Qubits traveling through a quantum channel often interact with the environment which causes errors at the receiving end. These errors are often indistinguishable from errors caused by an eavesdropper and therefore must be corrected before a quantum key exchange protocol proceeds forward. Logical qubits are often used in order to make error correction possible. In this paper, we apply logical qubits to detect collective rotational errors and discuss how they can be corrected in the context of three-stage quantum key distribution protocol.
Qubits traveling through a quantum channel often interact with the environment which causes errors at the receiving end. These errors are often indistinguishable from errors caused by an eavesdropper and therefore must be corrected before a quantum key exchange protocol proceeds forward. Logical qubits are often used in order to make error correction possible. In this paper, we apply logical qubits to detect collective rotational errors and discuss how they can be corrected in the context of three-stage quantum key distribution protocol.
This paper discusses correcting small rotation errors in the three-stage quantum key distribution (QKD) protocol using only two logical qubits thereby increasing communication efficiency. Further, we can correct errors before they accumulate at every stage ensuring that the errors remain small. Three-stage QKD is tolerant of multi-photon pulses for key exchange and therefore more applicable in real world scenarios. However, given that it requires back and forth communication, any channel errors that occur accumulate. We discuss the proposed error correction protocol in detail and workout each step. We show how the two transacting parties can correct small rotation errors using just two logical qubits in a majority of cases. We compute the efficiency increase and bound on the magnitude of rotation errors that can be tolerated.
Quantum key distribution protocols (QKD) identify eavesdroppers on quantum channel based on laws of quantum mechanics. In the original BB84 protocol, unauthorized measurements on qubits are discovered after Alice and Bob sacrifice some random resulting key bits as a test and find out a mismatch rate. Decoy state protocol alerts photon number splitting attack when the decoy multiphoton pulses deliberately positioned by Alice are registered abnormally higher at Bob’s detectors than the single photon pulses are. E91 protocol is the first QKD protocol that ever brought about entangled atoms. Based on Bell’s theorem, a probability coefficient is constrained within a fixed range under the circumstances of interception. While in practice, bit error rate (BER) is not necessarily associated with vicious eavesdropping. Detection inefficiency, transmission loss, imperfect entanglement sources and many other factors contribute as false alarms. Error correction is an essential post-processing procedure to tolerate implementation limits, yet secure the accuracy of the transmitted key. Quantifying third party contaminations also helps setting an optimal BER threshold to decide if one should abandon all previous communications. In this work, we summarize major causes of bit error in various practical QKD protocols mentioned above and study whether error correction models, such as low-density parity-check code (LDPC), perform accordingly to different kinds of errors.
Quantum cryptography is essentially the quantum key distribution (QKD). In the context of QKD, one from two partners (Alice) generates and sends a sequence of qubits through a private quantum channel to another partner (Bob) and Bob receives the sequence and measures the state of each qubit. After the quantum transmission stage, Alice and Bob have almost identical qubit sequences. The erros are due to physical imperfections in the channel and presence of an eavesdropper. The next stage in QKD is key reconciliation (i.e. finding and correcting discrepancies between Alice's string and that of Bob). This reconciliation can be done by public discussion. Let us suppose there is a secret quantum channel between Alice and Bob through which Alice transmits a n-bit string A=(A1, A2,...,An)ε{0,1}n. Then Bob receives a n-bit string B=(B1, B2,...,Bn)ε{0,1)n. The string B differs from A due to the presence of noise and eavesdropper in the channel. One can estimate the bit error probability in the channel. For example, Bob can choose a random subset from his string and send it to Alice in public. Then Alice compares the received string with her corresponding subset and calculates the total number of protocol steps. The cascade scheme uses the interaction over the public channel to correct the secret strings by dividing them into the blocks of a fixed length. The length is determined from the bit error probability. A simple interactive routine is applied in each of these blocks. An error found in some block results in some action with other blocks. It is important to optimize the error-finding routines in standalone blocks as well as to organize the effective constrution of blocks with the object of protocol benchmark, information leakage and number of interactions between partners.
Error correction is a crucial stage in quantum key distribution (QKD) protocols—a promising field of modern cryptography where the secrecy of the shared key information is guaranteed by the laws of quantum mechanics. Currently, there are many effective approaches to error correction in QKD. However, most of them, due to their generic nature, fail to leverage the specific features of particular protocol implementations. This work demonstrates that accounting for the hardware specifics of a QKD system implementing the time-bin protocol enables a significant increase in error correction performance. For the considered QKD system, we have experimentally obtained estimates of the Quantum Bit Error Rate (QBER) observed for each combination of bit and detector. The differences in the obtained estimates reveal that the quantum channel can be modeled as a non-uniform binary channel. Furthermore, based on computational experiments with a model of the quantum channel, it was established that adapting the error correction procedure to its properties can achieve up to a 2.7-fold reduction in the LDPC code decoding failure rate at low error levels.
CASCADE protocol is an error detection and correction (EDC) method proposed firstly for use in quantum key distribution (QKD) systems. It is used to detect and correct all the errors in keys transmitted over a noisy quantum channel. This is done by sending some redundant information about the key to receiver as usual. However, just as differently, this extra information is sent over another noiseless classical channel after the quantum transmission is completely finished. Briefly, all the errors in noisy quantum communication are detected and corrected by a later noiseless classical communication using CASCADE protocol. In QKD literature, this EDC process is also called as information reconciliation (IR) or secret key reconciliation (SKR). For an IR protocol in QKD, one of the main performance measures is efficiency which depends on the amount of redundant information sent to make EDC possible. Since this extra information is transmitted over public channels, everyone can get it easily. Because this can damage the secrecy of keys that must be kept secret from third parties, more efficient, that is revealing less information about keys, IR methods are needed. In this paper, we present more efficient implementations of CASCADE protocol, using some inherent information already available in the protocol, exactly known bits and already known parities. This information is used in error detection and correction steps of the protocol to decrease the redundancy in redundant information. Our experiments have shown that the resulting protocols have higher efficiency than both all the previous CASCADE versions and several other more recently proposed IR methods.
Quantum key distribution (QKD) enables secure communication by using the principles of quantum mechanics. A critical stage in QKD protocols such as BB84 is information reconciliation, where the communicating parties correct errors in their sifted sequences without revealing extra information to a potential eavesdropper. The CASCADE protocol is a widely used interactive error-correction algorithm for this purpose. The classical CASCADE and its known modifications perform well under the assumption of uniformly distributed errors in the quantum channel. However, this assumption can break down in real conditions, where short-term noise bursts create clusters of errors. This paper proposes a modification of the CASCADE designed to improve its efficiency in channels with time-varying, non-uniform error distributions. The main idea is to identify and discard blocks with a relatively high concentration of errors during reconciliation, preventing inefficient correction attempts and reducing the number of communication rounds. Two new modifications based on existing CASCADE variants are presented. The proposed approach reduces the number of interactions, which is a critical performance metric for reconciliation protocols.