Quantum information investigates the possibility of enhancing our ability to process and transmit information by directly exploiting quantum mechanical laws. When searching for improvement opportunities, one typically starts by assessing the range of outcomes classically attainable, and then investigates to what extent control over the quantum features of the system could be helpful, as well as the best performance that could be achieved. In this thesis we provide examples of these aspects, in linear optics, quantum metrology, and quantum communication. We start by providing a criterion able to certify whether the outcome of a linear optical evolution cannot be explained by the classical wave-like theory of light. We do so by identifying a tight lower bound on the amount of correlations that could be detected among output intensities, when classical electrodynamics theory is used to describe the fields. Rather than simply detecting nonclassicality, we then focus on its quantification. In particular, we consider the characterisation of the amount of squeezing encoded on selected quantum probes by an unknown external device, without prior information on the direction of application. We identify the single-mode Gaussian probes leading to the largest average precision in noiseless and noisy conditions, and discuss the advantages arising from the use of correlated two-mode probes. Finally, we improve current bounds on the ultimate performance attainable in a quantum communication scenario. Specifically, we bound the number of maximally entangled qubits, or private bits, shared by two parties after a communication protocol over a quantum network, without restrictions on their classical communication. As in previous investigations, our approach is based on the evaluation of the maximum amount of entanglement that could be generated by the channels in the network, but it includes the possibility of changing entanglement measure on a channel-by-channel basis. Examples where this is advantageous are discussed.
Quantum information investigates the possibility of enhancing our ability to process and transmit information by directly exploiting quantum mechanical laws. When searching for improvement opportunities, one typically starts by assessing the range of outcomes classically attainable, and then investigates to what extent control over the quantum features of the system could be helpful, as well as the best performance that could be achieved. In this thesis we provide examples of these aspects, in linear optics, quantum metrology, and quantum communication. We start by providing a criterion able to certify whether the outcome of a linear optical evolution cannot be explained by the classical wave-like theory of light. We do so by identifying a tight lower bound on the amount of correlations that could be detected among output intensities, when classical electrodynamics theory is used to describe the fields. Rather than simply detecting nonclassicality, we then focus on its quantification. In particular, we consider the characterisation of the amount of squeezing encoded on selected quantum probes by an unknown external device, without prior information on the direction of application. We identify the single-mode Gaussian probes leading to the largest average precision in noiseless and noisy conditions, and discuss the advantages arising from the use of correlated two-mode probes. Finally, we improve current bounds on the ultimate performance attainable in a quantum communication scenario. Specifically, we bound the number of maximally entangled qubits, or private bits, shared by two parties after a communication protocol over a quantum network, without restrictions on their classical communication. As in previous investigations, our approach is based on the evaluation of the maximum amount of entanglement that could be generated by the channels in the network, but it includes the possibility of changing entanglement measure on a channel-by-channel basis. Examples where this is advantageous are discussed.
Entanglement is a physical property, emerging from the superposition of composite quantum systems, and manifested through non-classical correlations of quantum observables. In the field of Quantum Information, entanglement is considered the resource for various quantum protocols, so the ability to quantify it would allow us to associate it with the success of those protocols. Entanglement of formation is a proper way to quantify entanglement, but an analytical expression for this measure exists only for special cases. In this thesis, we focus on two-mode Gaussian states, and we derive narrow upper and lower bounds for this measure that get tight for several special cases. We further study how quantum teleportation and entanglement distillation can be employed in order to error-correct information encoded on a Gaussian state that suffers from Gaussian noise. In particular, we derive every physical state able to simulate a given phase-insensitive Gaussian channel through teleportation with finite-energy resources, and show how error-correction of a state is related to the simulation of a less decohering channel that the state has to pass through. We also discuss how the premise that the whole environment is under control of the adversary in quantum key distribution can be eliminated if we consider a teleportation-based eavesdropping attack. More specifically, we propose an all-optical teleportation attack that under collective measurements can reach optimality in the limit of infinite amount of entanglement, while for finite entanglement resources it outperforms the corresponding optimal individual attack. Finally, we show how using a class of finite-energy resource states we can increasingly approximate the infinite-energy bounds for decreasing purity, so that they provide tight upper bounds to the secret-key capacity of single-mode phase-insensitive Gaussian channels.
