The interaction with an environment provokes decoherence in quantum systems, which gradually suppresses their capability to display interference traits. Hence carpet-type structures, which arise after the release of a localized state inside a quantum cavity, constitute an ideal laboratory to study and analyze the robustness of the interference process that underlies this phenomenon against the harmful effects of decoherence. Such a released localized state may represent a radiation mode inserted into a multimode interference device or a cold-atom system released in an optical trap, for instance. Here, without losing any generality, for simplicity, the case of a particle with a mass $m$ is considered and described by a localized state corresponding to the ground state of a square box of width $w$, which is released inside a wider cavity (with a width $L>w$). The effects of decoherence are then numerically investigated by means of a simple dynamical model that captures the essential features of the phenomenon under Markovian conditions, leaving aside extra complications associated with a more detailed dynamical description of the system-environment interaction. As it is shown, this model takes into account and reproduces the fact that decoherence effects are stronger as energy levels become more separated (in energy), which translates into a progressive collapse of the energy density matrix to its main diagonal. However, because energy dissipation is not considered, an analogous behavior is not observed in the position representation, where a proper spatial localization of the probability density does not take place, but rather a delocalized distribution. This result emphasizes the fact that classicality is reached only if both decoherence and dissipation coexist; otherwise, nonclassical traits might still persist. Actually, as it is also shown, in the position representation some off-diagonal correlations indeed survive unless an additional spatial-type factor is included in the model. This makes evident the rather complex nature of the decoherence phenomenon and hence the importance to have a familiarity with how it manifests in different representations, particularly with the purpose to determine and design reliable control mechanisms.
The interaction with an environment provokes decoherence in quantum systems, which gradually suppresses their capability to display interference traits. Hence carpet-type structures, which arise after the release of a localized state inside a quantum cavity, constitute an ideal laboratory to study and analyze the robustness of the interference process that underlies this phenomenon against the harmful effects of decoherence. Such a released localized state may represent a radiation mode inserted into a multimode interference device or a cold-atom system released in an optical trap, for instance. Here, without losing any generality, for simplicity, the case of a particle with a mass m is considered and described by a localized state corresponding to the ground state of a square box of width w, which is released inside a wider cavity (with a width L>w). The effects of decoherence are then numerically investigated by means of a simple dynamical model that captures the essential features of the phenomenon under Markovian conditions, leaving aside extra complications associated with a more detailed dynamical description of the system-environment interaction. As it is shown, this model takes into account and reproduces the fact that decoherence effects are stronger as energy levels become more separated (in energy), which translates into a progressive collapse of the energy density matrix to its main diagonal. However, because energy dissipation is not considered, an analogous behavior is not observed in the position representation, where a proper spatial localization of the probability density does not take place, but rather a delocalized distribution. This result emphasizes the fact that classicality is reached only if both decoherence and dissipation coexist; otherwise, nonclassical traits might still persist. Actually, as it is also shown, in the position representation some off-diagonal correlations indeed survive unless an additional spatial-type factor is included in the model. This makes evident the rather complex nature of the decoherence phenomenon and hence the importance to have a familiarity with how it manifests in different representations, particularly with the purpose to determine and design reliable control mechanisms.
