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.
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.
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.
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.
Quantum communication uses photons to transmit quantum bits (qubits) over long distances. By using this quantum technology, quantum key distribution (QKD), a secure communication protocol, ensures the security of encryption key exchange. Due to noise and eavesdropping in the quantum channel, errors can occur in the shared qubits after QKD key agreement phase. Therefore, we need a key verification phase to deal with inconsistent qubits (i.e. the wrong qubits at the receiving end). This key verification is also called information reconciliation. Recently, some reconciliation algorithms in QKD (RQKD) using polynomial consistency have been proposed. These RQKDs use the consistency property to find the correct polynomial (converted from the qubits) and then check the correctness of other qubits based on this polynomial to achieve reconciliation. All previous consistency-based RQKDs required such an extra step to check the correctness of other qubits after finding the correct polynomial. In this paper, we propose Enhanced RQKD (ERQKD), which uses consistency in a new way to improve key verification efficiency without requiring additional checking steps. Theoretical analysis and experiments indeed show that our ERQKD outperforms the two previous RQKDs.
One of the largest obstacles to building a quantum computer is gate error, where the physical evolution of the state of a qubit or group of qubits during a gate operation does not match the intended unitary transformation. Gate error stems from a combination of control errors and random single qubit errors from interaction with the environment. While great strides have been made in mitigating control errors, intrinsic qubit error remains a serious problem that limits gate fidelity in modern qubit architectures. Simultaneously, recent developments of small error-corrected logical qubit devices promise significant increases in logical state lifetime, but translating those improvements into increases in gate fidelity is a complex challenge. In this Letter, we construct protocols for gates on and between small logical qubit devices which inherit the parent device's tolerance to single qubit errors which occur at any time before or during the gate. We consider two such devices, a passive implementation of the three-qubit bit flip code, and the author's own [E. Kapit, Phys. Rev. Lett. 116, 150501 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.150501] very small logical qubit (VSLQ) design, and propose error-tolerant gate sets for both. The effective logical gate error rate in these models displays superlinear error reduction with linear increases in single qubit lifetime, proving that passive error correction is capable of increasing gate fidelity. Using a standard phenomenological noise model for superconducting qubits, we demonstrate a realistic, universal one- and two-qubit gate set for the VSLQ, with error rates an order of magnitude lower than those for same-duration operations on single qubits or pairs of qubits. These developments further suggest that incorporating small logical qubits into a measurement based code could substantially improve code performance.
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.
Standard security proofs of quantum-key-distribution (QKD) protocols often rely on symmetry arguments. In this paper, we prove the security of a three-state protocol that does not possess rotational symmetry. The three-state QKD protocol we consider involves three qubit states, where the first two states $\ensuremath{\mid}{0}_{z}⟩$ and $\ensuremath{\mid}{1}_{z}⟩$ can contribute to key generation, and the third state $\ensuremath{\mid}+⟩=(\ensuremath{\mid}{0}_{z}⟩+\ensuremath{\mid}{1}_{z}⟩)∕\sqrt{2}$ is for channel estimation. This protocol has been proposed and implemented experimentally in some frequency-based QKD systems where the three states can be prepared easily. Thus, by founding on the security of this three-state protocol, we prove that these QKD schemes are, in fact, unconditionally secure against any attacks allowed by quantum mechanics. The main task in our proof is to upper bound the phase error rate of the qubits given the bit error rates observed. Unconditional security can then be proved not only for the ideal case of a single-photon source and perfect detectors, but also for the realistic case of a phase-randomized weak coherent light source and imperfect threshold detectors. Our result in the phase error rate upper bound is independent of the loss in the channel. Also, we compare the three-state protocol with the Bennett-Brassard 1984 (BB84) protocol. For the single-photon source case, our result proves that the BB84 protocol strictly tolerates a higher quantum bit error rate than the three-state protocol, while for the coherent-source case, the BB84 protocol achieves a higher key generation rate and secure distance than the three-state protocol when a decoy-state method is used.