In this thesis we study the information transmission through Gaussian quantum channels. Gaussian quantum channels model physical communication links, such as free space communication or optical fibers and therefore, may be considered as the most relevant quantum channels. One of the central characteristics of any communication channel is its capacity. In this work we are interested in the classical capacity, which is the maximal number of bits that can be reliably transmitted per channel use. An important lower bound on the classical capacity is given by the Gaussian capacity, which is the maximal transmission rate with the restriction that only Gaussian encodings are allowed: input messages are encoded in so-called Gaussian states for which the mean field amplitudes are Gaussian distributed. We focus in this work mainly on the Gaussian capacity for the following reasons. First, Gaussian encodings are easily accessible experimentally. Second, the difficulty of studying the classical capacity, which arises due to an optimization problem in an infinite dimensional Hilbert space, is greatly reduced when considering only Gaussian input encodings. Third, the Gaussian capacity is conjectured to coincide with the classical capacity, even though this longstanding conjecture is unsolved until today. We start with the investigation of the capacities of the single-mode Gaussian channel. We show that the most general case can be reduced to a simple, fiducial Gaussian channel which depends only on three parameters: its transmissivity (or gain), the added noise variance and the squeezing of the noise. Above a certain input energy threshold, the optimal input variances are given by a quantum water-filling solution, which implies that the optimal modulated output state is a thermal state. This is a quantum extension (or generalization) of the well-known classical water-filling solution for parallel Gaussian channels. Below the energy threshold the solution is given by a transcendental equation and only the less noisy quadrature is modulated. We characterize in detail the dependence of the Gaussian capacity on its channel parameters. In particular, we show that the Gaussian capacity is a non-monotonous function of the noise squeezing and analytically specify the regions where it exhibits one maximum, a maximum and a minimum, a saddle point or no extrema. Then, we investigate the case of n-mode channels with noise correlations (i.e. memory), where we focus in particular on the classical additive noise channel. We consider memory models for which the noise correlations can be unraveled by a passive symplectic transformation. Therefore, we can simplify the problem to the study of the Gaussian capacity in an uncorrelated basis, which corresponds to the Gaussian capacity of n single-mode channels with a common input energy constraint. Above an input energy threshold the solutions is given by a global quantum water-filling solution, which implies that all modulated single-mode output states are thermal states with the same temperature. Below the threshold the channels are divided into three sets: i) those that are excluded from information transmission, ii) those for which only the less noisy quadrature is modulated, and iii) those for which the quantum water-filling solution is satisfied. As an example we consider a Gauss-Markov correlated noise, which in the uncorrelated basis corresponds to a collection of single-mode classical additive noise channels. When rotating the collection of optimal single-mode input states back to the original, correlated basis the optimal multi-mode input state becomes a highly entangled state. We then compare the performance of the optimal input state with a simple coherent state encoding and conclude that one gains up to 10% by using the optimal encoding. Since the preparation of the optimal input state may be very challenging we consider sub-optimal Gaussian-matrix product states (GMPS) as input states as well. GMPS have a known experimental setup and, though being heavily entangled, can be generated sequentially. We demonstrate that for the Markovian correlated noise as well as for a non-Markovian noise model in a wide range of channel parameters, a nearest-neighbor correlated GMPS achieves more than 99.9% of the Gaussian capacity. At last, we introduce a new noise model for which the GMPS is the exact optimal input state. Since GMPS are known to be ground states of quadratic Hamiltonians this suggests a starting point to develop links between optimization problems of quantum communication and many body physics.
Quantum resources, such as entanglement or quantum communication, offer significant communication advantages in information processing. We develop an operational framework for realizing these communication advantages in resource-constrained quantum networks. The framework computes linear bounds on the input/output probabilities of classical networks with limited communication and globally shared randomness. Since the violation of these classical bounds witnesses nonclassicality, a measurable communication advantage, the framework maximizes the violation of the classical bound using variational quantum optimization methods tailored to the communication network and quantum resources. This operational framework for nonclassicality can be scaled on quantum computers or deployed in the field to optimize noisy quantum networks for communication advantages. Applying this framework, we investigate the nonclassicality of communication networks that are assisted by quantum resources. We find that entanglement between communication-constrained parties is sufficient for nonclassicality to be found, whereas in networks with multiple senders, quantum communication with no entanglement-assistance is sufficient for nonclassicality to be found. As a result, entanglement is necessary for nonclassicality when a single sender broadcasts to multiple receivers.
Quantum states and measurements are two central physical objects in the theory of quantum mechanics. The preparation, control and measurement of quantum states lies at the heart of modern quantum information processing protocols ranging from secure communication to quantum computation and precision sensing. And yet, the reliable operation of these advanced protocols ultimately rests on a far more essential prerequisite - our ability to calibrate, certify and benchmark the quantum states we prepare and the quantum measurements we perform. Quantum information theory provides a natural framework for these tasks, meaningfully connecting the resources we expend for characterisation with the accuracy and precision we can expect in return. While decades of advances in quantum information have refined our understanding of quantum characterisation and sharpened our practical ability to calibrate with enhanced precision, important questions about the fundamental limits of quantum characterisation remain unanswered. Although incorporating entanglement at the measurement stage is known to enhance the estimation of unknown quantum states, the extent of this improvement remains poorly understood. This leaves open a fundamental question on the utility of complex entangling measurement strategies, impeding progress towards bridging the significant gap between practically achievable precision and the ultimate theoretical quantum limit. Complementary to quantum state estimation, which is relatively well-established in theory and practice, the characterisation of quantum measurements lacks a rigorous information-theoretic foundation, leading to a dearth of principled benchmarks and provably optimal strategies despite growing experimental interest. This thesis develops and applies information-theoretic tools to answer questions in quantum characterisation, with an eye to enabling practical improvements beyond current techniques in the field. First, we introduce a computable measure of entanglement enhancement for quantum state estimation and study its variation across general multi-parameter estimation problems for higher-dimensional quantum states. We show that the entanglement enhancement is maximised for full qudit state tomography but grows only linearly with system dimension even when allowing an asymptotically large number of entangling operations. Our proposed tight upper bound to entanglement enhancement therefore constitutes a strong limitation on the utility of such entangling measurements. Next, we formulate the dual problem of quantum detector estimation, developing a comprehensive framework for maximally precise calibration centred around a newly introduced quantity - the detector quantum Fisher information. This information-theoretic measure stipulates the ultimate precision attainable for measurement calibration and identifies the optimal input states that achieve this precision. Further, our framework enables the first provably optimal detector estimation experiment and reveals the scope for entanglement-based enhancements, thereby placing measurement characterisation on equal footing with state characterisation. Considered together, these results suggest two contrasting conclusions about quantum characterisation. On the one hand, they show that for quantum state estimation, increasingly powerful entangling measurements offer only diminishing returns at the ultimate precision limit. On the other hand, they highlight practical quantum advantages available for detector estimation by providing a framework that can improve calibration performance and guide future experimental design. More broadly, these results complete and advance the triad of state, process, and detector characterisation, positioning quantum information measures as not merely abstract bounds, but practical guides for deciding when complex quantum resources are genuinely worth deploying and where near-term quantum advantages are most likely to be realised.
