In this work, the asymmetry properties of quantum states associated with the Hamiltonian generator of the dynamics of the magnetic dipole interaction are investigated and their relationships with the production of entanglement are identified. Are also explored the types of separable or partially entangled quantum states that can be used as a resource in the entanglement distribution protocol, where we use IBM quantum processors to test the results with simulations and experiments performed remotely. Furthermore, a state preparation algorithm is presented that allows simulating and performing experiments with general quantum measurements and quantum instruments, as well as noisy quantum channels. In the topic about the properties of asymmetry and entanglement production, classes of pure and mixed quantum states consisting of 2 qubits evolved under magnetic dipole interaction (MDI) are considered.The asymmetry measure used is based on the Wigner-Yanase skew information between the quantum state and the Hamiltonian of the IDM, whose dependence is provided by the interaction parameters and initial conditions of the system. The local asymmetry associated with the evolved state is investigated, which is characterized by its dependence on the interaction parameters, local and temporal parameters, allowing the establishment of indirect relationships with the entanglement dynamics generated by MDI. The asymmetry related to the element of the unitary group responsible for the dynamics of the MDI is also analyzed, being useful to understand the dynamic character regarding the Wigner-Yanase asymmetry and to establish dynamic links with other properties. On the other hand, regarding the entanglement distribution protocol, the role of separable and partially entangled states are explored in the context of the Bell-diagonal class of states, analyzing the probabilistic entanglement distribution, where it involves selective projective measures, and the deterministic entanglement distribution, where it involves the action of non-selective general quantum measurements. Finally, with the proposal of a state preparation algorithm based on the relationship between the action of quantum channels and isometry, it was possible to carry out simulations and experiments on IBM quantum processors in general quantum measurements, quantum instruments and noisy quantum channels applied to qudits, allowing, in this way, to handle and develop in a simpler way the applications that until then were complex to simulate.
In this work, the asymmetry properties of quantum states associated with the Hamiltonian generator of the dynamics of the magnetic dipole interaction are investigated and their relationships with the production of entanglement are identified. Are also explored the types of separable or partially entangled quantum states that can be used as a resource in the entanglement distribution protocol, where we use IBM quantum processors to test the results with simulations and experiments performed remotely. Furthermore, a state preparation algorithm is presented that allows simulating and performing experiments with general quantum measurements and quantum instruments, as well as noisy quantum channels. In the topic about the properties of asymmetry and entanglement production, classes of pure and mixed quantum states consisting of 2 qubits evolved under magnetic dipole interaction (MDI) are considered.The asymmetry measure used is based on the Wigner-Yanase skew information between the quantum state and the Hamiltonian of the IDM, whose dependence is provided by the interaction parameters and initial conditions of the system. The local asymmetry associated with the evolved state is investigated, which is characterized by its dependence on the interaction parameters, local and temporal parameters, allowing the establishment of indirect relationships with the entanglement dynamics generated by MDI. The asymmetry related to the element of the unitary group responsible for the dynamics of the MDI is also analyzed, being useful to understand the dynamic character regarding the Wigner-Yanase asymmetry and to establish dynamic links with other properties. On the other hand, regarding the entanglement distribution protocol, the role of separable and partially entangled states are explored in the context of the Bell-diagonal class of states, analyzing the probabilistic entanglement distribution, where it involves selective projective measures, and the deterministic entanglement distribution, where it involves the action of non-selective general quantum measurements. Finally, with the proposal of a state preparation algorithm based on the relationship between the action of quantum channels and isometry, it was possible to carry out simulations and experiments on IBM quantum processors in general quantum measurements, quantum instruments and noisy quantum channels applied to qudits, allowing, in this way, to handle and develop in a simpler way the applications that until then were complex to simulate.