The title of the present dissertation Decoherence in Quantum Network sounds very general and all-inclusive. Indeed it embraces two topics (decoherence and quantum network) from the area of Quantum Mechanics each of which is described in all respects by a huge literature developed in the last three decades [...]. Quantum decoherence, as the name lets it mean, is the mechanism that makes a quantum system loose its coherence properties, and with them the capability of giving rise to interference phenomena or to other interesting quantum effects [...]. The key idea promoted by decoherence is the insight that realistic quantum systems are never isolated, but are immersed in the surrounding environment and interact continuously with it [...]. As an example one may consider a two-level quantum system (i.e. a quantum bit, usually shortened with a terminology from information science to \\qubit" ) in contact with a wide environment. Hence, quantum systems are open systems, and continuously interact or exchange information with an external environment whose degrees of freedom are too numerous to be monitored. The resulting correlation between the system and the environment spoils quantum coherence and brings about the transition from a pure quantum state to a mixture of quantum state resulting a classical state. To describe decoherence different kind of approaches can be used (for example Master equation, random matrix, etc). A quantum network typically consists of a number of quantum objects (e.g., atoms, ions, quantum dots, cavities, etc.), to be referred to hereafter as the sites or the nodes of the network. They can interact and the interactions (or their correlations) will be usually described by the edges of a graph. Quantum networks can address different information processing tasks. For instance a quantum state can be transferred from qubit to qubit down a chain solely due to the interactions, that is according to the laws of quantum physics [...]. Quantum networks offer us new opportunities and phenomena as compared to classical networks. An extension to large scale of the idea of a quantum network could lead to a futurible quantum internet [...]. The study of networks has traditionally been the territory of graph theory [...], also with the advent of their quantum versions. Within simple quantum network model information processing is usually described by assuming perfect control of the underlying graph. However, this is not much realistic since randomness is often present and it leads to decoherence effects [...]. In contrast, the conservation of coherence is essential for any quantum information process [...], hence there is a persistent interest in decoherence effects in quantum networks, which motivate us to study models for describing such noisy effects. We consider a simple model of quantum network, employing qubits (spin-1/2 particles) attached to the nodes of an underlying graph and we study the simplest task, namely information storage (on a single and two qubits), when the graph randomly changes in time. Actually we randomly add edges to an initially disconnected graph according to the Gilbert model characterized by a weighting parameter ex [...] and in an identically and independent way at each time step. We find that by increasing ex the dynamics of relevant quantities like fidelity, entropy or concurrence, gradually transforms from damped to damped oscillatory and finally to purely oscillatory. That leads to the paper [see, Information dissipation in random quantum networks, by U. Farooq and S. Mancini, OSID 21(3), 1450004, 2014]. We also study a system composed by pairs of qubits attached to each node of a linear chain, a model that stems from quantum dot arrays. Here we use the approach of evolution with a stochastic Hamiltonian to describe the noisy effects. We then evaluate the effect of two most common disorders, namely exchange coupling and hyperfine interaction fluctuations, in adiabatic preparation of ground state in such model. We show that the adiabatic ground state preparation is highly robust against these disorders making the chain a good analog simulator. Moreover, we also study the adiabatic information transfer, using singlet-triplet states, across the chain. In contrast to ground state preparation the transfer mechanism is highly affected by disorders. This suggested that for communication tasks across such chains adiabatic evolution is not as effective and quantum quenches would be preferable. That leads to the paper [see, Adiabatic many-body state preparation and information transfer in quantum dot arrays, by U. Farooq, A. Bayat, S. Mancini and S. Bose Phys. Rev. B 91, 134303, 2015]. The present work is organized as follows. In chapter 1, we shall give a survey of the various types of approach which can be employed to analyse the dynamics of open quantum systems that leads to decoherence effects. In chapter 2, we shall give a general description about quantum network and its possible applications. In chapter 3, we shall discuss the problem of quantum state transfer in qubit network and shall give a brief overview of some scheme that enable nearly prefect state transfer. In chapter 4, we shall discuss singlet-triplet networks, that is networks having on each site a pair of (generally entangled) qubit. Then within this framework we propose a model stemming from quantum dot array. There we shall address the problem of ground state preparation and state transfer. Finally we shall describe the inherent entanglement of the ground state of strongly correlated systems can be exploited for both classical and quantum communications. In chapter 5, we shall propose a decoherence model for qubit networks based on edges representing XY interactions randomly added to a disconnected graph accordingly to a suitable probability distribution. In this way we shall describe dissipation of information initially localize in single or two qubits all over the network. In chapter 6 we shall model the noisy effects in the quantum dot array introduced in chapter 4 and investigate their consequences on the preparation of ground state and quantum state transfer mechanism. Finally we shall draw conclusions.
The effects of fluctuating boundaries on a superposition state of a quantum particle in a box is studied. We consider a model in one space dimension in which the initial state is a coherent superposition of two energy eigenstates. The locations of the walls of the box are assumed to undergo small fluctuation with a Gaussian probability distribution. The spatial probability density of the particle contains an interference term, which is found to decay in time due to the boundary fluctuations. At late times, this term vanishes and the quantum coherence is lost. The system is now described by a density matrix rather than a pure quantum state.This model gives a simple illustration of how environment-induced decoherence can take place in quantum systems. It can also serve as an analog model for the effects of spacetime geometry fluctuations on quantum systems.
