classical capacity and entanglement cost generally requires regularization over many channel uses. We remove both regularizations for every qubit-to-qubit channel admitting a pure output. For each such channel, Holevo information, channel entanglement of formation, and parallel entanglement cost are additive with those of any finite-dimensional partner channel. This class includes all qubit-to-qubit channels of Kraus rank at most two. For the amplitude damping channel with damping probability ppp, the unassisted classical capacity equals the known single-use Holevo information, attained by a binary pure-state ensemble with collective decoding, and the entanglement cost is h2((1+p)/2)h_2((1+\sqrt p)/2)h2​((1+p​)/2) ebits per use. The common mechanism is a support criterion for strong superadditivity of entanglement of formation: one marginal has no support on the sector in which both local systems are orthogonal to fixed distinguished vectors. We prove this criterion in arbitrary finite dimensions using a triangular block-matrix entropy inequality and decompositions preserving two expectations. For amplitude damping, we also derive an exact finite-block Holevo deficit, identify the unique optimal average input for p<1p<1p<1, and construct a binary Kraus representation attaining the uniform formation bound.
We study entanglement-assisted quantum and classical communication over a single use of a quantum channel, which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise. We obtain characterizations of the corresponding one-shot capacities by establishing upper and lower bounds on them in terms of the difference of two smoothed entropic quantities. In the case of a memoryless channel, the upper and lower bounds converge to the known single-letter formulas for the corresponding capacities, in the limit of asymptotically many uses of it. Our results imply that the difference of two smoothed entropic quantities characterizing the one-shot entanglement-assisted capacities serves as a one-shot analog of the mutual information, since it reduces to the mutual information, between the output of the channel and a system purifying its input, in the asymptotic, memoryless scenario.
The primary objective of quantum Shannon theory is to evaluate the capacity of quantum channels. In spite of the existence of rigorous coding theorems that quantify the transmission of information through quantum channels, superadditivity effects limit our understanding of the channel capacities. In this paper, we mainly focus on a family of channels known as multilevel amplitude damping channels. We investigate some of the information capacities of the simplest member of the multilevel amplitude damping channel, a qutrit channel, in the presence of correlations between successive applications of the channel. We find the upper bounds of the single-shot classical capacities and calculate the quantum capacities associated with a specific class of maps after investigating the degradability property of the channels. Additionally, the quantum and classical capacities of the channels have been computed in entanglement-assisted scenarios.
We derive explicit, absolutely convergent series formulas for the quantum, unassisted classical, and entanglement-assisted classical capacities of the qubit amplitude damping channel, eliminating residual optimizations and implicit roots. We also obtain analytical upper and lower bounds on two-way assisted quantum and private communication capacities by evaluating a balanced-squashing bound and optimizing the reverse coherent information. Our results characterize the optimal input populations, establish convergence and truncation properties, and provide analytical benchmarks for quantum and classical communication over dissipative channels.
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.