In this work we consider a bipartite system consisting of magnetic dipoles, initially characterized by product-states uncorrelated until the dynamics of evolution is established by magnetic dipole interaction. We reproduce the dynamic behavior of the entanglement produced by the magnetic dipole interaction through its temporal dependence, connection with local quantum coherences or symmetries of initial states and interaction parameters, thus establishing criteria that extremize the entanglement. We also investigated the entanglement production capacity of the magnetic dipole interaction for some classes of states with lower purities, with and without initial entanglement, thus identifying relevant aspects between purity, symmetry and necessary local quantum coherences. We show, above all, that some classes of partially entangled states can preserve or generate maximum entanglement under magnetic dipole interaction for different instants of time.
Bell-diagonal states are extremely important for understanding the dynamics and applications of some quantum resources. Quantum properties such as steering, entanglement, and coherence, among others, can be used as resources in quantum computing. Because of this, we believe it is necessary to understand the preparation of these states. We create an adjustable quantum circuit, which we implement on the International Business Machines (IBM) quantum computer. These computers are an excellent possibility for carrying out experiments like this. We implement the circuit on three different quantum chips that are available on the online platform. As an example, we measure non-locality, steering, entanglement, discord and non-local coherence for Werner states, which are a special type of the Bell-diagonal. We compare the theoretical results with the experimental data. We note the harmful effect that noise can have on quantum circuits, bringing undesirable decoherence effects to the system. We model noise in a simple way, using two quantum channels, amplitude damping and phase damping. We investigate the direct relationship between measures of discord and entanglement, as well as the sudden change of discord. But, even carrying out these tests on several quantum chips, it was not possible to carry out such verification with great clarity. On the other hand, the great importance of Bohr’s Complementarity Principle for Quantum Mechanics is well known. However, the search for quantifiers to measure wave or particle characteristics, in a quantum system, has always been very intense. Recently, a formalism was developed based on basic properties of the density matrix ( 0; Tr = 1). We use the IBM quantum computer to check the complementarity relationships based on these properties. We calculate quantum coherence, predictability and quantum correlations for a particular class of quantum states of one qubit and also for random quantum states of one, two and three qubits. We note that for both cases, the interaction of the system with the environment, and the consequent creation of correlation, generates a decrease in the sum of quantum coherence and predictability but which is compensated by the increase in quantum correlations between system and environment.
Dynamical symmetries in closed systems lead to conservation laws and to selection rules that are based on those conservation laws. However, conservation laws are not applica- ble to open systems that undergo irreversible transformations. More general selection rules are needed to determine whether, given two states, the transition from one state to the other is possible. Characterizing the asymmetry properties of quantum states using quantum information theoretical tools and methods is particularly fruitful for this purpose. This thesis is concerned with the problem of finding new general selection rules that hold for both open and closed systems. The usual approach to this problem relies heavily on group theory and involves a detailed study of the structure of the symmetry group. In this thesis, we approach the problem in a completely new way. Our approach is to use entanglement to investigate the asymmetry properties of quantum states. In order to do that, we embed the system’s Hilbert space in a larger tensor product Hilbert space, whereby all symmetric states are mapped to separable states, asymmetric states are mapped to entangled states, and the symmetric transformations between two states are replaced by local operations on their bipartite images. Our method is not restricted to only a specific group but applies, in general, to all symmetries that are associated with semi-simple compact Lie groups and their associated Lie algebras. The mapping of the original states to bipartite states that act on the larger Hilbert space enables us to use the well studied theory of entanglement to investigate the consequences of dynamic symmetries. For example, the monotonicity condition on measures of entanglement provide us with new selection rules. Under reversible transfor- mations, the entanglement of the bipartite image states becomes a conserved quantity. These entanglement-based conserved quantities are new and different from the conserved quantities based on expectation values of the Hamiltonian symmetry generators.