The challenge of making nano-scale quantum systems experimentally accessible is being overcome for an increasing diversity of systems by improved fabrication techniques and experimental control. Despite rapid progress, one of the main hindrances in all experiments is the difficulty of isolating the quantum system from the surrounding environment and its fluctuations. This experimental “noise” perturbs the quantum system, a process that is generally referred to as decoherence: the system slowly loses its distinguishing quantum features. In this thesis the effects of spatial correlations in the noise environment with a finite correlation length are investigated. The consequences for the experimental design of controlled quantum systems as well as the dynamics of solid state systems are presented. We utilize the Bloch-Redfield formalism, a Markovian master equation approach, which gives a close connection to the underpinning system-environment model. We show how to use this formalism to model any spatial correlation function of the noise environment. Using microscopic environmental models, several correlation functions are derived and their properties connected to the environmental parameters. Several phenomenological correlation functions are also studied and a mapping to the Lindblad master equation is presented, which provides a test of positivity for phenomenological models. For quantum transport through spin chains and networks, noise is generally detrimental. Spatial correlations however reduce the effect of dephasing noise and can reinstate the transport dynamics. The critical correlation length proves to be closely connected to the maximal packet width of one excitation in the transfer process. For dissipation noise, relaxation-free states emerge with spatial correlations. The decay of an excitation is therefore fundamentally modified into a fast decay towards an intermediate relaxation-reduced state and a subsequent decay to the ground state on a much longer time scale. In quantum metrology noise correlations have been observed in experiments with trapped ions, in which they limit the use of such experiments for metrology. Quantum advantage, i.e. a better precision scaling than the standard quantum limit has been proven impossible in the presence of uncorrelated Markovian noise only. We show that for certain optimized states the best possible quantum advantage, Heisenberg scaling, can be achieved in the presence of noise with a finite spatial decay of correlations. We furthermore identify how dephasing effects change and a topology dependence arises in strength with increasing correlation length for entangled states in a general way. Biological photosynthetic complexes have recently been found to potentially include quantum coherent dynamics, particularly in the process of transmitting an exciton from the point of creation to the reaction centre. We show how the formalism of spatially correlated decoherence adapts to this significantly different energy regime. Typical effects of decoherence in this field are presented and we show how the light-harvesting efficiency is influenced by spatial correlations in the noise. This thesis highlights the fundamental relevance of noise correlations to several fields of quantum physics and the importance of the efficient and comprehensive modelling techniques presented.
Based on the superposition principle, any two states of a quantum system may be coherently superposed to yield a novel state. Such a simple construction is at the heart of genuinely quantum phenomena such as interference of massive particles or quantum entanglement. Yet, these superpositions are susceptible to environmental influences, eventually leading to a complete disappearance of the system's quantum character. In principle, two distinct mechanisms responsible for this process of decoherence may be identified. In a classical decoherence setting, on the one hand, stochastic fluctuations of classical, ambient fields are the relevant source. This approach leads to a formulation in terms of stochastic Hamiltonians; the dynamics is unitary, yet stochastic. In a quantum decoherence scenario, on the other hand, the system is described in the language of open quantum systems. Here, the environmental degrees of freedom are to be treated quantum mechanically, too. The loss of coherence is then a direct consequence of growing correlations between system and environment. The purpose of the present thesis is to clarify the distinction between classical and quantum decoherence. It is known that there exist decoherence processes that are not reconcilable with the classical approach. We deem it desirable to have a simple, feasible model at hand of which it is known that it cannot be understood in terms of fluctuating fields. Indeed, we find such an example of true quantum decoherence. The calculation of the norm distance to the convex set of classical dynamics allows for a quantitative assessment of the results. In order to incorporate genuine irreversibility, we extend the original toy model by an additional bath. Here, the fragility of the true quantum nature of the dynamics under increasing coupling strength is evident. The geometric character of our findings offers remarkable insights into the geometry of the set of non-classical decoherence maps. We give a very intuitive geometrical measure---a volume---for the quantumness of dynamics. This enables us to identify the decoherence process of maximum quantumness, that is, having maximal distance to the convex set of dynamics consistent with the stochastic, classical approach. In addition, we observe a distinct correlation between the decoherence potential of a given dynamics and its achievable quantumness. In a last step, we study the notion of quantum decoherence in the context of a bipartite system which couples locally to the subsystems' respective environments. A simple argument shows that in the case of a separable environment the resulting dynamics is of classical nature. Based on a realistic experiment, we analyze the impact of entanglement between the local environments on the nature of the dynamics. Interestingly, despite the variety of entangled environmental states scrutinized, no single instance of true quantum decoherence is encountered. In part, the identification of the classical nature relies on numerical schemes. However, for a large class of dynamics, we are able to exclude analytically the true quantum nature.
