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International Journal of Quantum Information

SOFT-PROCESSING FOR INFORMATION RECONCILIATION IN QKD APPLICATIONS

M. Mondin, MARIA DELGADO, Fabio Mesiti, F. Daneshgaran

Published Jan 1, 2011• 7 citations
Publisher

Abstract

In this manuscript, a composite channel model for quantum key distribution is considered, including both a "hard output" quantum channel and a "soft output" classic channel. The metrics derived from the two channels are jointly processed at the receiver, exploiting capacity achieving soft-metric based iteratively decoded block codes, and soft-information based information reconciliation and privacy amplification techniques are proposed. The performance of the proposed mixed-soft-metric algorithms is analyzed as a function of the system parameters.

DOI
10.1142/s0219749911007174

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In this manuscript, a composite channel model for quantum key distribution is considered, including both a "hard output" quantum channel and a "soft output" classic channel. The metrics derived from the two channels are jointly processed at the receiver, exploiting capacity achieving soft-metric based iteratively decoded block codes, and soft-information based information reconciliation and privacy amplification techniques are proposed. The performance of the proposed mixed-soft-metric algorithms is analyzed as a function of the system parameters.
This paper deals with soft-information based information reconciliation and data sifting for Quantum Key Distribution (QKD).We propose a novel composite channel model for QKD, which includes both a hard output quantum channel and a soft output classic channel. The metrics derived from the two channels are jointly processed at the receiver, exploiting capacity achieving soft-metric based iteratively decoded block codes. The performance of the proposed mixed-softmetric algorithms are studied via simulations as a function of the system parameters. The core ideas of the paper are: a) employing FEC coding as opposed to two-way communication for information reconciliation, b) exploiting all the available information for data processing at the receiver including information available from the quantum channel, since optimized use of this information can lead to significant performance improvement.
This thesis deals with soft-information based information reconciliation and data sifting for Quantum Key Distribution (QKD). A novel composite channel model for QKD is identified, which includes both a hard output quantum channel and a soft output classic channel. The Log-Likelihood Ratios, - also called soft-metrics - derived from the two channels are jointly processed at the receiver, exploiting capacity achieving soft-metric based iteratively decoded block codes. The performance of the proposed mixed-soft-metric algorithms are studied via simulations as a function of the system parameters. The core ideas of the thesis are employing Forward Error Correction (FEC) coding as opposed to two-way communication for information reconciliation in QKD schemes, exploiting all the available information for data processing at the receiver including information available from the quantum channel, since optimized use of this information can lead to significant performance improvement, and providing a security versus secret-key rate trade-off to the end-user within the context of QKD systems.
This paper deals with the use of sparse-graph codes (and in particular, Low density Parity Check - LDPC - codes) for information reconciliation and pre-data sifting in Quantum Key Distribution (QKD). We model the overall channel used in QKD as the parallel of the quantum channel, where the actual quantum key is transmitted, and a public Additive White Gaussian Noise (AWGN) channel, where the parity check bits are transmitted. The metrics derived from the two channels are jointly processed at the receiver by properly combining the metrics derived from the two channels and exploiting capacity achieving soft-metric based iteratively decoded sparse-graph codes. The information derived from the iterative decoder are used to (1) perform error correction of the received q-bits; (2) detect the possible presence of unauthorized eavesdroppers; (3) perform pre-data sifting. The performance of the proposed mixed-soft-metric algorithms are studied via simulations as a function of the system parameters. The core ideas of the paper are: a) employing FEC coding as opposed to two-way communication for information reconciliation, minimizing the interactions between transmitter and receiver; b) exploiting all the available information for data processing at the receiver including information available from the quantum channel; c) using convergence properties of the code to estimate QBER and presence of an eavesdropper.
