The study of entanglement has gained prominence in recent years due to the advent of fields such as Quantum Optics and Quantum Information Theory — advances that have harnessed such counter-intuitive quantum phenomena into elements of everyday life, improving it in the process. Ideal quantum systems, “closed” to the outside world, remain quantum forever and thus manage to retain entanglement. Real quantum systems, however, are “open” to the environment and are therefore susceptible to the phenomenon of decoherence. The resultant loss of entanglement is a major hindrance to the effectiveness of quantum information tasks. In this thesis we have studied the evolution of entanglement in various types of open quantum systems (OQS) coupled in various ways to local baths. We have also studied existing ways and means of controlling the decay of entanglement and have proposed a new method of doing so. We have studied the evolution of entanglement in OQS undergoing Markovian dynamics by using the Lindblad master equation as well as the method of quantum trajectories. We have analyzed the onset of the phenomenon of entanglement sudden death in finite as well as infinite dimensional OQS, connected either locally to a thermal bath or its squeezed variant, or via a quantum non-demolition-type (QND-type) interaction to a local thermal bath. We have found that the QND-type system-bath interaction works best to conserve entanglement in finite dimensional systems, whereas a squeezed thermal bath causes entanglement sudden death even at zero temperature. We have also studied some well-known methods of controlling decoherence in open systems with respect to their ability of preserving entanglement. Some of these procedures include coupling the system to a thermal bath of photonic crystals where the photonic band gap suppresses decoherence, modulation of the systembath frequency in an attempt to contain decoherence, using the method of resonance fluorescence where an external field modulates the transition frequency of the two-qubit systems with each qubit being a two-state atomic system to contain decoherence, and using high-frequency radio waves to decouple the system and bath dynamically and thus reducing decoherence. Our study has revealed a rather startling fact — some of these decoherence control procedures actually result in an elevated rate of loss and a resultant quicker death of entanglement. This is a 6 surprising and extremely counter-intuitive result. Finally, we have proposed a new method of shielding the entanglement in the system from dissipative environmental effects. In this procedure, an ancillary system in a fixed initial state is allowed to interact with the main system through exchange interactions. We have, through numerical computation, showed that an ancilla in the ground state extends the lifespan of entanglement in the main system. Increasing the size of the ancilla, that is, increasing the value of n in an n-qubit ancilla slows down entanglement loss for a two-qubit system connected locally to a thermal bath.
The study of entanglement has gained prominence in recent years due to the advent of fields such as Quantum Optics and Quantum Information Theory — advances that have harnessed such counter-intuitive quantum phenomena into elements of everyday life, improving it in the process. Ideal quantum systems, “closed” to the outside world, remain quantum forever and thus manage to retain entanglement. Real quantum systems, however, are “open” to the environment and are therefore susceptible to the phenomenon of decoherence. The resultant loss of entanglement is a major hindrance to the effectiveness of quantum information tasks. In this thesis we have studied the evolution of entanglement in various types of open quantum systems (OQS) coupled in various ways to local baths. We have also studied existing ways and means of controlling the decay of entanglement and have proposed a new method of doing so. We have studied the evolution of entanglement in OQS undergoing Markovian dynamics by using the Lindblad master equation as well as the method of quantum trajectories. We have analyzed the onset of the phenomenon of entanglement sudden death in finite as well as infinite dimensional OQS, connected either locally to a thermal bath or its squeezed variant, or via a quantum non-demolition-type (QND-type) interaction to a local thermal bath. We have found that the QND-type system-bath interaction works best to conserve entanglement in finite dimensional systems, whereas a squeezed thermal bath causes entanglement sudden death even at zero temperature. We have also studied some well-known methods of controlling decoherence in open systems with respect to their ability of preserving entanglement. Some of these procedures include coupling the system to a thermal bath of photonic crystals where the photonic band gap suppresses decoherence, modulation of the systembath frequency in an attempt to contain decoherence, using the method of resonance fluorescence where an external field modulates the transition frequency of the two-qubit systems with each qubit being a two-state atomic system to contain decoherence, and using high-frequency radio waves to decouple the system and bath dynamically and thus reducing decoherence. Our study has revealed a rather startling fact — some of these decoherence control procedures actually result in an elevated rate of loss and a resultant quicker death of entanglement. This is a 6 surprising and extremely counter-intuitive result. Finally, we have proposed a new method of shielding the entanglement in the system from dissipative environmental effects. In this procedure, an ancillary system in a fixed initial state is allowed to interact with the main system through exchange interactions. We have, through numerical computation, showed that an ancilla in the ground state extends the lifespan of entanglement in the main system. Increasing the size of the ancilla, that is, increasing the value of n in an n-qubit ancilla slows down entanglement loss for a two-qubit system connected locally to a thermal bath.