Description The Quantum Underlying Entanglement Event Time–Entropy Retention model, abbreviated QUEETER, is a speculative framework designed to explore whether the history of a quantum entanglement event can continue to influence a system after that event has already occurred. The model begins with the familiar idea that two or more quantum systems can become entangled. When systems are entangled, their properties are connected through correlations that cannot always be explained by treating each system independently. These correlations can remain observable even when the systems are separated.In ordinary quantum theory, the present condition of a system is described by its quantum state. For realistic systems, this state is often represented by a density matrix, which contains the measurable probabilities, coherences, and correlations available at a given time. QUEETER asks whether this present-state description is always sufficient. Its central proposal is that an entanglement event may leave behind a temporary historical influence. This influence would depend on when the entanglement event occurred and on the amount of entropy produced or encountered after that event. The model calls this continuing influence event retention, or QUEETER retention.Under this proposal, an entanglement event is not treated merely as an instantaneous preparation step. Instead, it is treated as the beginning of a history that may continue to affect later quantum behavior. An entanglement event is any physical interaction that creates or significantly changes entanglement between quantum systems. This event could occur through a controlled quantum gate, the emission of correlated particles, a collision, a shared interaction, or another physical process capable of generating quantum entanglement. QUEETER assigns importance to the time at which this event occurs. That moment becomes the starting point for the event’s retention history. As time passes, the event becomes older. During that period, the system may also interact with its environment, experience thermal noise, undergo measurements, lose energy, or participate in other irreversible processes. QUEETER proposes that both the age of the event and the entropy associated with its later history may influence how much of the event’s original historical effect remains.Time is one of the central elements of the QUEETER model. The model proposes that the influence of an entanglement event gradually weakens as the event becomes older. A recently created entangled system may therefore possess a stronger event-retention effect than a system whose entanglement was created much earlier. This does not simply mean that older systems are expected to have less entanglement. That ordinary effect is already explained by decoherence, noise, and other forms of environmental disturbance.The stronger QUEETER claim is that event age may affect future behavior even when two systems have been adjusted so that their present measurable quantum states are the same. In other words, two systems could appear identical at the beginning of an experiment but evolve differently because one system’s entanglement event happened more recently than the other’s.Entropy is the second major historical element in QUEETER. In this context, entropy represents the irreversible spreading, loss, or inaccessibility of information during the system’s history. A quantum system may accumulate entropy through interactions with a thermal environment, uncontrolled noise, scattering, dissipation, measurement-like processes, or other physical mechanisms that distribute information into surrounding degrees of freedom. QUEETER proposes that greater accumulated entropy exposure reduces event retention. This means that two entangled systems of the same age might still possess different retention values if one experienced a more disruptive or entropy-producing history. The model therefore distinguishes between the system’s present environment and its environmental history. Two systems may currently be held at the same temperature, exposed to the same controls, and placed in the same apparatus while still having experienced different amounts of entropy production in the past. QUEETER suggests that this difference in past entropy exposure may influence later quantum evolution.QUEETER retention is the proposed remaining influence of the original entanglement event. It is not meant to be identical to entanglement itself. A system may still be entangled even after its QUEETER retention has become very small. Similarly, a nonzero retention value would not automatically prove that the system remains strongly entangled. Entanglement refers to a property of the quantum state, while retention refers to the proposed continuing effect of the event history that created or shaped that state. Retention is also not intended to be the same as ordinary coherence. Quantum coherence describes phase relationships that are already visible in the present quantum state. QUEETER retention is meant to carry information about the event’s age and entropy history, even when that information is not directly visible through ordinary measurements of the present reduced state. The model treats retention as an additional descriptive variable. This variable would be strongest near the time of the entanglement event and would gradually fade as time passes and entropy accumulates.Decoherence