Quantum Zero-Error Capacity (original) (raw)

Zero-error capacity of quantum channels and noiseless subsystems

2006 International Telecommunications Symposium, 2006

This paper investigates connections between the theory of quantum noiseless subsystems and the zero-error capacity of quantum channels. In particular, we show that if we have a noiseless subsystem state ρ supported by a projector P , then any quantum state with components in the subspace P ⊥ is adjacent to ρ. This result has some interesting implications for the quantum states of the optimum (S, P) for which the zero-error capacity is reached.

Quantum states characterization for the zero-error capacity

2006

The zero-error capacity of quantum channels was defined as the least upper bound of rates at which classical information can be transmitted through a quantum channel with probability of error equal to zero. This paper investigates some properties of input states and measurements used to attain the quantum zero-error capacity. We start by reformulating the problem of finding the zero-error capacity in the language of graph theory. This alternative definition is used to prove that the zero-error capacity of any quantum channel can be reached by using tensor products of pure states as channel inputs, and projective measurements in the channel output. We conclude by presenting an example that illustrates our results.

Capacity of Quantum Arbitrarily Varying Channels

2006 IEEE International Symposium on Information Theory, 2006

We prove that the average error capacity C q of a quantum arbitrarily varying channel (QAVC) equals 0 or else the random code capacityC (Ahlswede's dichotomy). We also establish a necessary and sufficient condition for C q > 0.

Zero-Error Capacity of Quantum Channels

Quantum Zero-Error Information Theory, 2016

Je voudrais remercier tout d'abord mon épouse chérie, pour sa présence dans tous les moments de ma thèse. Je la remercie pour son amour, sa confiance, son soutien et, surtout, pour avoir renoncé à ses projets au profit des miens. Merci à toute ma famille pour son inconditionnel soutien. J'ai un immense plaisir à remercier mes deux directeurs de thèse : Francisco Assis et Gérard Cohen. Ils m'ont donné l'occasion de faire cette thèse qui est une expérience extrêmement enrichissante. Je remercie, plus particulièrement, le Professeur Assis pour son amitié et sa complicité dès le début de mon master, et, le Professeur Cohen pour le parfait accueil que j'ai reçu à TELECOM ParisTech. Je remercie l'ensemble des membres de mon jury qui m'ont fait l'honneur de siéger à ma soutenance. En particulier, je tiens à remercier les deux rapporteurs de ma thèse, Professeurs Gilles Zémor et Valdemar Rocha. Leur lecture attentive et leurs suggestions ont contribué à l'amélioration de la qualité de ce rapport. Je tiens aussi à exprimer ma plus profonde gratitude aux Professeurs Romain Alléaume et Hugues Randriam qui m'ont beaucoup apporté dans ma recherche. J'ai beaucoup apprécié les échanges d'idées que nous avons eus, et j'espère que nous pourrons encore collaborer pour très longtemps. Je voudrais remercier les institutions qui ont apporté le soutien financier à ma thèse : le CNPq, le TELECOM ParisTech et l'AlBan Office. Je remercie aussi le personnel de TELECOM ParisTech, UFCG/Copele et AlBan Office, qui ont été très efficaces face aux questions administratives. Je remercie plus spécialement, Sophie Bérenger, Florence Besnard, Ângela et Salete Figueiredo. Pour finir, je tiens à remercier mes amis qui ont partagé mes désespérances mais aussi mes joies tout au long de cette thèse :

Tema con variazioni: quantum channel capacity

New Journal of Physics, 2004

Channel capacity describes the size of the nearly ideal channels, which can be obtained from many uses of a given channel, using an optimal error correcting code. In this paper we collect and compare minor and major variations in the mathematically precise statements of this idea which have been put forward in the literature. We show that all the variations considered lead to equivalent capacity definitions. In particular, it makes no difference whether one requires mean or maximal errors to go to zero, and it makes no difference whether errors are required to vanish for any sequence of block sizes compatible with the rate, or only for one infinite sequence.

On quantum fidelities and channel capacities

IEEE Transactions on Information Theory, 2000

We show the equivalence of two different notions of quantum channel capacity: that which uses the entanglement fidelity as its criterion for success in transmission, and that which uses the minimum fidelity of pure states in a subspace of the input Hilbert space as its criterion. As a corollary, any source with entropy less than the capacity may be transmitted with high entanglement fidelity. We also show that a restricted class of encodings is sufficient to transmit any quantum source which may be transmitted on a given channel. This enables us to simplify a known upper bound for the channel capacity. It also enables us to show that the availability of an auxiliary classical channel from encoder to decoder does not increase the quantum capacity.

Classical capacity of a noiseless quantum channel assisted by noisy entanglement

2001

We derive the general formula for the capacity of a noiseless quantum channel assisted by an arbitrary amount of noisy entanglement. In this capacity formula, the ratio of the quantum mutual information and the von Neumann entropy of the sender's share of the noisy entanglement plays the role of mutual information in the completely classical case. A consequence of our

Entanglement-Assisted Classical Capacity of Noisy Quantum Channels

Physical Review Letters, 1999

Prior entanglement between sender and receiver, which exactly doubles the classical capacity of a noiseless quantum channel, can increase the classical capacity of some noisy quantum channels by an arbitrarily large constant factor depending on the channel, relative to the best known classical capacity achievable without entanglement. The enhancement factor is greatest for very noisy channels, with positive classical capacity but zero quantum capacity. We obtain exact expressions for the entanglement-assisted capacity of depolarizing and erasure channels in d dimensions.

Quantum communication via noisy channels

2011

Quantum communication is at the heart of the quantum information theory. We study two types of quantum communication protocols over noisy transmission channels, i.e. super dense coding and cryptography protocols. In the first part of this thesis, for various scenarios, it is discussed how the super dense coding capacity is influenced by noisy quantum channels. The case of memoryless channels as well as those channels with memory which are modelled by uncorrelated and correlated noise, respectively, are considered. Explicitly Pauli channels over arbitrary dimensions are treated and the super dense coding capacity for some resource states is derived. For the qubit depolarizing channel, when noise is uncorrelated, the super dense coding capacity with respect to the input state is also optimized. This illustrates a threshold value of the noise parameter below which the super dense coding capacity is optimized by a maximally entangled initial state, while above the threshold value the su...