The main focus of this thesis is quantum entanglement and, more specifically, pro- tocols that allow its distribution between distant places. In the last decades, with the rise of attention on quantum technologies, entangle- ment is mostly seen as a resource, that could be exchanged, measured, and ideally stored and used when convenient. However, entanglement is not as stable and cheap as the classical resources. One reason for this is that entanglement between two quantum systems is easily disrupted by the interaction with the environment that surrounds them. The presence of noise is even more significant when we wish to entangle two systems that are very far away, a task that is essential for quantum communication technologies. In this case, what can disrupt the entanglement is not only the noise that the particles experience locally, but also the noise in the quantum channel during the communication process, which can be significant over long distances. For this reason, it is important to design distribution protocols that work well in such conditions. In 2003, Cubitt et al. showed the existence of a very curious class of protocols, often called entanglement distribution with separable states (EDSS). They proved that a non-entangled (separable) carrier can be used to increase, or even gener- ate entanglement between two already distant parties. From this, some questions arise. First, what limits or allows an entanglement distribution protocol, if not the entanglement that is sent. Quantum discord was shown to be a necessary, but not sufficient, resource for entanglement distribution. Another natural question is whether these protocols can beat others, for technological purposes, especially in noisy conditions. I will describe some work I have done in an attempt to partially 9 address both of these questions. After introducing various tools and concepts that are useful to understand this topic (chapter 1) and motivate the necessity of entanglement distribution in quantum communication (chapter 2), I will describe a proof-of-principle experiment demon- strating EDSS schemes (chapter 3). Later (chapter 4), I will introduce a more general classification of distribution protocols (excessive or non-excessive protocols), based on whether the entanglement gain is larger than the one that is communicated, describing specific examples and general properties of such protocols. I will then partially address the problem regarding the robustness to the noise of communica- tion protocols (chapter 5). Finally, in chapter 6, I will describe how entanglement of a bipartite state can grow with a quantum measurement with unknown results. I discuss the properties of the measurement and of the initial state that make this process effective.
The interaction with the environment is one of the main obstacles to be circumvented in practical implementations of quantum information tasks. The use of local unitaries, while not changing the initial entanglement present in a given state, can enormously change its dynamics through a noisy channel, and consequently its ability to be used as a resource. This way, local unitaries provide an easy and accessible way to enhance quantum correlations in a variety of different experimental platforms. Given an initial entangled state and a certain noisy channel, what are the local unitaries providing the most robust dynamics? In this paper we solve this question considering two qubits states, together with paradigmatic and relevant noisy channels, showing its consequences for teleportation protocols and identifying cases where the most robust states are not necessarily the ones imprinting the least information about themselves into the environment. We also derive a general law relating the interplay between the total correlations in the system and environment with their mutual information built up over the noisy dynamics. Finally, we employ the IBM Quantum Experience to provide a proof-of-principle experimental implementation of our results.
This thesis investigates the use of concepts from quantum information theory to analyze and quantify symmetry breaking in extended quantum systems, particularly focusing on the key measure known as Entanglement Asymmetry. The core of the work introduces and applies Entanglement Asymmetry. This quantity is defined based on the difference in information content between a quantum state and a version of that state where the symmetry has been enforced (or "symmetrized"). It represents an alternative approach to traditional, often problematic, local order parameters for measuring symmetry breaking: asymmetry is zero only if the state perfectly preserves the symmetry. The major contributions of the thesis are structured as follows: Symmetry Breaking in Bulk Critical Systems: The research analyzes Entanglement Asymmetry in two-dimensional Conformal Field Theories (CFTs) where the symmetry is explicitly broken. This work derives the asymptotic behavior of the asymmetry as a function of the subsystem size, extending earlier finite-size results to the critical continuum limit. Boundary Effects and Quenches: The analysis is extended to cases where the symmetry holds in the bulk of a CFT but is broken at the edge by a boundary condition. The thesis provides formulas describing this boundary-induced asymmetry, including power-law corrections whose exponents are linked to the properties of boundary-changing operators. It also explores the time evolution of asymmetry in quantum quench protocols. Generalization of Asymmetry to Modern Symmetries: The concept of Entanglement Asymmetry is generalized to include finite generalized symmetries, such as higher-form and non-invertible symmetries, which are a major topic in modern QFT. This involves establishing a generalized procedure for "symmetrizing" a state without relying on traditional group mathematics. Entanglement in Non-Hermitian Systems: The final chapter shifts focus to explore other entanglement properties, specifically symmetry-resolved entanglement and the entanglement Hamiltonian, within non-Hermitian models and their corresponding non-unitary CFTs.