Rex A. C. Medeiros

QUANTUM ZERO-ERROR CAPACITY

We define a new kind of quantum channel capacity by extending the concept of zero-error capacity for a noisy quantum channel. The necessary requirement for which a quantum channel has zero-error capacity greater than zero is given. Finally, we point out some directions on how to calculate the zero-error capacity of such channels.

Zero-Error Capacity of a Quantum Channel

We define the quantum zero-error capacity, a new kind of classical capacity of a noisy quantum channel. Moreover, the necessary requirement for which a quantum channel has zero-error capacity greater than zero is also given.

Quantum Zero‐Error Capacity and HSW Capacity

We give in this paper a formal proof that the zero‐error capacity of a noisy quantum channel is less than or equal to the Holevo‐Schumacher‐Westmoreland capacity.

A Hybrid Protocol for Quantum Authentication of Classical Messages

Quantum authentication of classical messages is discussed. We propose a non-interactive hybrid protocol reaching informationtheoretical security, even when an eavesdropper possesses infinite quantum and classical computer power. We show that, under certain conditions, a quantum computer can only distinguish a sequence of pseudo random bits from a truly sequence of random bits with an exponentially small probability. This suggests the use of such generator together with hash functions in order to provide an authentication scheme reaching a desirable level of security.

Fundamentals of Information Theory

This chapter introduces some elementary concepts regarding information theory. First, we present entropy and other measures of information. Then, we discuss a very important quantity in classical information theory, the capacity of a discrete noisy channel. In the second part of this chapter, we give a brief introduction to the quantum information theory. We start with the von Neumann entropy and other measures of information. Then, we introduce the mathematical formulation of quantum channels, including the Choi-Jamiolkowski isomorphism. Accessible information, Holevo quantity and quantum channel capacities are discussed; the classical capacity of quantum channels is presented, as well as a brief introduction to the other kinds of quantum channel capacities.

Quantum Zero-Error Information Theory

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Fundamentals of Quantum Information Processing

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Zero-Error Secrecy Capacity

We give a brief introduction to Quantum Information Processing. We start by defining the qubit, the fundamental unity of information in a quantum system. Then, we describe how the evolution is carried out in a quantum system and how we can bring information from a quantum system to a classical level by means of projective measurements and positive operator-value measurements. The density operator formalism is presented and its importance to quantum communications is discussed. We give an introduction to quantum entanglement, which does not have a classical counterpart. Finally, the four postulates of the quantum mechanics are presented using the formalist of density operators.

Classical Zero-Error Information Theory

This chapter introduces the zero-error secrecy capacity of quantum channels (ZESC), defined as the higher transmission rate that can be achieved by noisy quantum channels, allowing for the transmission of classical information without errors in an unconditionally secure way. We start by presenting some background concepts about incoherence-free subspaces and subsystems. Then, we formally define the zero-error secrecy capacity together with the communication model. The relation between ZESC and graph theory is discussed. We demonstrate the security provided by this approach and we give a number of examples considering different scenarios. Finally, we discuss some recent developments in the literature that are intrinsically connected with the zero-error secrecy capacity.

Recent Developments in Quantum Zero-Error Information Theory

This chapter aims to introduce the main concepts of the classical zero-error information theory. We begin by defining the zero-error capacity of a discrete memoryless channel and presenting some basic concepts, like adjacency and adjacency-reducing mappings. Then, we show how the problem of finding the zero-error capacity can be stated in terms of a graph quantity. The Lovasz theta function and some of its properties are presented and, lastly, the zero-error capacity of the sum and product of channels is discussed.