This thesis investigates the feasibility of utilising classical error-correcting codes in quantum communications, specifically in the entanglement-assisted communication of classical information over quantum depolarising channels. A classical-quantum communication system is presented, which relies on error-correction in the classical domain to achieve a classical information rate that approaches the entanglement-assisted capacity of a depolarising channel. Classical information is transmitted over the quantum channel by means of the superdense coding protocol. Different scenarios for the system are considered, including the noiseless and noisy distribution of initial entanglement resources and the use of higher-order entangled states. The overall transmission model corresponding to each scenario is shown to reduce to a classical, discrete and memoryless channel. The capacities of these equivalent classical channels are derived, and an inherent capacity loss when binary classical error correcting codes are employed is identified, motivating the use of non-binary codes. It is ultimately demonstrated that duo-binary turbo codes outperform binary turbo codes in all investigated scenarios, a result of the former's ability to exploit correlations between the pairs of classical bits communicated via the superdense coding protocol.
This thesis investigates the feasibility of utilising classical error-correcting codes in quantum communications, specifically in the entanglement-assisted communication of classical information over quantum depolarising channels. A classical-quantum communication system is presented, which relies on error-correction in the classical domain to achieve a classical information rate that approaches the entanglement-assisted capacity of a depolarising channel. Classical information is transmitted over the quantum channel by means of the superdense coding protocol. Different scenarios for the system are considered, including the noiseless and noisy distribution of initial entanglement resources and the use of higher-order entangled states. The overall transmission model corresponding to each scenario is shown to reduce to a classical, discrete and memoryless channel. The capacities of these equivalent classical channels are derived, and an inherent capacity loss when binary classical error correcting codes are employed is identified, motivating the use of non-binary codes. It is ultimately demonstrated that duo-binary turbo codes outperform binary turbo codes in all investigated scenarios, a result of the former's ability to exploit correlations between the pairs of classical bits communicated via the superdense coding protocol.
We investigate the use of non-binary classical error-correcting codes in facilitating reliable, entanglement-assisted communication of classical information over quantum depolarising channels. A classical-quantum communication system is presented, which relies on error-correction in the classical domain to achieve an information rate that approaches the entanglement-assisted capacity of the quantum channel. Classical information is transmitted over the channel by means of the superdense coding protocol, and the impact of the noisy distribution of initial entanglement resources on the achievable information rate is considered. In this context, the transmission model is equivalent to a non-binary discrete symmetric classical channel, which motivates the use of non-binary error-correcting codes capable of exploiting correlations between the pairs of classical bits communicated via the superdense coding protocol. We illustrate this principle by showing that duo-binary turbo codes significantly outperform binary turbo codes in the considered scenarios.
We have conceived a near-capacity code design for entanglement-assisted classical communication over the quantum depolarizing channel. The proposed system relies on efficient near-capacity classical code designs for approaching the entanglement-assisted classical capacity of a quantum depolarizing channel. It incorporates an Irregular Convolutional Code (IRCC), a Unity Rate Code (URC) and a soft-decision aided Superdense Code (SD), which is hence referred to as an IRCC-URC-SD arrangement. Furthermore, the entanglement-assisted classical capacity of an N-qubit superdense code transmitted over a depolarizing channel is invoked for benchmarking. It is demonstrated that the proposed system operates within 0.4 dB of the achievable noise limit for both 2-qubit as well as 3-qubit SD schemes. More specifically, our design exhibits a deviation of only 0.062 and 0.031 classical bits per channel use from the corresponding 2-qubit and 3-qubit capacity limits, respectively. The proposed system is also benchmarked against the classical convolutional and turbo codes.
We introduce a robust quantum communication protocol that integrates classical error-control coding, entanglement distribution, and superdense coding. Classical error-correcting codes are used to mitigate dark counts and photon losses by determining the positions of qubit transmissions and protecting the data embedded through superdense coding. We derive conditions on the employed codes that guarantee successful error correction under a bounded error-frequency model. Moreover, upper bounds are derived on the performance of conventional superdense coding protected by classical error correction. It is shown that, under the same constraints on error frequency, suitable code configurations of the proposed protocol can exceed those upper bounds both in terms of data rate and energy efficiency. Finally, we develop a physical error model based on fiber attenuation, detector efficiency, dark counts, and time-slot duration, and use it to evaluate the effective performance of different configurations of error-correcting codes. The proposed approach is primarily suited for short-distance quantum links, as in Quantum Local Area Network (QLAN) where it can provide high communication throughput while integrating entanglement distribution directly into the communication process.