The effect of a number of mechanisms designed to suppress decoherence in open quantum systems are studied with respect to their effectiveness at slowing down the loss of entanglement. The effect of photonic band-gap materials and frequency modulation of the system-bath coupling are along expected lines in this regard. However, other control schemes, like resonance fluorescence, achieve quite the contrary: increasing the strength of the control leads to a faster decay of entanglement. The effect of dynamic decoupling schemes on two qualitatively different system-bath interactions are studied in depth. Dynamic decoupling control has the expected effect of slowing down the decay of entanglement in a two-qubit system coupled to a harmonic oscillator bath under a nondemolition interaction. However, nontrivial phenomena are observed when a Josephson charge qubit, strongly coupled to a random telegraph noise bath, is subject to decoupling pulses. The most striking of these reflects the resonance fluorescence scenario, in that an increase in the pulse strength decreases decoherence but also speeds up the sudden death of entanglement. This demonstrates that the behavior of decoherence and entanglement in time can be qualitatively different in the strong-coupling non-Markovian regime.
Entanglement is very susceptible to decoherence and can rapidly decay or even completely disappear in finite time. A universal dynamical control of the disentanglement approach is presented, whereby one locally modulates entangled systems weakly coupled to thermal baths. We show that these local modulations can reduce the entanglement's decay rate and may facilitate controlled oscillations of entanglement that result in entanglement partial resuscitation. In the case of separate systems, we show that controlling the asymmetry between the systems' decoherence rates may result in partial resuscitation in non-Markovian time scales. Furthermore, controlling the time-dependent cross-decoherence of systems coupled to the same bath may exhibit partial resuscitation on longer time scales, dictated by the local modulations.
An open quantum system is a quantum system that interacts with some environment whose degrees of freedom have been coarse grained away. This model describes non-equilibrium processes more general than scattering-matrix formulations. Furthermore, the microscopically-derived environment provides a model of noise, dissipation and decoherence far more general than Markovian (white noise) models. The latter are fully characterized by Lindblad equations and can be motivated phenomenologically. Non-Markovian processes consistently account for backreaction with the environment and can incorporate effects such as finite temperature and spatial correlations. We consider linear systems with bilinear coupling to the environment, or quantum Brownian motion, and nonlinear systems with weak coupling to the environment. For linear systems we provide exact solutions with analytical results for a variety of spectral densities. Furthermore, we point out an important mathematical subtlety which led to incorrect master-equation coefficients in earlier derivations, given nonlocal dissipation. For nonlinear systems we provide perturbative solutions by translating the formalism of canonical perturbation theory into the context of master equations. It is shown that unavoidable degeneracy causes an unfortunate reduction in accuracy between perturbative master equations and their solutions. We also extend the famous theorem of Lindblad, Gorini, Kossakowski and Sudarshan on completely positivity to non-Markovian master equations. Our application is primarily to model atoms interacting via a common electromagnetic field. The electromagnetic field contains correlations in both space and time, which are related to its relativistic (photon-mediated) nature. As such, atoms residing in the same field experience different environmental effects depending upon their relative position and orientation. Our more accurate solutions were necessary to assess sudden death of entanglement at zero temperature. In contrast to previous claims, we found that all initial states of two-level atoms undergo finite-time disentanglement. We were also able to access regimes which cannot be described by Lindblad equations and other simpler methods, such as near resonance. Finally we revisit the infamous Abraham-Lorentz force, wherein a single particle in motion experiences backreaction from the electromagnetic field. This leads to a number of well-known problems including pre-acceleration and runaway solutions. We found a more a more-suitable open-system treatment of the nonrelativistic particle to be perfectly causal and dissipative without any extraneous requirements for finite size of the particle, weak coupling to the field, etc..
