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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Application and Manipulation of Bipartite and Multipartite Entangled States

Fortescue, Benjamin 24 September 2009 (has links)
The phenomenon of quantum entanglement is a fundamental feature of quantum mechanics which, as a counterintuitive and inherently ”quantum” phenomenon (with no classical analogue) has been the subject of much study, especially in quantum information theory. One fruitful approach to the description of entanglement has been in its operational description - that is, in the consideration of what can be achieved using entangled states under certain restrictions, typically the regime of local operations and classical communications. We present results here related to the operational characterisation of entanglement in the resource model, in both bipartite and multipartite cases. First, we consider the conversion between pure bipartite entangled states in terms of an often-ignored resource - the classical communication cost. Using prior results for more specific conversions, we derive lower bounds on this cost (and the related quantity of the conversion inefficiency) for general bipartite pure states. We also consider pure-state conversions of multipartite entanglement, in particular the class of protocols in which multipartite states are converted to states shared between fewer parties. We have found a previously-unconsidered variety of such conversions, in which the target state of the conversion is a state shared between a random subset of the parties. We find that when such post-selection of parties in the protocol is permitted allows for a wider variety of achievable target states; certain states which can not be reliably obtained between predetermined parties (even some where the probability of doing so is arbitrarily small) can be obtained between random parties. We consider a variety of states in which this phenomenon occurs, as well as bounds on such protocols can achieve. Finally we consider a practical use of entanglement as a resource, in an experimental implementation of a multipartite QKD protocol. This is based on the tripartite GHZ entangled state, but can be implemented using only bipartite entanglement. We adapt existing QKD results for both the bipartite and multipartite case to derive a secure key rate for this implementation, taking into account the ways in which it differs from the idealised theoretical case.
2

Application and Manipulation of Bipartite and Multipartite Entangled States

Fortescue, Benjamin 24 September 2009 (has links)
The phenomenon of quantum entanglement is a fundamental feature of quantum mechanics which, as a counterintuitive and inherently ”quantum” phenomenon (with no classical analogue) has been the subject of much study, especially in quantum information theory. One fruitful approach to the description of entanglement has been in its operational description - that is, in the consideration of what can be achieved using entangled states under certain restrictions, typically the regime of local operations and classical communications. We present results here related to the operational characterisation of entanglement in the resource model, in both bipartite and multipartite cases. First, we consider the conversion between pure bipartite entangled states in terms of an often-ignored resource - the classical communication cost. Using prior results for more specific conversions, we derive lower bounds on this cost (and the related quantity of the conversion inefficiency) for general bipartite pure states. We also consider pure-state conversions of multipartite entanglement, in particular the class of protocols in which multipartite states are converted to states shared between fewer parties. We have found a previously-unconsidered variety of such conversions, in which the target state of the conversion is a state shared between a random subset of the parties. We find that when such post-selection of parties in the protocol is permitted allows for a wider variety of achievable target states; certain states which can not be reliably obtained between predetermined parties (even some where the probability of doing so is arbitrarily small) can be obtained between random parties. We consider a variety of states in which this phenomenon occurs, as well as bounds on such protocols can achieve. Finally we consider a practical use of entanglement as a resource, in an experimental implementation of a multipartite QKD protocol. This is based on the tripartite GHZ entangled state, but can be implemented using only bipartite entanglement. We adapt existing QKD results for both the bipartite and multipartite case to derive a secure key rate for this implementation, taking into account the ways in which it differs from the idealised theoretical case.
3

Multipartite Entanglement: Transformations, Quantum Secret Sharing, Quantum Error Correction

