Quantum information is promising in solving certain computational problems and information \nsecurity. The power of its speed up and privacy is based on one of the most \ntested physical theory: quantum mechanics. Many of the promises of quantum information \nhas already been demonstrated in different implementations, which could also be viewed \nas witness of quantum mechanics. As we progress further in quantum information, we find \nthat some of the aspects of quantum mechanics could be tested in a novel way. Performing \nthose tests may lead to new physical theory or at least reinforce our belief of the accuracy \nof quantum mechanics. In this thesis, I report a few different approaches in testing the \nfoundation of quantum mechanics using results obtained from quantum optics. While developing \nsuch test, quantum state tomography is heavily used to characterize our system. \nI also report a simplified way of performing quantum state tomography for quantum state \nthat is close to pure state.
Quantum information is promising in solving certain computational problems and information \nsecurity. The power of its speed up and privacy is based on one of the most \ntested physical theory: quantum mechanics. Many of the promises of quantum information \nhas already been demonstrated in different implementations, which could also be viewed \nas witness of quantum mechanics. As we progress further in quantum information, we find \nthat some of the aspects of quantum mechanics could be tested in a novel way. Performing \nthose tests may lead to new physical theory or at least reinforce our belief of the accuracy \nof quantum mechanics. In this thesis, I report a few different approaches in testing the \nfoundation of quantum mechanics using results obtained from quantum optics. While developing \nsuch test, quantum state tomography is heavily used to characterize our system. \nI also report a simplified way of performing quantum state tomography for quantum state \nthat is close to pure state.
This thesis details two experimental tests that can be applied to particular quantum states to reveal important information. We begin by discussing the relevant background in quantum information. We introduce qubits and qudits as basic quantum states, and we discuss the evolution and measurement of quantum states. We then discuss quantum state tomography as a means by which to obtain complete information about a state, followed by a discussion of state discrimination as a means by which to determine the state given the promise that it is drawn from some known set. We then discuss relevant experimental techniques in quantum optics, including measurement, generation of entanglement, and generation of single photons from entanglement. \n \nThe first experiment we discuss deals with the causal structure of a system, which is the description of the origin of correlations between two or more states. The causal structure can be direct-cause, meaning that one state causes the other; common-cause, meaning that both states are caused by another; or hybrid-cause, which is a combination of the two. We perform the first implementation of a new type of tomography to determine the causal structure; this is called causal tomography and functions regardless of whether two qubits are related by a common state, a process, or some combination thereof. We implement a process on two entangled photons so that we can select the exact causal structure that results, which ranges continuously between direct-cause and common-cause structures. Using causal tomography, we recover causal structures that closely match expected results and demonstrate that quantum mechanics provides an advantage in causal inference. \n \nThe second experiment we discuss deals with the unambiguous discrimination of multiple quantum states. For the first time, we apply the principles of unambiguous state discrimination to high-dimensional systems. Given a state chosen randomly out of d possible states encoded in d dimensions, we implement a procedure for determining which state was chosen; this procedure in theory functions without error. We encode and detect the states in the orbital angular momentum degree of freedom up to dimension d=14. Although no experiment can provide perfectly error-free measurement due to inevitable imperfections, we obtain an error rate below the theoretical error rate of minimum-error state discrimination for dimensions up to d=12. At the time of submission of this thesis, this work has been accepted for publication in Physical Review Letters.
This thesis explores a broad range of topics in the foundations of relativity and quantum information theory. The first and main topic of this thesis is on relativistic quantum information theory. Here we construct a reformulation of quantum information, which is consistent with relativity theory. We will see that by providing a rigorous formulation starting with the field equations for a massive fermion and a photon we can construct a theory for relativistic quantum information. In particular we provide a measurement formalism, a transport equation which describes the unitary evolution of a state through spacetime as well as how to extend this to multipartite systems. The second topic concerns the nature of time, duration and clocks in current physical theories and in particular for Newtonian mechanics. We analyse the relationship between the readings of clocks in Newtonian mechanics with absolute time. We will see that in order to answer this question we must provide not only a model for a clock but also solve what is referred to as Newton’s Scholium problem. We then compare this with other dynamical theories in particular quantum mechanics and general relativity where the treatment of time is quite different from Newtonian mechanics. The final topic is rather different from the first two. In this chapter we investigate a range of methods to perform tomography in a solid-state qubit device, for which a priori initialization and measurement of the qubit is restricted to a single basis of the Bloch sphere. We explore and compare several methods to acquire precise descriptions of additional states and measurements, quantifying both stochastic and systematic errors, ultimately leading to a tomographically-complete set that can be subsequently used in process tomography. We focus in detail on the example of a spin qubit formed by the singlet-triplet subspace of two electron spins in a GaAs double quantum dot, although our approach is quite general.
