We investigate aspects, in various contexts, of entanglement and the wave particle duality. We show that the dynamics of tripartite systems which interact via one excitation exchange leads to a direct connection between entanglement sudden death and the appearance of genuine entanglement. We also show that this is valid (not with the same generality) also for a four partite system in the context of the double JaynesCummings model. Moreover we show that the entanglement dynamics in this case can be completely expressed in geometrical terms. Using the same system we show that by performing adequate Zeno like measurements it is possible to freeze, increase, or even revive the initial entanglement. This intriguing result is also associated to entanglement sudden death. As far as wave particle duality and entanglement are concerned we studied a particle going through an interferometer equipped with a whichway device. We quantified the quality of the probe and exhibit its connection with the availability of the whichway information provided by the probe system. When the probe system information is unaccessible only the particle character will be observed. We obtain limits for a good (quantum regime) and for a bad (classical regime) whichway detector (probe system). We used our results to interpret a recent experiment set up to test the quantumclassical border where the probe covers from the quantum to the classical limit. We showed that the experimental errors influenced the conclusion inferred form the data about having achieved the classical limit. Finally we analyze the Ramsey zones from the point of view of our findings and provide for a transparent physical interpretation. In this case the classical limit of the probe system is reached due to a source plus strong dissipation dynamics, which swaps whichway information to a system containing an infinite number of degrees of freedom, making thus sure that any whichway information becomes unavailable.
We investigate aspects, in various contexts, of entanglement and the wave particle duality. We show that the dynamics of tripartite systems which interact via one excitation exchange leads to a direct connection between entanglement sudden death and the appearance of genuine entanglement. We also show that this is valid (not with the same generality) also for a four partite system in the context of the double JaynesCummings model. Moreover we show that the entanglement dynamics in this case can be completely expressed in geometrical terms. Using the same system we show that by performing adequate Zeno like measurements it is possible to freeze, increase, or even revive the initial entanglement. This intriguing result is also associated to entanglement sudden death. As far as wave particle duality and entanglement are concerned we studied a particle going through an interferometer equipped with a whichway device. We quantified the quality of the probe and exhibit its connection with the availability of the whichway information provided by the probe system. When the probe system information is unaccessible only the particle character will be observed. We obtain limits for a good (quantum regime) and for a bad (classical regime) whichway detector (probe system). We used our results to interpret a recent experiment set up to test the quantumclassical border where the probe covers from the quantum to the classical limit. We showed that the experimental errors influenced the conclusion inferred form the data about having achieved the classical limit. Finally we analyze the Ramsey zones from the point of view of our findings and provide for a transparent physical interpretation. In this case the classical limit of the probe system is reached due to a source plus strong dissipation dynamics, which swaps whichway information to a system containing an infinite number of degrees of freedom, making thus sure that any whichway information becomes unavailable.
We studied the entanglement dynamics of a many body system. The model that we used consists of a harmonic oscillator (main oscillator) linearly coupled to N others. Initially, the main oscillator is prepared in a superposition of two coherent states and the N others in the ground states. From this initial state we obtain the temporal evolution of the system analytically. We divide this system in three arbitrary partitions and we quantify the entanglement, by concurrence, between any two partitions. We show that the concurrence of any two partitions depends on the overlap between the two coherent states forming the initial superposition of the main oscillator and the distribution of excitations in the partitions. We also show that the residual entanglement is always present. Finally, we obtain a hierarchy of entanglement between the main oscillator and partitions formed by the N others. For long times, the excitations of the main oscillator are completely transferred to the N others and these are found entangled.
In this work we studied the issue of quantification of entanglement in quantum systems performing a detailed analysis since its fundamental principles, i.e, the postulates of the theory of entanglement measures, and thus justifying the expected properties of "good quantifiers" of entanglement. We presented some examples of entanglement measures for distinguishable particles, and we approach finally the case where the particles are indistinguishable from each other. We saw that, in this case, the quantification of entanglement is a subject of great controversies with different proposals to their approach, each with its own singular interpretation. After discussing these approaches, analysing their main characteristics and foundations, we present our proposed method to quantify them based on the use of entanglement witnesses.
