Quantum mechanics contains a fresh and mysterious view of reality.Besides the philosophical intrigue, it has also produced and continues to inspire tantalizing new technological innovations.In any technological system, the designers must contend with the problem of noise.This thesis studies classical noise in two different quantum settings.The first is the classical capacity of a quantum channel with memory.Adding forgetfulmemory, attempts to push the boundaries of our understanding of how best to transmit information in the presence of correlated noise.We study the noise within two different frameworks; Algebraic Measure theory and Monte Carlo simulations.Both tools are used to calculate the capacity of the channel as correlations in the noise are increased.The second classical-quantum system investigated is atomic clocks.Using power spectral density methods we study aliasing noise induced by periodic-correction which includes the Dick Effect.We propose a novel multi-window scheme that extends the standard method of noise correction and exhibits better anti-aliasing properties.A uniting thread that emerges is that correlations can be put to good use.In the classical capacity setting, correlations occur between uses of the quantum channel.We show that stronger correlations increase the classical capacity.The benefits of correlation are even seen at a meta-level within the framework of Monte Carlo simulations.Correlations are designed into the algorithm which have nothing to do with real-world correlations, but are abstract correlations created by a Markov chain employed in the algorithm to help efficiently sample from a distribution of exponential size.Finally, in the atomic clock setting, correlations in the measured noise are used to help predict and cancel noise on a short time-scale while trying to limit aliasing.Channel capacity and precise time-keeping are distinct topics and require very different approaches to study.However, common to both topics is their application to communication and other tasks, the need to overcome noise and the benefits of exploiting correlations in the noise.
Quantum mechanics contains a fresh and mysterious view of reality.Besides the philosophical intrigue, it has also produced and continues to inspire tantalizing new technological innovations.In any technological system, the designers must contend with the problem of noise.This thesis studies classical noise in two different quantum settings.The first is the classical capacity of a quantum channel with memory.Adding forgetfulmemory, attempts to push the boundaries of our understanding of how best to transmit information in the presence of correlated noise.We study the noise within two different frameworks; Algebraic Measure theory and Monte Carlo simulations.Both tools are used to calculate the capacity of the channel as correlations in the noise are increased.The second classical-quantum system investigated is atomic clocks.Using power spectral density methods we study aliasing noise induced by periodic-correction which includes the Dick Effect.We propose a novel multi-window scheme that extends the standard method of noise correction and exhibits better anti-aliasing properties.A uniting thread that emerges is that correlations can be put to good use.In the classical capacity setting, correlations occur between uses of the quantum channel.We show that stronger correlations increase the classical capacity.The benefits of correlation are even seen at a meta-level within the framework of Monte Carlo simulations.Correlations are designed into the algorithm which have nothing to do with real-world correlations, but are abstract correlations created by a Markov chain employed in the algorithm to help efficiently sample from a distribution of exponential size.Finally, in the atomic clock setting, correlations in the measured noise are used to help predict and cancel noise on a short time-scale while trying to limit aliasing.Channel capacity and precise time-keeping are distinct topics and require very different approaches to study.However, common to both topics is their application to communication and other tasks, the need to overcome noise and the benefits of exploiting correlations in the noise.
This thesis studies the capacities of quantum channels under repeated noisy evolution, with a focus on the long-time behavior of classical and quantum information transmission. The main goal is to understand how much information can still be preserved or recovered when a quantum channel is applied many times, and to develop structural, analytic, and algorithmic tools for characterizing these capacities.The core results are presented in Chapter 2. First, the thesis investigates the infinite-time regime and shows that the asymptotic capacities of quantum channels are determined by the structure of their peripheral subspace. This leads to explicit characterizations of the infinite-time classical capacity and bounds on the infinite-time quantum capacity, together with results on additivity and extensions to more general settings. The thesis then studies the finite-time behavior for GNS-symmetric channels and proves explicit exponential convergence bounds, showing that the capacities approach their infinite-time values rapidly. In addition, algorithmic methods are developed for computing the peripheral structure and the associated capacity quantities efficiently.Chapter 3 explores a related optimization-based direction motivated by Sum-of-Squares methods and semidefinite programming. Using ideas inspired by separability and SDP hierarchies, this part investigates whether machine-learning-assisted ansatz discovery can help construct more efficient SOS certificates. Although this direction is not yet complete in the specific capacity setting, it provides promising intermediate results and suggests new computational approaches for related problems in quantum information theory. Overall, this thesis provides a structural and quantitative understanding of the long-time information-carrying capabilities of noisy quantum dynamical systems, while also opening new perspectives through optimization and machine-learning-based methods.