The field of quantum optics has witnessed significant theoretical and experimental developments in recent years. This book provides an in-depth and wide-ranging introduction to the subject, emphasising throughout the basic principles and their applications. The book begins by developing the basic tools of quantum optics, and goes on to show the application of these tools in a variety of quantum optical systems, including lasing without inversion, squeezed states and atom optics. The final four chapters are devoted to a discussion of quantum optical tests of the foundations of quantum mechanics, and to particular aspects of measurement theory. Assuming only a background of standard quantum mechanics and electromagnetic theory, and containing many problems and references, this book will be invaluable to graduate students of quantum optics, as well as to researchers in this field.
Quantum information processing devices promise to solve some problems more efficiently than their classical counterparts. The source of the speedup is the structure of quantum theory itself. In that sense, the physical units that are the building blocks of such devices are its power. The quest then is to find or manufacture a system that behaves according to quantum theory, and yet is controllable in such a way that the desired algorithms can be implemented. Candidate systems are benchmarked against general criteria to evaluate their success. In this thesis, I advance a particular system and present the progress made towards each of these criteria. The system is a three-qubit 13C solid-state nuclear magnetic resonance (NMR) based quantum processor. I report results concerning system characterization and control, pseudopure state preparation, and quantum error correction. I also report on using the system to test a central question in the foundation of quantum mechanics.
Born about a century ago, Quantum Mechanics has revolutionized the description and the interpretation of Physics at sub-microscopic level. In the last decades, due to the influence of mathematical and engineering research fields, Quantum Mechanics has given birth to related research areas like Quantum Computation, Quantum Information and Quantum Communication. With the discovery of the laser, and later the development of fiber optics and satellite networks, Quantum Communication and Quantum Optics seems to have a natural field of application in Communication Systems. Despite this, the interest in this technology and studies for communication purpose has been overshadowed by the great results in communication networks achieved in the last decades with classical paradigms. However, due to the increasing demand of communication data rate, system designers are now looking at Quantum Mechanics for new and more performanting solutions in communication purposes. Early theoretical studies on Quantum Discrimination Theory and Quantum Information predict better performance for Communication Systems that take advantage of the quantum laws. In addition, Quantum Mechanics provides the deepest description of the physical phenomena, and there are scenarios where a quantum model fits best, as in in deep space communications, where the received signal is really weak, or in a satellite networks, where we are interested in strongly reducing the power of transmitted signals, possibly without sacrificing performance significantly. However, if on one side Quantum Communication Theory promises great gains in the performance of communication systems, on the other hand it fails to describe how to implement physical devices that reach these ultimate limits. So far, only a few architectures achieving these performances are known, and only for simple modulation formats. We are interested in the scenario of optical communications, where the message transmitted is encoded in a sequence of coherent states. Transmitter devices for coherent modulation are well known and consist in laser pulse generators. Instead, receiver implementations working at the quantum limit performance limit are yet to be found. In this Thesis I deal with different topics in the quantum transmission scenario. First, I review existing classical (suboptimal) and quantum (suboptimal and optimal) receiver schemes for the binary coherent modulation. I present a new formulation of the optimal scheme known as Dolinar Receiver with the multiple copies problem, focusing on the information gained during the measurement. Second, I analyze the binary communication in a noisy environment, studying the error probability and the capacity of the binary channel induced. Given the description of the quantum channel, I optimize both the transmitted quantum states and the measurement operators employed in the communication. Third, I consider the Pulse Position Modulation, that is particularly suitable for space and satellite communication due to its simplicity of implementation and high capacity. I review some known suboptimal receivers, and I propose a receiver scheme which approaches the limit performance predicted with quantum theory outperforming the existing schemes. To sum up the results of this Thesis, in order to approach the limit performance predicted by Quantum Mechanics, an optimization is always necessary to exceed the classical effects and trigger the quantum phenomena. In particular, the information gained during the measurement plays an important role, for example in the definition of adaptive receivers. In this Thesis both these aspects have been deeply investigated.