Classical locally recoverable codes (LRCs) have become indispensable in distributed storage systems. They provide efficient recovery in terms of localized errors. Quantum LRCs have very recently been introduced for th...
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Classical locally recoverable codes (LRCs) have become indispensable in distributed storage systems. They provide efficient recovery in terms of localized errors. Quantum LRCs have very recently been introduced for their potential application in quantum data storage. In this paper, we use classical LRCs to investigate quantum LRCs. We prove that the parameters of quantum LRCs are bounded by their classical counterparts. We deduce bounds on the parameters of quantum LRCs from bounds on the parameters of the classical ones. We establish a characterization of optimal pure quantum LRCs based on classical codes with specific properties. Using well-crafted classical LRCs as ingredients in the construction of quantum css codes, we offer the first construction of several families of optimal pure quantum LRCs.
A novel, practical and convenient approach to constructing Calderbank-Shor Steane (css) codes based on factor graphs is presented in this paper. Our proposed method is applied to solve two problems associated with con...
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A novel, practical and convenient approach to constructing Calderbank-Shor Steane (css) codes based on factor graphs is presented in this paper. Our proposed method is applied to solve two problems associated with constructing CCS codes. One is judging whether a code is a weakly self-dual code or not, the other is finding the generator matrix and parity-check matrix of a weakly self-dual code. The novelty, practicality and convenience of the approach are shown as follows. First, the approach is a hitherto unexplored one to constructing css codes. Second, the judgment of a weakly self-dual code is entirely based on factor graphs. Namely, we consider a code a weakly self-dual one when the Tanner graph or convolutional factor graph of its dual code can be obtained by that of its own via our proposed transform TR-->L. Finally, we can obtain the generator matrix and parity-check Matrix of a weakly self-dual code via factor graphs other than conventional algebra methods, which allow us avoid matrix Computation to get them. An example is given to show how to construct quantum css code based on factor graphs. The method can be extended to other css codes. (C) 2007 Elsevier Inc. All rights reserved.
Quantum key distribution (QKD) allows authenticated parties to share secure keys. Its security comes from quantum physics rather than computational complexity. The previous work has been able to demonstrate the securi...
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Quantum key distribution (QKD) allows authenticated parties to share secure keys. Its security comes from quantum physics rather than computational complexity. The previous work has been able to demonstrate the security of the BB84 protocol based on the uncertainty principle, entanglement purification and information theory. In the security proof method based on entanglement purification, it is assumed that the information of Calderbank-Shor-Steane (css) error correction code cannot be leaked, otherwise, it is insecure. However, there is no quantitative analysis of the relationship between the parameter of css code and the amount of information leaked. In the attack and defense strategy of the actual quantum key distribution system, especially in the application of the device that is easy to lose or out of control, it is necessary to assess the impact of the parameter leakage. In this paper, we derive the relationship between the leaked parameter of css code and the amount of the final key leakage based on the BB84 protocol. Based on this formula, we simulated the impact of different css code parameter leaks on the final key amount. Through the analysis of simulation results, the security of the BB84 protocol is inversely proportional to the value of n - k(1) and k(1) - k(2) in the case of the css code leak.
We consider the secure quantum communication over a network with the presence of a malicious adversary who can eavesdrop and contaminate the states. The network consists of noiseless quantum channels with the unit cap...
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We consider the secure quantum communication over a network with the presence of a malicious adversary who can eavesdrop and contaminate the states. The network consists of noiseless quantum channels with the unit capacity and the nodes which applies noiseless quantum operations. As the main result, when the maximum number $m_code$ of the attacked channels over the entire network uses is less than a half of the network transmission rate $m_code$ (i.e., $m_code < m_code/2$ ), our code implements secret and correctable quantum communication of the rate $m_code-2m_code$ by using the network asymptotic number of times. Our code is universal in the sense that the code is constructed without the knowledge of the specific node operations and the network topology, but instead, every node operation is constrained to the application of an invertible matrix to the basis states. Moreover, our code requires no classical communication. Our code can be thought of as a generalization of the quantum secret sharing.
In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasicyclic (QC) low-density parity-check (LDPC) codes. Using the proposed approach one may construct some ne...
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In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasicyclic (QC) low-density parity-check (LDPC) codes. Using the proposed approach one may construct some new quantum codes with various lengths and rates of no cycles-length 4 in their Tanner graphs. In addition, these constructed codes have the advantages of simple implementation and low-complexity encoding. Finally, the decoding approach for the proposed quantum QC LDPC is investigated.
Quantum private comparison (QPC) allows us to protect private information during its comparison. In the past, various three-party quantum protocols have been proposed that claim to work well under noisy conditions. He...
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Quantum private comparison (QPC) allows us to protect private information during its comparison. In the past, various three-party quantum protocols have been proposed that claim to work well under noisy conditions. Here, we tackle the problem of QPC under noise. We analyze the EPR-based protocol under depolarizing noise, bit flip and phase flip noise. We show how noise affects the robustness of the EPR-based protocol. We then present a straightforward protocol based on css codes to perform QPC which is robust against noise and secure under general attacks.
We give a construction of quantum LDPC codes of dimension Theta(logN) and distance Theta(N/logN) as the code length N -> infinity. Using a product of chain complexes this construction also provides a family of quan...
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We give a construction of quantum LDPC codes of dimension Theta(logN) and distance Theta(N/logN) as the code length N -> infinity. Using a product of chain complexes this construction also provides a family of quantum LDPC codes of distance Omega(N1-alpha/2/logN) and dimension Omega(N-alpha logN), where 0 <= alpha < 1. We also introduce and study a new operation called lifted product, which naturally generalizes the product operations for quantum codes and chain complexes. Moreover, as a simple byproduct of our results on quantum codes, we obtain a new result on classical codes. We show that for any fixedR < 1 there exists an asymptotically good family of classical quasi-cyclic LDPC codes of rate at least R with, in some sense, optimal circulant size Omega(N/logN) as the code length N -> infinity.
We investigate css and css-T quantum error-correcting codes from the point of view of their existence, rarity, and performance. We give a lower bound on the number of pairs of linear codes that give rise to a css code...
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We investigate css and css-T quantum error-correcting codes from the point of view of their existence, rarity, and performance. We give a lower bound on the number of pairs of linear codes that give rise to a css code with good correction capability, showing that such pairs are easy to produce with a randomized construction. We then prove that css-T codes exhibit the opposite behaviour, showing also that, under very natural assumptions, their rate and relative distance cannot be simultaneously large. This partially answers an open question on the feasible parameters of css-T codes. We conclude with a simple construction of css-T codes from Hermitian curves. The paper also offers a concise introduction to css and css-T codes from the point of view of classical coding theory.
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