Any physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be characterized from the point of view of communication theory, i.e., in terms of its ability to transfer information. Quantum information provides a theoretical framework and the proper mathematical tools to accomplish this. In this context the notion of codes and communication capacities have been introduced by generalizing them from the classical Shannon theory of information transmission and error correction. The underlying assumption of this approach is to consider the channel not as acting on a single system, but on sequences of systems, which, when properly initialized allow one to overcome the noisy effects induced by the physical process under consideration. While most of the work produced so far has been focused on the case in which a given channel transformation acts identically and independently on the various elements of the sequence (memoryless configuration in jargon), correlated error models appear to be a more realistic way to approach the problem. A slightly different, yet conceptually related, notion of correlated errors applies to a single quantum system which evolves continuously in time under the influence of an external disturbance which acts on it in a non-Markovian fashion. This leads to the study of memory effects in quantum channels: a fertile ground where interesting novel phenomena emerge at the intersection of quantum information theory and other branches of physics. A survey is taken of the field of quantum channels theory while also embracing these specific and complex settings.
With the rapid deployment of quantum computers and quantum satellites, there is a pressing need to design and deploy quantum and hybrid classical-quantum networks capable of exchanging classical information. In this context, we conduct the foundational study on the impact of a mixture of classical and quantum noise on an arbitrary quantum channel carrying classical information. The rationale behind considering such mixed noise is that quantum noise can arise from different entanglement and discord in quantum transmission scenarios, like different memories and repeater technologies, while classical noise can arise from the coexistence with the classical signal. Towards this end, we derive the distribution of the mixed noise from a classical system’s perspective, and formulate the achievable channel capacity over an arbitrary distributed quantum channel in presence of the mixed noise. Numerical results demonstrate that capacity increases with the increase in the number of photons per usage.
Quantum phenomena such as superposition and entanglement imbue quantum systems with information processing power in excess of their classical counterparts. These properties of quantum states are, however, highly fragile. As we enter the era of noisy intermediate-scale quantum (NISQ) devices, this vulnerability to noise is a major hurdle to the experimental realisation of quantum technologies. In this thesis we explore the role of noise in quantum information processing from two different perspectives. In Part I we consider noise from the perspective of quantum error correcting codes. Error correcting codes are often analysed with respect to simplified toy models of noise, such as iid depolarising noise. We consider generalising these techniques for analysing codes under more realistic noise models, including features such as biased or correlated errors. We also consider designing customised codes which not only take into account and exploit features of the underlying physical noise. Considering such tailored codes will be of particular importance for NISQ applications in which finite-size effects can be significant. In Part II we apply tools from information theory to study the finite-resource effects which arise in the trade-offs between resource costs and error rates for certain quantum information processing tasks. We start by considering classical communication over quantum channels, providing a refined analysis of the trade-off between communication rate and error in the regime of a finite number of channel uses. We then extend these techniques to the problem of resource interconversion in theories such as quantum entanglement and quantum thermodynamics, studying finite-size effects which arise in resource-error trade-offs. By studying this effect in detail, we also show how detrimental finite-size effects in devices such as thermal engines may be greatly suppressed by carefully engineering the underlying resource interconversion processes.
