Caracterização de coerência em sistemas quânticos de dimensão finita

Abstract

The last decade has witnessed important theoretical and experimental advances aimed at understanding quantum coherence, a quantum resource that finds applications in quantum metrology, quantum computing, and quantum thermodynamics. In this context, the formalism proposed by Baumgratz-Cramer-Plenio (BCP) stands out, which allows characterizing coherence through measures of distinguishability of quantum states. Due to the nonuniqueness character of these measures, it follows that several coherence quantifiers derive from this formalism, for example, the ℓ1-norm of coherence, and the relative entropy of coherence. In contrast, the study of coherence can also be implemented through the coherence order formalism. In turn, such a technique involves the analysis of the interference effects between quantum states and fixed basis vectors. In this work, we investigate the characterization of coherence in finite-dimensional quantum systems. We compare the BCP formalism with the coherence order approach. We show the existence of a link between both cases for 1-qubit states. In particular, we derive an invariant that relates coherence and purity of finite-dimensional states. We study the dynamics of coherence in open quantum systems, mainly evaluating 1-qubit and 2-qubit states. We investigate the evolution of coherence measures of bipartite systems whose non-unitary dynamics is described by the dephasing map. Finally, we address the effective dynamics of 2-qubit states in terms of the amplitude damping map, which exhibits crossovers between the Markovian and non-Markovian regimes. In this case, we show that the coherence characterization allows us to certify memory effects through non-Markov signatures of the dynamics of the open quantum system.