Control at the interface between the classical and the quantum world is fundamental in quantum physics. In particular, how classical control is enhanced by coherence effects is an important question both from a theoretical as well as from a technological point of view. In this work, we establish a resource theory describing this setting and explore relations to the theory of coherence, entanglement and information processing. Specifically, for the coherent control of quantum systems the relevant resources of entanglement and coherence are found to be equivalent and closely related to a measure of discord. The results are then applied to the DQC1 protocol and the precision of the final measurement is expressed in terms of the available resources.
Control at the interface between the classical and the quantum world is fundamental in quantum physics. In particular, how classical control is enhanced by coherence effects is an important question both from a theoretical as well as from a technological point of view. In this work, we establish a resource theory describing this setting and explore relations to the theory of coherence, entanglement and information processing. Specifically, for the coherent control of quantum systems the relevant resources of entanglement and coherence are found to be equivalent and closely related to a measure of discord. The results are then applied to the DQC1 protocol and the precision of the final measurement is expressed in terms of the available resources.
Abstract Control at the interface between the classical and the quantum world is fundamental in quantum physics. In particular, how classical control is enhanced by coherence effects is an important question both from a theoretical as well as from a technological point of view. In this work, we establish a resource theory describing this setting and explore relations to the theory of coherence, entanglement and information processing. Specifically, for the coherent control of quantum systems, the relevant resources of entanglement and coherence are found to be equivalent and closely related to a measure of discord. The results are then applied to the DQC1 protocol and the precision of the final measurement is expressed in terms of the available resources.
One of the fundamental features that separates quantum physics from classical physics is the idea of quantum superposition, also known as coherence. This thesis concentrates on understanding quantum coherence in the mathematical framework of resource theories, viewing it both as a resource to be harnessed and as a way to quantitatively characterise quantum states in contrast to classical states. We first examine the type of coherence resource theory which has emerged recently to cope with general settings where the physical nature of the medium encoding information is not crucial, such as computation. We identify the set of quantum processes in which coherence is neither created nor used, and use these to provide a physically motivated resource theory pictured in terms of interferometry. Using the same concepts, we then find connections between coherence and discord, a type of quantum correlation. In particular, we show how coherence can be used to generate discord, and explore basis-dependent discord as an intermediate quantity. The second part of the thesis applies the resource theory framework to quantify quantum macroscopicity, taken here to mean the extent to which coherence exists in a system on a macroscopic scale. We find the appropriate type of resource theory for this purpose, giving criteria for good measures of macroscopic coherence. We use these criteria to evaluate some previously proposed measures and highlight the role of the quantum Fisher information. Next, we build up measures based on the concept of macroscopic distinguishability and use them to show that macroscopic quantum states are fragile to noise induced by interaction with an environment. Finally, we apply measures based on the Fisher information to a range of experiments involving mechanical degrees of freedom, in order to compare their macroscopicity.
Quantum resource theories allow us to quantify a useful quantum phenomenon, to develop new protocols for its detection and determine the exact processes that maximize its use for practical tasks. These theories aim at transforming physical phenomena, such as entanglement and quantum coherence, into useful properties for the execution of concrete tasks related to quantum information. In this thesis, we focus on the resource theories of entanglement, discord-like quantum correlations, and quantum coherence, the most intriguing quantum phenomena exploited so far in quantum information theory. We begin by presenting in detail the theoretical tools of these quantum resources, focusing on the most remarkable techniques and computational problems. In this sense, we discuss several mathematical methods that solve some problems related to their quantifications, and some analytical results for bipartite quantum systems are given. We also examine the intrinsic connections between these quantum resources by extracting the links that unite the corresponding measures. In contrast, the revolution of quantum technology has led to a growing interest in quantum metrology, and quantum entanglement has been employed to overcome the classical limit in several quantum estimation protocols. In this work, we analyze the role of quantum correlations beyond entanglement in improving the accuracy of an unknown parameter. According to our results, correlations can be captured using quantum Fisher information, and quantum discord correlations can be exploited to ensure the accuracy of phase estimation protocols. This thesis includes also the contributions on the dynamics of these quantum resources in various models of open quantum systems. Among our objectives, is to study the effects of the environment on these quantum resources and to obtain techniques to protect them from the effects of intrinsic decoherence.
