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arXiv:quant-ph/0212032 · Physical Review A

Time-correlated quantum amplitude-damping channel

Ye Yeo, Andrew Skeen

Published Jun 27, 2003• 92 citations
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Abstract

We analyze the problem of sending classical information through qubit channels where successive uses of the channel are correlated. This work extends the analysis of Macchiavello and Palma to the case of a non-Pauli channel---the amplitude damping channel. Using the channel description outlined by Daffer et al., we derive the correlated amplitude damping channel. We obtain a result similar to that obtained by Macchiavello and Palma, that is, under certain conditions on the degree of channel memory, the use of entangled input signals may enhance the information transmission compared to the use of product input signals.

DOI
10.1103/physreva.67.064301

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We analyze the problem of sending classical information through qubit channels where successive uses of the channel are correlated. This work extends the analysis of Macchiavello and Palma to the case of a non-Pauli channel---the amplitude damping channel. Using the channel description outlined by Daffer et al., we derive the correlated amplitude damping channel. We obtain a result similar to that obtained by Macchiavello and Palma, that is, under certain conditions on the degree of channel memory, the use of entangled input signals may enhance the information transmission compared to the use of product input signals.
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.
The combined effects of memory effects due to correlated actions of the amplitude damping channel on two qubits and temporal correlations in the time evolution of each qubit on the average steered coherence (ASC) are explored. For the input Bell states, it is shown that the two kinds of memory effects are beneficial for enhancing ASC of the output states in a wide time region. In particular, the ASC is immune to decoherence for some input states if the actions of the amplitude damping channel are fully correlated. Moreover, in the infinite-time limit, the positive role of the non-Markovian effect on the steady-state ASC disappears, whereas the correlated actions of the channel are still beneficial to certain input states.
The amount of classical information that is reliably transmitted over two uses of general Pauli channels with memory, modeled as a correlated noise between a single pair of uses, is investigated. The maximum of the mutual information between the input and the output is proven to be achieved by a class of product states that is explicitly given in terms of the relevant channel parameters below some memory threshold, and by maximally entangled states above this threshold. In particular, this proves a conjecture on the depolarizing channel by Macchiavello and Palma [Phys. Rev. A 65, 050301(R) (2002)]. Furthermore, it also shows that no other scenario can occur for Pauli channels as for example the existence of an intermediate optimal degree of entanglement reported for some Gaussian channels with memory.
The problem of sending a single classical bit through a generalized amplitude damping channel is considered. When two transmissions through the channel are available as a resource, we find that two entangled transmissions can enhance the capability of receiver's judging information correctly under certain conditions compared with two product-state transmissions. In addition, we find a special case in which the two entangled transmissions can always make a classical bit more effectively disable the noise influence.