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International Journal of Quantum Information

HAMILTONIAN MODELS FOR QUANTUM MEMORY CHANNELS

Antonio D’Arrigo, Giuliano Benenti, G. Falci

Published Mar 1, 2011• 1 citation
Publisher

Abstract

Quantum memory channels are attracting growing interest, motivated by both realistic possibilities of transferring information by means of quantum hardware and inadequacies of the memoryless approximation. In fact, subsequent uses of the same quantum transmission resource can be significantly correlated. In this paper we review two Hamiltonian models describing memory effects in a purely dephasing spin-boson channel and in a channel with damping visualized by a micromaser system, respectively. In both cases, we show that the quantum information transmission rates are higher than in the memoryless limit.

DOI
10.1142/s0219749911007903

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Quantum memory channels are attracting growing interest, motivated by both realistic possibilities of transferring information by means of quantum hardware and inadequacies of the memoryless approximation. In fact, subsequent uses of the same quantum transmission resource can be significantly correlated. In this paper we review two Hamiltonian models describing memory effects in a purely dephasing spin-boson channel and in a channel with damping visualized by a micromaser system, respectively. In both cases, we show that the quantum information transmission rates are higher than in the memoryless limit.
Any physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be characterized from the point of view of communication theory, i.e., in terms of its ability to transfer information. Quantum information provides a theoretical framework and the proper mathematical tools to accomplish this. In this context the notion of codes and communication capacities have been introduced by generalizing them from the classical Shannon theory of information transmission and error correction. The underlying assumption of this approach is to consider the channel not as acting on a single system, but on sequences of systems, which, when properly initialized allow one to overcome the noisy effects induced by the physical process under consideration. While most of the work produced so far has been focused on the case in which a given channel transformation acts identically and independently on the various elements of the sequence (memoryless configuration in jargon), correlated error models appear to be a more realistic way to approach the problem. A slightly different, yet conceptually related, notion of correlated errors applies to a single quantum system which evolves continuously in time under the influence of an external disturbance which acts on it in a non-Markovian fashion. This leads to the study of memory effects in quantum channels: a fertile ground where interesting novel phenomena emerge at the intersection of quantum information theory and other branches of physics. A survey is taken of the field of quantum channels theory while also embracing these specific and complex settings.
We consider the transfer of quantum information down a single-mode quantum transmission line. Such a quantum channel is modeled as a damped harmonic oscillator, the interaction between the information carriers -a train of N qubits- and the oscillator being of the Jaynes-Cummings kind. Memory effects appear if the state of the oscillator is not reset after each channel use. We show that the setup without resetting is convenient in order to increase the transmission rates, both for the transfer of quantum and classical private information. Our results can be applied to the micromaser.
Abstract Quantum memory channels represent a very general, yet simple and comprehensible model for causal processes. As such they have attracted considerable research interest, mostly aimed on their transfer capabilities and structure properties. Most notably it was shown that memory channels can be implemented via physically naturally motivated collision models. We also define the concept of repeatable channels and show that only unital channels can be implemented repeatably with pure memory channels. In the special case of qubit channels we also show that every unital qubit channel has a repeatable implementation. We also briefly explore the possibilities of stroboscopical simulation of channels and show that all random unitary channels can be stroboscopically simulated. Particularly in qubit case, all indivisible qubit channels are also random unitary, hence for qubit all indivisible channels can be stroboscopically simulated. Memory channels also naturally capture the framework of correlated experiments. We develop methods to gather and interpret data obtained in such setting and in detail examine the two qubit case. We also show that for control unitary interactions the measured data will never contradict a simple unitary evolution. Thus no memory effects can be spotted then.
A dynamical model for quantum channels is introduced which allows one to pass continuously from the memoryless case to the case in which memory effects are present. The quantum and classical communication rates of the model are defined and explicit expression is provided in some limiting case. In this context, we introduce noise attenuation strategies where part of the signals are sacrificed to modify the channel environment. The case of qubit channel with phase damping noise is analysed in detail.
A dynamical model for quantum channel is introduced which allows one to pass continuously from the memoryless case to the case in which memory effects are present. The quantum and classical communication rates of the model are defined and explicit expression are provided in some limiting case. In this context we introduce noise attenuation strategies where part of the signals are sacrificed to modify the channel environment. The case of qubit channel with phase damping noise is analyzed in details.