The evolution of the entanglement between oscillators that interact with the same environment displays highly non-trivial behavior in the long time regime. When the oscillators only interact through the environment, three dynamical phases were identified and a simple phase diagram characterizing them was presented. Here we generalize those results to the cases where the oscillators are directly coupled and we show how a degree of mixidness can affect the final entanglement. In both cases, entanglement dynamics is fully characterized by three phases (SD: sudden death, NSD: no-sudden death and SDR: sudden death and revivals) which cover a phase diagram that is a simple variant of the previously introduced one. We present results when the oscillators are coupled to the environment through their position and also for the case where the coupling is symmetric in position and momentum (as obtained in the RWA). As a bonus, in the last case we present a very simple derivation of an exact master equation valid for arbitrary temperatures of the environment.
A great effort has been devoted to understand Quantum InformationTheory. This interest comes from the fact that this field has given us advanced methods to process and store information. Among these proposals we can cite the teleportation, the quantum cryptography, and the quantum computation. Interestingly, entanglement is the main resource that puts the quantum approach in a higher level than the classical counterpart. On the other hand, the theory of entanglement allows also a better understanding of physical phenomena already treated by the fields of condensed matter, statistical physics, and quantum optics among others. In this dissertation we aim to review the main topics concerning the Theory of Entanglement and propose new results on this theme as well. Firstly, we will discuss how the notion of entanglement raises naturally, how to determine whether a state is entangled, and how to quantify it. Moving on to the three qubit context,we will show a tomographic process able to determine the quantum stateof a system using only two detectors. It will be shown the connection between multipartite entanglement and the exceptions to our process. In the multipartite scenario we will obtain novel results in the formalism of the theory.Specifically, we study the question: are all maximally entangled statespure? While for bipartite systems almost all entanglement quantifiers agree in a positive answer, in a more general context this is not the case. Indeed, we will show a multipartite entanglement quantifier for which all maximally entangled states are pure. Finally, we address some questions on identical particle entanglement, i.e.: the entanglement coming just from the indistinguishabilityof quantum particles.
Wave--particle duality demonstrates the peculiar nature of quantum mechanics. In which-way experiments, depending on the measurement scheme, a particle exhibits either wave-like or particle-like properties, as summarized by Bohr's principle of complementarity. In this work, we implement Mach-Zehnder (MZ) interferometry on a two-dimensional (2D) superconducting quantum processor. With precise control of the which-way measurement strength, we demonstrate the transition of a photon from wave-like to particle-like behavior. Furthermore, by performing quantum state tomography on two qubits located in the two paths, we demonstrate that which-way measurements break the entanglement and coherence between the two paths and cause information leakage from the quantum system to the environment. To capture this behavior quantitatively, we derive complementarity relations between the entropy and the fringe visibility. By applying a continuous which-way measurement during the evolution, we also observe the quantum Zeno effect that partially obstructs the interferometer path, giving rise to nonmonotonic behavior of purity and von Neumann entropy. Our experiments provide a detailed characterization of the full interferometer dynamics, reveal the relation between wave--particle duality and quantum information, and demonstrate the potential of superconducting quantum processors for testing quantum foundations under high precision and controllability.
We analyze the effect of a classical noise into the entanglement dynamics between two particles, initially entangled, subject to continuous time quantum walks in a one-dimensional lattice. The noise is modeled by randomizing the transition amplitudes from one site to another. Both Markovian and non-Markovian environments are considered. For the Markov regime an exponential decay of the initial quantum correlation is found, while the loss of coherence of the quantum state increases monotonically with time up to a saturation value depending upon the degrees of freedom of the system. For the non-Markov regime the presence or absence of entanglement revival and entanglement sudden death phenomena is found or deduced depending on the peculiar characteristics of the noise. Our results indicate that the entanglement dynamics in the non-Markovian regime is affected by the persistence of the memory effects of the environment and by its intrinsic features.