Quantum parallel processing techniques are capable of solving certain complex problems at a substantially lower complexity than their classical counterparts. From the perspective of telecommunications, this quantum-domain parallel processing provides a plausible solution for achieving full-search based multi-stream detection, which is vital for future gigabit-wireless systems. The peculiar laws of quantum mechanics have also spurred interest in the absolutely secure quantum-based communication systems. Unfortunately, quantum decoherence imposes a hitherto insurmountable impairment on the practical implementation of quantum computation as well as on quantum communication systems, which may be overcome with the aid of efficient error correction codes. In this thesis, we design error correction codes for the quantum domain, which is an intricate journey from the realm of classical channel coding theory to that of the Quantum Error Correction Codes (QECCs). Since quantum-based communication systems are capable of supporting the transmission of both classical and quantum information, we initially focus our attention on the code design for entanglementassisted classical communication over the quantum depolarizing channel. We conceive an Extrinsic Information Transfer (EXIT) chart aided near-capacity classical-quantum code design, which invokes a classical Irregular Convolutional Code (IRCC) and a Unity Rate Code (URC) in conjunction with our proposed soft-decision aided SuperDense Code (SD). Hence, it is referred to as an ‘IRCC-URCSD’ arrangement. The proposed scheme is intrinsically amalgamated both with 2-qubit as well as 3-qubit SD coding protocols and it is benchmarked against the corresponding entanglement-assisted classical capacity. Since the IRCC-URC-SD scheme is a bit-based design, it incurs a capacity loss. As a further advance, we design a symbol based concatenated code design, referred to as a symbol-based ‘CC-URC-SD’, which relies on a single-component classical Convolutional Code (CC). Additionally, for the sake of reducing the associated decoding complexity, we also investigate the impact of the constraint length of the convolutional code on the achievable performance. Our initial designs, namely IRCC-URC-SD and CC-URC-SD, exploit redundancy in the classical domain. By contrast, QECCs relying on the quantum-domain redundancy are indispensable for conceiving a quantum communication system supporting the transmission of quantum information and also for quantum computing. Therefore, we next provide insights into the transformation from the family of classical codes to the class of quantum codes known as ‘Quantum Stabilizer Codes’ (QSC), which invoke the classical syndrome decoding. Particularly, we detail the underlying quantum-to classical isomorphism, which facilitates the design of meritorious families of QECCs from the known classical codes. We further study the syndrome decoding techniques operating over classical channels, which may be exploited for decoding QSCs. In this context, we conceive a syndrome-based block decoding approach for the classical Turbo Trellis Coded Modulation (TTCM), whose performance is investigated for transmission over an Additive White Gaussian Noise (AWGN) channel as well as over an uncorrelated Rayleigh fading channel. Pursuing our objective of designing efficient QECCs, we next consider the construction of Hashingbound-approaching concatenated quantum codes. In this quest, we appropriately adapt the conventional non-binary EXIT charts for Quantum Turbo Codes (QTCs) by exploiting the intrinsic quantumto- classical isomorphism. We further demonstrate the explicit benefit of our EXIT-chart technique for achieving a Hashing-bound-approaching code design. We also propose a generically applicable structure for Quantum Irregular Convolutional Codes (QIRCCs), which can be dynamically adapted to a specific application scenario with the aid of the EXIT charts. More explicitly, we provide a detailed design example by constructing a 10-subcode QIRCC and use it as an outer code in a concatenated quantum code structure for evaluating its performance. Working further in the direction of iterative code structures, we survey Quantum Low Density Parity Check (QLPDC) codes from the perspective of code design as well as in terms of their decoding algorithms. Furthermore, we propose a radically new class of high-rate row-circulant Quasi-Cyclic QLDPC (QC-QLDPC) codes, which can be constructed from arbitrary row-circulant classical QC LDPC matrices. We also conceive a modified non-binary decoding algorithm for homogeneous Calderbank-Shor-Steane (CSS)-type QLDPC codes, which is capable of alleviating the problems imposed by the unavoidable length-4 cycles. Our modified decoder outperforms the state-of-the-art decoders in terms of their Word Error Rate (WER) performance, despite imposing a reduced decoding complexity. Finally, we intricately amalgamate our modified decoder with the classic Uniformly-ReWeighted Belief Propagation (URW-BP) for the sake of achieving further performance improvement.
Quantum communication is at the heart of the quantum information theory. We study two types of quantum communication protocols over noisy transmission channels, i.e. super dense coding and cryptography protocols. In the first part of this thesis, for various scenarios, it is discussed how the super dense coding capacity is influenced by noisy quantum channels. The case of memoryless channels as well as those channels with memory which are modelled by uncorrelated and correlated noise, respectively, are considered. Explicitly Pauli channels over arbitrary dimensions are treated and the super dense coding capacity for some resource states is derived. For the qubit depolarizing channel, when noise is uncorrelated, the super dense coding capacity with respect to the input state is also optimized. This illustrates a threshold value of the noise parameter below which the super dense coding capacity is optimized by a maximally entangled initial state, while above the threshold value the super dense coding capacity is optimized by a product state. For Pauli channels, with correlated noise, the case of non unitary encoding is studied and the super dense coding capacity is derived. The first part of this thesis is concluded with an example for multipartite super dense coding.
In the second part of the thesis, the problem of optimal eavesdropping on noisy states in quantum key distribution is investigated. The case of the six state protocol, when the signal states are mixed with white noise, is considered. This situation may arise either when Alice deliberately adds noise to the signal states before they leave her lab, or, in a realistic scenario when the eavesdropper (referred to as Eve) is not assumed to replace the noisy quantum channel by a noiseless one. For individual attacks, we find Eve's optimal mutual information with Alice as a function of the quantum bit error rate. Finally, the results illustrate that adding noise on the quantum level can make quantum key distribution more robust against eavesdropping.
Abstract Entanglement-assisted classical communication (EACC) aims to enhance communication systems using entanglement as an additional resource. However, there is a scarcity of explicit protocols designed for finite transmission scenarios, which presents a challenge for real-world implementation. In response, we introduce a new EACC scheme capable of correcting a fixed number of erasures/errors. It can be adjusted to the available amount of entanglement and sends classical information over a quantum channel. We establish a general framework to accomplish such a task by reducing it to a classical problem. Comparing with specific bounds, we identify optimal parameter ranges. The scheme requires only the implementation of super-dense coding which has been demonstrated successfully in experiments. Furthermore, our results show that an adaptable entanglement use confers a communication advantage. Overall, our work sheds light on how entanglement can elevate various finite-length communication protocols, opening new avenues for exploration in the field.