相关论文: Quantum MacWilliams Identities

A hybrid code can simultaneously encode classical and quantum information into quantum digits such that the information is protected against errors when transmitted through a quantum channel. It is shown that a hybrid code has the…

In this paper, we consider codes over finite fields, finite abelian groups, and finite Frobenius rings. For such codes, the complete weight enumerator and the Hamming weight enumerator serve as powerful tools. These two types of weight…

We study two complementary diagnostics of bipartite quantum channels, namely fidelity preservation across different classes of input states and entanglement generation from product inputs, given by properly defined entangling power for…

The weight generating functions associated with convolutional codes (CCs) are based on state space realizations or the weight adjacency matrices (WAMs). The MacWilliams identity for CCs on the WAMs was first established by Gluesing-…

In the 1960s, MacWilliams proved that the Hamming weight enumerator of a linear code over a finite field completely determines, and is determined by, the Hamming weight enumerator of its dual code. In particular, if two linear codes have…

We study sequences of linear or affine codes with uniform weight spectrum, i.e., a part of codewords with any fixed weight tends to zero. It is proved that a sequence of linear codes has a uniform weight spectrum if the number of vectors…

In this note we show that the weight enumerators of a real quantum error correcting code with $ X $ and $ Z $ exactly transversal must satisfy certain identities. One consequence of these identities is that if the code is error detecting…

Quantum channels depending on a number of classical control parameters are considered. Assuming the stochastic fluctuations of the control parameters in the small errors limit it is shown that the channel fidelity is equal to the average…

The paper analyzes the behavior of quantum channels, particularly in large dimensions, by proving various properties of the quantum gate fidelity. Many of these properties are of independent interest in the theory of distance measures on…

We analyze the performance of quantum stabilizer codes, one of the most important classes for practical implementations, on both symmetric and asymmetric quantum channels. To this aim, we first derive the weight enumerator (WE) for the…

Classification of different forms of quantum entanglement is an active area of research, central to development of effective quantum computers, and similar to classification of error-correction codes, where code duality is broadened to…

We study tree kinds of quantum fidelity. Usual Uhlmann's fidelity, minus of f-divergence when $f(x)=-\sqrt{x}$, and the one introduced by the author via reverse test. All of them are quantum extensions of classical fidelity, where the first…

Burst errors are very common in practice. There have been many designs in order to control and correct such errors. Recently, a new class of byte error control codes called spotty byte error control codes has been specifically designed to…

We derive universal codes for simultaneous transmission of classical messages and entanglement through quantum channels, possibly under attack of a malignant third party. These codes are robust to different kinds of channel uncertainty. To…

General properties of quantum systems which interact with stochastic environment are studied with a strong emphasis on the role of physical symmetries. The similarity between the fidelity which is used to characterize the stability of such…

This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable (in principle rather than in practice). Various problems in the context of…

We study the generalized rank weight distribution of a linear code. First, we provide a MacWilliams-type identity which relates the distributions of a code and its dual. Then, we give a formula for the enumerator polynomial. Finally, we…

We derive a general limit on the fidelity of a quantum channel conveying an ensemble of pure states. Unlike previous results, this limit applies to arbitrary coding and decoding schemes, including nonunitary decoding. This establishes the…

Fidelity is a fundamental measure for the closeness of two quantum states, which is important both from a theoretical and a practical point of view. Yet, in general, it is difficult to give good estimates of fidelity, especially when one…

Past few years have seen an extensive use of RAM chips with wide I/O data (e.g. 16, 32, 64 bits) in computer memory systems. These chips are highly vulnerable to a special type of byte error, called an $m$-spotty byte error, which can be…