Known as decoherence, the unavoidable interaction of a quantum system with its surrounding environment is usually considered to be detrimental for quantum information processing. In this thesis the coherent, open loop control of such open systems is studied. Concepts from quantum control theory and the theory of open quantum system are adopted in order to fight decoherence and implement quantum gates in a noiseless manner. In particular, Lie algebraic methods and numerical optimization tools are used to investigate the control properties of a single spin interacting with a spin environment. We show that, independent of the size of the environment, every unitary transformation can be implemented on the system spin through a single control field. We proceed by investigating dynamical decoupling, a method to suppress the interactions with the environment, for finite- and for in- finite dimensional systems. We prove that every finite dimensional system can be protected from decoherence, even if the environment is infinite dimensional, whereas for noise described by a Lindblad master equation dynamical decoupling will never succeed. This will lead to a new method to distinguish decoherence from intrinsic noise terms. We further prove that not every infinite dimensional system can be protected from decoherence through dynamical decoupling. Afterwards we investigate dynamical decoupling of systems that are described by quadratic Hamiltonians, showing that such interactions can always be suppressed with two simple operations. In the last part we investigate the coherent control of a Lindblad master equation. We show that a strong noise process exhibiting a decoherence free subspace can substantially increase the number of unitary operations that can be implemented, allowing us to fully control parts of the system. Afterwards we develop a scheme to make Hamiltonians and Lindbladians commutative by adding an auxiliary system. The old, possibly non-commutative dynamics, is recovered through a non-selective measurement.
Entanglement is a key resource in quantum information. It can be destroyed or sometimes created by interactions with a reservoir. In recent years, much attention has been devoted to the phenomena of entanglement sudden death and sudden birth, i.e., the sudden disappearance or revival of entanglement at finite times resulting from a coupling of the quantum system to its environment [1, 2, 3]. We investigate the evolution of the entanglement of noninteracting qubits coupled to reservoirs under monitoring of the reservoirs by means of continuous measurements. Because of these measurements, the qubits remain at all times in a pure state, which evolves randomly. To each measurement result (or "realization") corresponds a quantum trajectory in the Hilbert space of the qubits. We show that for two qubits coupled to independent baths subjected to local measurements, the average of the qubits' concurrence over all quantum trajectories is either constant or decays exponentially. The corresponding decay rate depends on the measurement scheme only. This result contrasts with the entanglement sudden death phenomenon exhibited by the qubits' density matrix in the absence of measurements. Our analysis applies to arbitrary quantum jump dynamics (photon counting) as well as to quantum state diffusion (homodyne or heterodyne detections) in the Markov limit. We discuss the best measurement schemes to protect the entanglement of the qubits. We also analyze the case of two qubits coupled to a common bath. Then, the average concurrence can vanish at discrete times and may coincide with the concurrence of the density matrix. The results explained in this article have been presented during the "Fifth International Workshop DICE2010" by the first author and have been the subject of a prior publication [4].
Abstract Entanglement is an essential resource for quantum information processing; however, it is highly susceptible to decoherence induced by environmental interactions. In this work, we investigate the entanglement dynamics of a two-qubit system subjected to Markovian noise and explore the effectiveness of external control fields in preserving quantum correlations. Using the Lindblad master equation, we model the evolution of the system under two decoherence channels, namely, amplitude damping (spontaneous emission) and phase damping (dephasing). We introduce periodic driving and optimal control protocols to mitigate entanglement loss and analyze their impact using concurrence as a quantifier of two-qubit entanglement. Our numerical results reveal certain conditions under which sudden death of entanglement can be delayed or even prevented. Additionally, in the case of the initial state being a mixed state, we identify time regimes where entanglement revival occurs, providing insights into quantum error correction strategies. The results contribute to the broader understanding of quantum coherence preservation and have implications for quantum computing, secure quantum communication, and quantum memory design.