The argument of this thesis might be summed up as the exploitation of the noise to generate better noise. More specifically this work is about the possibility of exploiting classic noise to effectively transmit quantum information and measuring quantum noise to generate better quantum randomness. What do i mean by exploiting classical noise to transmit effectively quantum information? In this case I refer to the task of sending quantum bits through the atmosphere in order set up transmissions of quantum key distribution (QKD) and this will be the subject of Chapter 1 and Chapter 2. In the Quantum Communications framework, QKD represents a topic with challenging problems both theoretical and experimental. In principle QKD offers unconditional security, however practical realizations of it must face all the limitations of the real world. One of the main limitation are the losses introduced by real transmission channels. Losses cause errors and errors make the protocol less secure because an eavesdropper could try to hide his activity behind the losses. When this problem is addressed under a full theoretical point of view, one tries to model the effect of losses by means of unitary transforms which affect the qubits in average according a fixed level of link attenuation. However this approach is somehow limiting because if one has a high level of background noise and the losses are assumed in average constant, it could happen that the protocol might abort or not even start, being the predicted QBER to high. To address this problem and generate key when normally it would not be possible, we have proposed an adaptive real time selection (ARTS) scheme where transmissivity peaks are instantaneously detected. In fact, an additional resource may be introduced to estimate the link transmissivity in its intrinsic time scale with the use of an auxiliary classical laser beam co-propagating with the qubits but conveniently interleaved in time. In this way the link scintillation is monitored in real time and the selection of the time intervals of high channel transmissivity corresponding to a viable QBER for a positive key generation is made available. In Chapter 2 we present a demonstration of this protocol in conditions of losses equivalent to long distance and satellite links, and with a range of scintillation corresponding to moderate to severe weather. A useful criterion for the preselection of the low QBER interval is presented that employs a train of intense pulses propagating in the same path as the qubits, with parameters chosen such that its fluctuation in time reproduces that of the quantum communication. For what concern the content of Chapter 3 we describe a novel principle for true random number generator (TRNG) which is based on the observation that a coherent beam of light crossing a very long path with atmospheric turbulence may generate random and rapidly varying images. To implement our method in a proof of concept demonstrator, we have chosen a very long free space channel used in the last years for experiments in Quantum Communications at the Canary Islands. Here, after a propagation of 143 km at an altitude of the terminals of about 2400 m, the turbulence in the path is converted into a dynamical speckle at the receiver. The source of entropy is then the atmospheric turbulence. Indeed, for such a long path, a solution of the Navier-Stokes equations for the {atmospheric flow in which the beam propagates is out of reach. Several models are based on the Kolmogorov statistical theory, which parametrizes the repartition of kinetic energy as the interaction of decreasing size eddies. However, such models only provide a statistical description for the spot of the beam and its wandering and never an instantaneous prediction for the irradiance distribution. These are mainly ruled by temperature variations and by the wind and cause fluctuations in the air refractive index. For such reason, when a laser beam is sent across the atmosphere, this latter may be considered as a dynamic volumetric scatterer which distorts the beam wavefront. We will evaluate the experimental data to ensure that the images are uniform and independent. Moreover, we will assess that our method for the randomness extraction based on the combinatorial analysis is optimal in the context of Information Theory. In Chapter 5 we will present a new approach for what concerns the generation of random bits from quantum physical processes. Quantum Mechanics has been always regarded as a possible and valuable source of randomness, because of its intrinsic probabilistic Nature. However the typical paradigm is employed to extract random number from a quantum system it commonly assumes that the state of said system is pure. Such assumption, only in theory would lead to full and unpredictable randomness. The main issue however it is that in real implementations, such as in a laboratory or in some commercial device, it is hardly possible to forge a pure quantum state. One has then to deal with quantum state featuring some degree of mixedness. A mixed state however might be somehow correlated with some other system which is hold by an adversary, a quantum eavesdropper. In the extreme case of a full mixed state, practically one it is like if he is extracting random numbers from a classical state. In order to do that we will show how it is important to shift from a classical randomness