In the works leading to this thesis the aim was to give a clear operational interpretation of different aspects of non-classicality. Doing so, enables to see the different properties as different aspects of the same underlying question, namely whether there is a classical explanation of the measurements at hand. If one incorporates the additional assumptions in the setting (such as locality by the separation of the two parties in entanglement theory), the question of whether some system is classical, boils down to ask whether one can simulate everything one can possibly observe by classical variables governed by a stochastic process. This new perspective allows to characterise dynamic properties of non-classicality, and also to connect them to more static types of non-classicality such as entanglement. Indeed we unify entanglement, discord and coherence from one single perspective. We do this by restricting our setting such that the operations have a clear classical interpretation and hence incorporating natural restrictions of classical systems, if the initial state of the system is not entangled does not have discord or does not have coherence. If the initial state of the system is different, we see the magic of quantum mechanics happening again. For instance we show for one specific quantum algorithm, which is thought to be better than any classical algorithm for its task, that the precision of the algorithm scales with the coherence present at its start. In other words, it is these resources (coherence, discord and entanglement) that make the magic possible and with our perspective we can interpret the role of the different resources and analyse how they are linked to each other. This does not give an explanation of the magic of quantum mechanics, but it does make the mechanisms more transparent allowing for new explanations and there are some examples already in this thesis. Finally we also look at the dual of when states are non-classical, asking, and answering, in a specific setting, what makes measurements non-classical.
Quantum physics currently provides our deepest description of nature. To understand precisely how it differs from classical physics is not only of foundational interest, but also important to advance technology: the advent of quantum information has led to the insight that certain quantum phenomena, e.g., entanglement and coherence, are resources which enable us to solve practical tasks that are unsolvable within the realm of classical physics. But how can we quantify quantum resources and how do we decide which resource is relevant for a specific operational advantage in quantum cryptography, quantum computation, or quantum metrology? How can we employ these resources optimally? Addressing these questions is the motivation for the development of quantum resource theories, a mathematically rigorous framework that allows us to investigate a specific quantum phenomenon as a resource. Formally, such theories emerge from restrictions which are imposed in addition to the laws of quantum mechanics. A prominent example is the restriction to local operations and classical communication, which singles out entanglement as a resource. Typically, such theories describe the value of quantum states, i.e., static resources. An important question in such theories concerns their structure as determined by the restriction under consideration, which is analyzed for coherence theory on qubits in this thesis. Only recently, so-called dynamical resource theories that quantify the value of operations were proposed, which are advantageous for several reasons: they include resource theories of states as special cases, allow us to quantify additional quantum properties such as the detection or usage of static resources, which will be a main topic of this thesis, and are more natural from an operational perspective. But are different types of dynamical resources present in quantum operations related? For the case of dynamical coherence and entanglement, it will be shown that there is not only a quantitative, but also a qualitative connection.
In this work (multipartite) entanglement, discord, and coherence are unified as different aspects of a single underlying resource theory defined through simple and operationally meaningful elemental operations. This is achieved by revisiting the resource theory defining entanglement, local operations, and classical communication (LOCC), placing the focus on the underlying quantum nature of the communication channels. Taking the natural elemental operations in the resulting generalization of LOCC yields a resource theory that singles out coherence in the wire connecting the spatially separated systems as an operationally useful resource. The approach naturally allows us to consider a reduced setting as well, namely, the one with only the wire connected to a single quantum system, which leads to discordlike resources. The general form of free operations in this latter setting is derived and presented as a closed form. We discuss in what sense the present approach defines a resource theory of quantum discord and in which situations such an interpretation is sound—and why in general discord is not a resource. This unified and operationally meaningful approach makes transparent many features of entanglement that in LOCC might seem surprising, such as the possibility to use a particle to entangle two parties, without it ever being entangled with either of them, or that there exist different forms of multipartite entanglement.