This article explores the performance of quantum communication systems in the presence of noise and focuses on finding the optimal encoding for maximizing the classical communication rate, approaching the classical capacity in some scenarios. Instead of theoretically bounding the ultimate capacity of the channel, we adopt a signal processing perspective to estimate the achievable performance of a physically available but otherwise unknown quantum channel. By employing a variational algorithm to estimate the trace distance between quantum states, we numerically determine the optimal encoding protocol for the amplitude damping and Pauli channels. Our simulations demonstrate the convergence and accuracy of the method with a few iterations, confirming that optimal conditions for binary quantum communication systems can be variationally determined with minimal computation. Furthermore, since the channel knowledge is not required at the transmitter or at the receiver, these results can be employed in arbitrary quantum communication systems, including satellite-based communication systems, a particularly relevant platform for the quantum Internet.
This article explores the performance of quantum communication systems in the presence of noise and focuses on finding the optimal encoding for maximizing the classical communication rate, approaching the classical capacity in some scenarios. Instead of theoretically bounding the ultimate capacity of the channel, we adopt a signal processing perspective to estimate the achievable performance of a physically available but otherwise unknown quantum channel. By employing a variational algorithm to estimate the trace distance between quantum states, we numerically determine the optimal encoding protocol for the amplitude damping and Pauli channels. Our simulations demonstrate the convergence and accuracy of the method with a few iterations, confirming that optimal conditions for binary quantum communication systems can be variationally determined with minimal computation. Furthermore, since the channel knowledge is not required at the transmitter or at the receiver, these results can be employed in arbitrary quantum communication systems, including satellite-based communication systems, a particularly relevant platform for the quantum Internet.
We propose a framework to variationally obtain detectable capacity bounds for quantum channels. The proposal of this framework is motivated by the difficulty of estimating the von Neumann entropy of an unknown quantum state. Instead of estimating the von Neumann entropy at the channel output, we propose to estimate the state purity---which can be measured by a single measurement setting---followed by bounding the von Neumann entropy from above and below. This procedure leads to new upper and lower bounds on various communication rates of quantum channels for some fixed input states. Then, by utilizing the variational method to find optimal input states we obtain lower bounds on (i) the quantum capacity of arbitrary channels, (ii) the entanglement-assisted classical capacity of arbitrary channels, and (iii) the classical capacity of covariant channels. Corresponding to these lower bounds, we also obtain upper bounds on (i) N-shot coherent information, (ii) the entanglement-assisted classical capacity, and (iii) the N-shot Holevo capacity of arbitrary quantum channels. All these bounds can be estimated by a single measurement setting without needing a full process tomography or any further a priori knowledge, e.g., preferred basis of the channel.
We study the problem of decoding classical information encoded on quantum states at the output of a quantum channel, with particular focus on increasing the communication rates towards the maximum allowed by Quantum Mechanics. After a brief introduction to the main theoretical formalism employed in the rest of the thesis, i.e., continuous-variable Quantum Information Theory and Quantum Communication Theory, we consider several decoding schemes. First, we treat the problem from an abstract perspective, presenting a method to decompose any quantum measurement into a sequence of easier nested measurements through a binary-tree search. Furthermore we show that this decomposition can be used to build a capacity-achieving decoding protocol for classical communication on quantum channels and to solve the optimal discrimination of some sets of quantum states. These results clarify the structure of optimal quantum measurements, showing that it can be recast in a more operational and experimentally-oriented fashion. Second, we consider a more practical approach and describe three receiver structures for coherent states of the electromagnetic field with applications to single-mode state discrimination and multi-mode decoding at the output of a quantum channel. We treat the problem bearing in mind the technological limitations faced nowadays in the field of optical communications: we evaluate the performance of general decoding schemes based on such technology and report increased performance of two schemes, the first one employing a non-Gaussian transformation and the second one employing a code tailored to be read out easily by the most common detectors. Eventually we characterize a large class of multi-mode adaptive receivers based on common technological resources, obtaining a no-go theorem for their capacity.
We consider the problem of estimating time-varying quantum noise. Specifically, we focus on Pauli qubit noise with time-variations and attempt to construct the most accurate instantaneous channel description. To this end, we propose an adaptive framework of simultaneous communication and parameter estimation (SCAPE) that efficiently and accurately estimates the time-varying Pauli channel while communicating reliably over the channel being estimated. This adaptive framework gives the informed control of communication rate–parameter estimation tradeoff to communicating parties. Interestingly, this adaptive SCAPE requires post-processing entirely on the receiver’s end and minimal feedback to the sender to increase, decrease, or continue with the same code rate of employed error correcting code. This procedure can be particularly useful in time-varying quantum channels with natural periodic deviations in channel conditions, e.g., in satellite communication channels.
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.
The engineering problem of building scalable quantum computers has prompted the development of a rich theory modeling the evolution of quantum systems as well as techniques to preserve quantum information in the presence of noise. Such techniques offer systems-level approaches to the problem of robustly encoding and preserving information and, as a result, see applicability in a wide variety of architectures for computing systems. In this thesis, we visit the mathematical underpinnings of quantum information and apply strategies inspired by quantum information processing to two non-quantum systems to demonstrate advantage. We first describe the construction of a quantum emulation device, an analog electronic system with the same mathematical structure as a gate-based quantum computer, and introduce novel time-domain information encoding methods to increase the computational capacity of the device. We confirm the sustained performance of the improved system by successfully transforming emulated states by randomly selected quantum gates. We then visit similarities between quantum information processing and signal processing in the noncoherent wireless communication setting, the latter being an environment characterized by a lack of instantaneous channel knowledge. We describe the theoretical underpinnings of the noncoherent communication environment from both an information theoretic and signal processing perspective. This leads us to propose a multi-antenna space-time code construction based on a family of quantum error correcting codes known as stabilizer codes. For this code, we derive the optimal decoder in Rayleigh and Ricean fading and benchmark the its performance against coherent and differential coding at comparable rates.
In this article, we focus on the joint design of channel training and data transmission for secure ultrareliable and low-latency communications (URLLCs) in mission-critical Internet of Things (IoT) scenarios, e.g., intelligent transportation and remote control. Specifically, we consider a multiple-input multiple-output multiantenna eavesdropper (MIMOME) system, and the role of artificial noise (AN) for securing URLLC in this system is studied. In the channel training phase, we use the two-way discriminatory channel estimation (DCE) protocol with AN injection to suppress the channel estimation accuracy at eavesdropper. Meanwhile, the AN-assisted secrecy beamforming scheme is adopted to mask the confidential data signals. Following by the security enhancements above, we provide a quantitative definition of achievable effective secrecy rate (AESR) to measure the performance of our URLLC system with imperfect channel state information (CSI) and short-packet feature. Then, a nonasymptotic closed-form lower bound of AESR is provided to make the numerical calculation tractable, and the asymptotic system performance in the high-SNR regime is also studied to gain a comprehensive insight. Based on the cyclic coordinated search method, we propose an iterative resource allocation algorithm to maximize the AESR of our system, where the blocklength and transmit power assigned to the reverse/forward pilots, confidential data signals, and AN are jointly optimized. In addition, numerical results reveal the AESR performance of our URLLC system for different system parameters, and demonstrate the convergence and superiority of our proposed algorithm.