The existing noise channel coding methods need to be optimised in terms of channel capacity and algorithm complexity. Based on the characteristics of the quantum 5-symbol confusion-channel model and the theory of matrices, a coding method is proposed which combines the 5-symbol confusion channel with the quantum-superposition-state coding. This coding method uses two isomorphism steps to obtain the zero-error code words, which are the isomorphism between quantum superposition states and vectors and the isomorphism between channels and matrices. The theoretical derivation proves that the channel capacity is able to increase by employing quantum zero-error coding other than its classical counterpart.
The existing noise channel coding methods need to be optimised in terms of channel capacity and algorithm complexity. Based on the characteristics of the quantum 5-symbol confusion-channel model and the theory of matrices, a coding method is proposed which combines the 5-symbol confusion channel with the quantum-superposition-state coding. This coding method uses two isomorphism steps to obtain the zero-error code words, which are the isomorphism between quantum superposition states and vectors and the isomorphism between channels and matrices. The theoretical derivation proves that the channel capacity is able to increase by employing quantum zero-error coding other than its classical counterpart.
The existing noise channel coding methods need to be optimised in terms of channel capacity and algorithm complexity. Based on the characteristics of the quantum 5-symbol confusion-channel model and the theory of matrices, a coding method is proposed which combines the 5-symbol confusion channel with the quantum-superposition-state coding. This coding method uses two isomorphism steps to obtain the zero-error code words, which are the isomorphism between quantum superposition states and vectors and the isomorphism between channels and matrices. The theoretical derivation proves that the channel capacity is able to increase by employing quantum zero-error coding other than its classical counterpart.
In view of the lack of effective coding schemes for quantum zero-error channel,based on the characteristics of quantum five-symbol confusion channel model and the theory of matrix theory,a coding method of five-symbol confusion channel combining quantum superposition state zero-error coding is proposed.In order to improve the channel capacity and reduce the algorithm complexity,zero-error coding is performed by using the isomorphism relationship between quantum superposition states and vectors and between channels and matrices.Analysis results show that this method has higher channel capacity and coding efficiency than the classical confusion channel coding method.
Today's sensor networks need robustness, security and efficiency with a high level of assurance. Error correction is an effective communicational technique that plays a critical role in maintaining robustness in informational transmission. The general way to tackle this problem is by using forward error correction (FEC) between two communication parties. However, by applying zero-error coding one can assure information fidelity while signals are transmitted in sensor networks. In this study, we investigate zero-error coding via both classical and quantum channels, which consist of n obfuscated symbols such as Shannon's zero-error communication. As a contrast to the standard classical zero-error coding, which has a computational complexity of , a general approach is proposed herein to find zero-error codewords in the case of quantum channel. This method is based on a n-symbol obfuscation model and the matrix's linear transformation, whose complexity dramatically decreases to . According to a comparison with classical zero-error coding, the quantum zero-error capacity of the proposed method has obvious advantages over its classical counterpart, as the zero-error capacity equals the rank of the quantum coefficient matrix. In particular, the channel capacity can reach n when the rank of coefficient matrix is full in the n-symbol multilateral obfuscation quantum channel, which cannot be reached in the classical case. Considering previous methods such as low density parity check code (LDPC), our work can provide a means of error-free communication through some typical channels. Especially in the quantum case, zero-error coding can reach both a high coding efficiency and large channel capacity, which can improve the robustness of communication in sensor networks.
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 zero-error classical capacity of a quantum channel is the asymptotic rate at which it can be used to send classical bits perfectly, so that they can be decoded with zero probability of error. The study of zero-error capacities dates right back to Shannon and the early days of information theory. We show that there exist pairs of quantum channels, neither of which individually have any zero-error capacity whatsoever (even if arbitrarily many uses of the channels are available), but such that access to even a single copy of both channels allows classical information to be sent perfectly reliably. In other words, we prove that the zero-error classical capacity can be superactivated. This result is the first example of superactivation of a classical capacity of a quantum channel. We further strengthen this result to show that there exist pairs of channels, neither of which have any zero-error classical capacity (as before), yet for which access to one copy of the joint channel even allows far more delicate quantum information to be transmitted perfectly. This subsumes the first result, and also implies that the quantum zero-error capacity can be superactivated. But it is strictly stronger than either of these. Indeed, this is the strongest conceivable form of superactivation, and nothing similar is possible for standard Shannon capacities of quantum channels or for zero-error capacities of classical channels.
The zero-error capacity of a channel is the rate at which it can send information perfectly, with zero probability of error, and has long been studied in classical information theory. We show that the zero-error capacity of quantum channels exhibits an extreme form of non-additivity, one which is not possible for classical channels, or even for the usual capacities of quantum channels. By combining probabilistic arguments with algebraic geometry, we prove that there exist channels E1 and E2 with no zero-error classical capacity whatsoever, C0(E1) = C0(E2) = 0, but whose joint zero-error quantum capacity is positive, Q0(E1 ⊗ E2) ≥ 1. We term this striking effect super-duper-activation, as it implies that both the classical and quantum zero-error capacities of these channels can be superactivated simultaneously, whilst being a strictly stronger property of capacities. Superactivation of the quantum zero-error capacity was not previously known.