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International Conference on Electronics, Hardware, Wireless and Optical Communications

Channel capacity restoration of noisy optical quantum channels

László Gyöngyösi, Sándor Imre

Published Feb 20, 2011• 1 citation
OpenAlex

Abstract

This paper defines a fundamentally new approach of capacity recovery of very noisy, practically completely useless optical quantum channels. The transmission of information through classical channels and quantum channels differs in many ways. The capacity recovery of very noisy communication channels cannot be imagined for classical systems, and this effect has no analogue in classical systems. The capacity recovery of very noisy quantum channels makes it possible to use two very noisy optical-fiber based quantum channels with a positive joint capacity at the output. Our method gives an algorithmic solution to the capacity recovery problem, and provides an efficient algorithmic solution for finding recoverable very noisy optical quantum channels.

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This paper defines a fundamentally new approach of capacity recovery of very noisy, practically completely useless optical quantum channels. The transmission of information through classical channels and quantum channels differs in many ways. The capacity recovery of very noisy communication channels cannot be imagined for classical systems, and this effect has no analogue in classical systems. The capacity recovery of very noisy quantum channels makes it possible to use two very noisy optical-fiber based quantum channels with a positive joint capacity at the output. Our method gives an algorithmic solution to the capacity recovery problem, and provides an efficient algorithmic solution for finding recoverable very noisy optical quantum channels.
The superactivation of zero-capacity quantum channels makes it possible to use two zero-capacity quantum channels with a positive joint capacity at the output. Currently, we have no theoretical results for describing all possible combinations of superactive zero-capacity channels, hence there should be many possible - still undiscovered - combinations. Our method gives an algorithmic solution to the superactivation problem, and provides an efficient algorithmic solution for discovering “superactive” zero-capacity optical quantum channels. We analyze the superactivation property of the amplitude damping quantum channel model. This model has great importance in practical communications, since this channel model describes energy dissipation due to the noise of the optical channel. To discover these superactive zero-capacity channels, an extremely large set of possible quantum states has to be analyzed, however an efficient algorithmic framework is still missing for this purpose. We show a fundamentally new method of finding the conditions for “superactive” zero-capacity optical quantum channels.
This paper introduces a fundamentally new method of finding the conditions for the superactivation of the zero-error capacity of quantum channels.The zero-error capacity of the quantum channel describes the amount of information which can be transmitted perfectly through a noisy quantum channel.The superactivation of the zero-error capacity of quantum channels makes it possible to use two quantum channels, each with zero zero-error capacity, with a positive joint zero-error capacity.Currently we have no theoretical background for describing all possible combinations of superactive quantum channels, hence there should be many other possible combinations.We give an algorithmic solution to the problem.To analyze the superactivation of the zero-error capacity, we introduce a new geometrical representation, called the quantum superball.Our method can be the first efficient algorithmic solution to discover the still unknown combinations to determine the superactivation of the zero-error capacity of quantum channels, without the extremely high computational costs.
The capacity of noisy quantum channels characterizes the highest rate at which information can be reliably transmitted and it is therefore of practical as well as fundamental importance. Capacities of classical channels are computed using alternating optimization schemes, called Blahut-Arimoto algorithms. In this work, we generalize classical Blahut-Arimoto algorithms to the quantum setting. In particular, we give efficient iterative schemes to compute the capacity of channels with classical input and quantum output, the quantum capacity of less noisy channels, the thermodynamic capacity of quantum channels, as well as the entanglement-assisted capacity of quantum channels. We give rigorousa priorianda posterioribounds on the estimation error by employing quantum entropy inequalities and demonstrate fast convergence of our algorithms in numerical experiments.
The applications of the general formulae of channel capacity developed in the quantum information theory to evaluation of information transmission capacity of optical channel are interesting subjects. In this review paper, we will point out that the formulation based on only classical-quantum channel mapping model may be inadequate when one takes into account a power constraint for noisy channel. To define the power constraint well, we should explicitly consider how quantum states are conveyed through a transmission channel. Basing on such consideration, we calculate a capacity formula for an attenuated noisy optical channel with genreral Gaussian state input; this gives certain progress beyond the example in our former paper.
We establish the classical capacity of optical quantum channels as a sharp transition between two regimes-one which is an error-free regime for communication rates below the capacity, and the other in which the probability of correctly decoding a classical message converges exponentially fast to zero if the communication rate exceeds the classical capacity. This result is obtained by proving a strong converse theorem for the classical capacity of all phase-insensitive bosonic Gaussian channels, a well-established model of optical quantum communication channels, such as lossy optical fibers, amplifier, and free-space communication. The theorem holds under a particular photon-number occupation constraint, which we describe in detail in this paper. Our result bolsters the understanding of the classical capacity of these channels and opens the path to applications, such as proving the security of noisy quantum storage models of cryptography with optical links.
We establish the classical capacity of optical quantum channels as a sharp transition between two regimes - one which is an error-free regime for communication rates below the capacity, and the other in which the probability of correctly decoding a classical message converges exponentially fast to zero if the communication rate exceeds the classical capacity. This result is obtained by proving a strong converse theorem for the classical capacity of all phase-insensitive bosonic Gaussian channels, a well-established model of optical quantum communication channels, such as lossy optical fibers, amplifier, and free-space communication. The theorem holds under a particular photon-number occupation constraint, which we describe in detail in this paper. Our result bolsters the understanding of the classical capacity of these channels and opens the path to applications, such as proving the security of noisy quantum storage models of cryptography with optical links.