This thesis establishes a number of connections between foundational issues in quantum theory, and some quantum information applications. It starts with a review of quantum contextuality and non-locality, multipartite entanglement characterisation, and of a few quantum information protocols. Quantum non-locality and contextuality are shown to be essential for different implementations of quantum information protocols known as quantum random access codes and quantum communication complexity protocols. I derive sufficient experimental conditions for tests of these quantum properties. I also discuss how the distribution of quantum information through quantum cloning processes can be useful in quantum computing. Regarding entanglement characterisation, some results are obtained relating two problems, that of additivity of the relative entropy of entanglement, and that of identifying different types of tripartite entanglement in the asymptotic regime of manipulations of many copies of a given state. The thesis ends with a description of an information processing task in which a single qubit substitutes for an arbitrarily large amount of classical communication. This result is interpreted in different ways: as a gap between quantum and classical computation space complexity; as a bound on the amount of classical communication necessary to simulate entanglement; and as a basic result on hidden-variable theories for quantum mechanics. I also show that the advantage of quantum over classical communication can be established in a feasible experiment.
In this thesis, we investigate the uses of entanglement and its verification in quantum communication. Typically, it is the presence of entanglement which allows quantum communication protocols to outperform their classical counterparts, or to achieve tasks which are infeasible with classical physics. Therefore, the verification of entanglement can provide fundamental tests to certify that experimental implementations of such protocols operate quantum mechanically. The main object here is to develop a verification procedure which is adaptable to a wide range of applications, and whose implementation has low requirements on experimental resources. We present such a procedure in the form of the Expectation Value Matrix. The structure of this thesis is as follows: Chapters 1 and 2 give a short introduction and background information on quantum theory and the quantum states of light. In particular, we discuss the basic postulates of quantum mechanics, quantum state discrimination, the description of quantum light and the homodyne detector. Chapter 3 gives a brief introduction to quantum information and in particular to entanglement, and we discuss the basics of quantum key distribution and teleportation. The general framework of the Expectation Value Matrix is introduced. The main matter of this thesis is contained in the subsequent three chapters, which describe different quantum communication protocols and the corresponding adaptation of the entanglement verification method. The subject of Chapter 4 is quantum key distribution, where the detection of entanglement is a means of excluding intercept-resend attacks, and the presence of quantum correlations in the raw data is a necessary precondition for the generation of secret key. We investigate a continuous-variable version of the two-state protocol and develop the Expectation Value Matrix method for such qubit-mode systems. Furthermore, we analyse the role of the phase reference with respect to the security of the protocol and raise awareness of a corresponding security threat. For this, we adapt the verification method to different settings of Stokes operator measurements. In Chapter 5, we investigate quantum memory channels and propose a fundamental bench- mark for these based on the verification of entanglement. After describing some physical effects which can be used for the coherent storage of light, we focus on the storage of squeezed light. This situation requires an extension of our verification procedure to sources of mixed input states. We propose such an extension, and give a detailed analysis of its application to squeezed thermal states, displaced thermal states and mixed qubit states. This is supplemented by finding the optimal entanglement-breaking channels for each of these situations, which provides us with an indication of the strength of the extension to our entanglement criterion. The subject of Chapter 6 is also the benchmarking of quantum memory or teleportation experiments. Considering a number of recently published benchmark criteria, we investigate the question which one is most useful to actual experiments. For this, a criterion must be both strong, i.e., easy to overcome, and it must be implementable with a reasonable amount of experimental resources. We first compare the different criteria for typical settings and sort them according to their resilience to excess noise. Then, we introduce a further improvement to the Expectation Value Matrix method, which results in the desired optimal benchmark criterion. Finally, we investigate naturally occurring phase fluctuations and find them to further simplify the implementation of our criterion. Thus, we formulate the first truly useful way of validating experiments for the quantum storage or transmission of light.