estimator, such as the min-classical entropy H-min(Z) of a random variable Z to quantum ones such as the min-entropy conditioned on quantum side information E. We have devised an effective protocol based on the entropic uncertainty principle for the estimation of the min-conditional entropy. The entropic uncertainty principle lets one to take in account the information which is shared between multiple parties holding a multipartite quantum system and, more importantly, lets one to bound the information a party has on the system state after that it has been measured. We adapted such principle to the bipartite case where an user Alice, A, is supplied with a quantum system prepared by the provider Eve, E, who could be maliciously correlated to it. In principle then Eve might be able to predict all the outcomes of the measurements Alice performs on the basis Z in order to extract random numbers from the system. However we will show that if Alice randomly switches from the measurement basis to a basis X mutually unbiased to Z, she can lower bound the min entropy conditioned to the side information of Eve. In this way for Alice is possible to expand a small initial random seed in a much larger amount of trusted numbers. We present the results of an experimental demonstration of the protocol where random numbers passing the most rigorous classical tests of randomness were produced. In Chapter 6, we will provide a secure generation scheme for a continuos variable (CV) QRNG. Since random true random numbers are an invaluable resource for both the classical Information Technology and the uprising Quantum one, it is clear that to sustain the present and future even growing fluxes of data to encrypt it is necessary to devise quantum random number generators able to generate numbers in the rate of Gigabit or Terabit per second. In the Literature are given several examples of QRNG protocols which in theory could reach such limits. Typically, these are based on the exploitation of the quadratures of the electro-magnetic field, regarded as an infinite bosonic quantum system. The quadratures of the field can be measured with a well known measurement scheme, the so called homodyne detection scheme which, in principle, can yield an infinite band noise. Consequently the band of the random signal is limited only by the passband of the devices used to measure it. Photodiodes detectors work commonly in the GHz band, so if one sample the signal with an ADC enough fast, the Gigabit or Terabit rates can be easily reached. However, as in the case of discrete variable QRNG, the protocols that one can find in the Literature, do not properly consider the purity of the quantum state being measured. The idea has been to extend the discrete variable protocol of the previous Chapter, to the Continuous case. We will show how in the CV framework, not only the problem of the state purity is given but also the problem related to the precision of the measurements used to extract the randomness.
Quantum mechanics has both deepened our understanding of the physical reality and allowed development of quantum technologies beating their classical counterparts in efficiency, security, and sensitivity. As a major downside, the quantum properties behind these technologies are very sensitive to the effects the system’s interaction with its environment. The theory of open quantum systems describes how such interaction influences the system, and as a consequence, how the quantum features are lost, controlled, and possibly returned by manipulating the environment. This thesis begins with a short description of the most relevant features and results of the open quantum system theory. We continue by presenting some commonly used measures to quantify the information encoded in quantum systems and the correlations between spatially or temporally separated parties. The literature review ends with discussion of non-Markovianity and memory effects which combine the fields of open quantum systems and quantum information in a natural way. The rest of the thesis presents the main results of Publications I – VII. We study the memory effects and physicality conditions of open system dynamics described by the vast family of phase-covariant master equations. We show how the open quantum system picture can be exploited to design probing protocols to extract information without knowing how the probe and system interact. Such protocols are considered also from the point-of view of efficiently obtaining the information required in the probing, both in theory and by experimental implementation. The experiment serves also as evidence for applicability of recently developed geometric tools to design informationally incomplete measurements for solving so-called membership problems. We present and experimentally realize a protocol where control over intial correlations between polarization and frequency gives full freedom to implement any dephasing dynamics in the open system polarization, thus dictating how its information content changes in time. We study the two-qubit memory effects of dephasing dynamics and compare them to the effect of such noise in the transmission efficiency in superdense coding. Optimal noise configurations in different situations are found. Finally, we characterize the families of initial states for which the decay of quantum correlations depends or does not depend on the noise location.