The focus of this research activity is to work on pragmatic information reconciliation applied to QKD schemes based on single photon or weak pulse laser (WPL) sources, so as to use feed-forward techniques which minimize the interaction between transmitter and receiver. The core ideas of the thesis are employing Forward Error Correction (FEC) coding as opposed to two-way communication for information reconciliation in QKD schemes, exploiting all the available information for data processing at the receiver including information available from the quantum channel, since optimized use of this information can lead to significant performance improvement, and providing a security versus secret-key rate trade-off to the end-user within the context of QKD systems. Moreover, as shown by accurate experimental studies, the communication channel used for quantum key exchange is not able to reach high levels of reliability (the Quantum Bit Error Rate -QBER may have a high value), both because of the inherent characteristics of the system, and of the presence of a possible attacker. In order to obtain acceptable residual error rates, it is necessary to use a parallel classical and public channel, characterized by high transmission rates and low error rates, on which to transmit only the redundancy bits of systematic channel codes with performance possibly close to the capacity limit. Furthermore, since the more redundancy is added by the channel code, the more the corresponding information can be used to decipher the private message itself, it becomes necessary to design high-rate codes obtained by puncturing a low-rate mother code, possibly achieving a redundancy such that elements of the secret message cannot be uniquely determined from the redundancy itself, so for that purpose we designed high rate LDPC codes. Using high rate codes increases the security with trade-off to performance. Other low photon number applications have also been considered, such as weak-laser pulses (WLP) communication. For that purpose, a low-complexity photon-counting receiver has been considered which may be employed in long-distance amplification-free classical optical communication schemes, and which is typically modeled as an equivalent Binary Symmetric Channel (BSC). We have developed a time varying Binary Input-Multiple Output (BIMO) channel model for this low-complexity photon-counting receiver, and analyzed its performance in presence of soft-metric based capacity approaching iteratively decoded error correcting codes, such as soft-metric based Low Density Parity Check (LDPC) codes and polar codes. We show that the classical channel capacity of the suggested BIMO model is higher than the capacity of the BSC model, and that the use of the BIMO model allows to feed the channel decoder with soft information, in the form of Log-Likelihood Ratios (LLRs), achieving a significant reduction in Bit Error Rate (BER) and Frame Error Rate (FER) with respect to classical hard-metric-based schemes which should be used in conjunction with a BSC channel model.
The postprocessing or secret-key distillation process in quantum key distribution (QKD) mainly involves two well-known procedures: information reconciliation and privacy amplification. Information or key reconciliation has been customarily studied in terms of efficiency. During this, some information needs to be disclosed for reconciling discrepancies in the exchanged keys. The leakage of information is lower bounded by a theoretical limit, and is usually parameterized by the reconciliation efficiency (or inefficiency), i.e. the ratio of additional information disclosed over the Shannon limit. Most techniques for reconciling errors in QKD try to optimize this parameter. For instance, the well-known Cascade (probably the most widely used procedure for reconciling errors in QKD) was recently shown to have an average efficiency of 1.05 at the cost of a high interactivity (number of exchanged messages). Modern coding techniques, such as rate-adaptive low-density parity-check (LDPC) codes were also shown to achieve similar efficiency values exchanging only one message, or even better values with few interactivity and shorter block-length codes.
Quantum key distribution (QKD) is a cryptographic communication protocol that utilizes quantum mechanical properties for provable absolute security against an eavesdropper. The communication is carried between two terminals using random photon polarization states represented through quantum states. Both these terminals are interconnected through disjoint quantum and classical channels. Information reconciliation using delay controlled joint decoding is performed at the receiving terminal. Its performance is characterized using data and error rates. Achieving low error rates is particularly challenging for schemes based on error correcting codes with short code lengths. This article addresses the decoding process using ordered statistics decoding for information reconciliation of both short and medium length Bose–Chaudhuri–Hocquenghem codes over a QKD link. The link’s quantum channel is modeled as a binary symmetric quantum depolarization channel, whereas the classical channel is configured with additive white Gaussian noise. Our results demonstrate the achievement of low bit error rates, and reduced decoding complexity when compared to other capacity achieving codes of similar length and configuration.