describes how quantum coherence and entanglement become weakened when a system interacts with its environment. It explains why quantum behavior becomes difficult to observe in large, warm, or uncontrolled systems. QUEETER does not replace decoherence. Instead, it proposes that the rate or pattern of decoherence may temporarily depend on the retained history of the original entanglement event.In the basic protective version of the model, greater retention slightly slows the loss of observable quantum correlations. As retention fades, the system’s behavior gradually returns to the ordinary decoherence rate. This produces the prediction that a recently entangled system may lose correlations differently from an older but otherwise matched system. However, simply observing different decay rates would not be enough to support QUEETER. Ordinary environmental differences can easily produce such an effect. The systems would need to be carefully matched and tested under the same present conditions.Quantum memory refers to a physical system or degree of freedom that stores quantum information. Examples include atomic ensembles, trapped particles, optical systems, or environmental modes that preserve information about earlier interactions. QUEETER retention is intended to be conceptually different. It is not initially described as a separate physical storage device or memory qubit. It is described as a property associated with the entanglement event and its history. This distinction is difficult to maintain scientifically. If the proposed retention effect can be explained by an unnoticed environmental memory, then QUEETER would not require a new physical theory. It would instead represent a different way of describing an already known memory process. For QUEETER to become genuinely distinct, it would need to predict something that cannot be reproduced by including the relevant environment and memory degrees of freedom in an ordinary quantum model.Non-Markovian quantum dynamics describes situations in which the future behavior of a system depends on its earlier interactions. In a simple memoryless process, the future depends only on the present state. In a non-Markovian process, information can flow between the system and the environment, allowing earlier events to influence later behavior. This area of physics is closely related to the idea behind QUEETER.For that reason, QUEETER cannot claim originality merely because it introduces history-dependent quantum behavior. That general idea is already well established. The proposed distinction is more specific. QUEETER suggests that the time and entropy history of a particular entanglement event may act as an additional effective state variable, even when the ordinary present quantum state and the relevant present environment have been matched. This is a much stronger claim because it suggests that the conventional description may be incomplete unless the event-retention history is included.The basic test of QUEETER uses two groups of entangled quantum systems. The first group has a recent entanglement-event history. The second group has an older entanglement-event history or has experienced more entropy-producing interactions. At first, the groups would naturally have different present states because the older or more disturbed group may have suffered more decoherence. To make the experiment meaningful, researchers would need to match the present quantum states of the two groups. This could involve carefully controlled noise, filtering, state preparation, or other procedures that bring both groups to nearly the same measured density matrix. The experimenters would then place both groups in the same test environment. They would expose the systems to the same controls, the same temperature, the same noise conditions, the same measurement schedule, and the same observation period.The later quantum correlations of the two groups would then be measured. Under the conventional null hypothesis, systems with the same complete relevant state and the same dynamics should produce the same future measurement statistics. Under QUEETER, the systems may evolve differently because their event-retention values are different.The primary QUEETER prediction is that two systems with nearly identical present quantum states may display different future correlation-decay behavior if their entanglement-event histories differ. In the protective version of the model, the system with the more recent and lower-entropy history retains its correlations for slightly longer.
We investigate system-environment correlations based on the exact dynamics of a qubit and its environment in the framework of pure decoherence (phase damping). We focus on the relation of decoherence and the buildup of system-reservoir entanglement for an arbitrary (possibly mixed) initial qubit state. In the commonly employed regime where the qubit dynamics can be described by a Markov master equation of the Lindblad type, we find that for almost all qubit initial states inside the Bloch sphere, decoherence is complete while the total state is still separable---no entanglement is involved. In general, both ``separable'' and ``entangling'' decoherence occurs, depending on the temperature and initial qubit state. Moreover, we find situations where classical and quantum correlations periodically alternate as a function of time in the regime of low temperatures.