Helwig, Wolfram Hugo 27 March 2014 (has links)
Most applications in quantum information processing make either explicit or implicit use of entanglement. It is thus important to have a good understanding of entanglement and the role it plays in these protocols. However, especially when it comes to multipartite entanglement, there still remain a lot of mysteries. This thesis is devoted to getting a better understanding of multipartite entanglement, and its role in various quantum information protocols. First, we investigate transformations between multipartite entangled states that only use local operations and classical communication (LOCC). We mostly focus on three qubit states in the GHZ class, and derive upper and lower bounds for the successful transformation probability between two states. We then focus on absolutely maximally entangled (AME) states, which are highly entangled multipartite states that have the property that they are maximally entangled for any bipartition. With them as a resource, we develop new parallel teleportation protocols, which can then be used to implement quantum secret sharing (QSS) schemes. We further prove the existence of AME states for any number of parties, if the dimension of the involved quantum systems is chosen appropriately. An equivalence between threshold QSS schemes and AME states shared between an even number of parties is established, and further protocols are designed, such as constructing ramp QSS schemes and open-destination teleportation protocols with AME states as a resource. As a framework to work with AME states, graph states are explored. They allow for efficient bipartite entanglement verification, which makes them a promising candidate for the description of AME states. We show that for all currently known AME states, absolutely maximally entangled graph states can be found, and we were even able to use graph states to find a new AME state for seven three-dimensional systems (qutrits). In addition, the implementation of QSS schemes from AME states can be conveniently described within the graph state formalism. Finally, we use the insight gained from entanglement in QSS schemes to derive necessary and sufficient conditions for quantum erasure channel and quantum error correction codes that satisfy the quantum Singleton bound, as these codes are closely related to ramp QSS schemes. This provides us with a very intuitive approach to codes for the quantum erasure channel, purely based on the entanglement required to protect information against losses by use of the parallel teleportation protocol.
4

Multipartite Entanglement: Transformations, Quantum Secret Sharing, Quantum Error Correction

Helwig, Wolfram Hugo 27 March 2014 (has links)
Most applications in quantum information processing make either explicit or implicit use of entanglement. It is thus important to have a good understanding of entanglement and the role it plays in these protocols. However, especially when it comes to multipartite entanglement, there still remain a lot of mysteries. This thesis is devoted to getting a better understanding of multipartite entanglement, and its role in various quantum information protocols. First, we investigate transformations between multipartite entangled states that only use local operations and classical communication (LOCC). We mostly focus on three qubit states in the GHZ class, and derive upper and lower bounds for the successful transformation probability between two states. We then focus on absolutely maximally entangled (AME) states, which are highly entangled multipartite states that have the property that they are maximally entangled for any bipartition. With them as a resource, we develop new parallel teleportation protocols, which can then be used to implement quantum secret sharing (QSS) schemes. We further prove the existence of AME states for any number of parties, if the dimension of the involved quantum systems is chosen appropriately. An equivalence between threshold QSS schemes and AME states shared between an even number of parties is established, and further protocols are designed, such as constructing ramp QSS schemes and open-destination teleportation protocols with AME states as a resource. As a framework to work with AME states, graph states are explored. They allow for efficient bipartite entanglement verification, which makes them a promising candidate for the description of AME states. We show that for all currently known AME states, absolutely maximally entangled graph states can be found, and we were even able to use graph states to find a new AME state for seven three-dimensional systems (qutrits). In addition, the implementation of QSS schemes from AME states can be conveniently described within the graph state formalism. Finally, we use the insight gained from entanglement in QSS schemes to derive necessary and sufficient conditions for quantum erasure channel and quantum error correction codes that satisfy the quantum Singleton bound, as these codes are closely related to ramp QSS schemes. This provides us with a very intuitive approach to codes for the quantum erasure channel, purely based on the entanglement required to protect information against losses by use of the parallel teleportation protocol.
5

Quantum Theory of Phonon-mediated Decoherence and Relaxation of Two-level Systems in a Structured Electromagnetic Reservoir

Roy, Chiranjeeb 02 March 2010 (has links)
In this thesis we study the role of nonradiative degrees of freedom on quantum optical properties of mesoscopic quantum dots placed in the structured electromagnetic reservoir of a photonic crystal. We derive a quantum theory of the role of acoustic and optical phonons in modifying the optical absorption lineshape, polarization dynamics, and population dynamics of a two-level atom (quantum dot) in the ``colored" electromagnetic vacuum of a photonic band gap (PBG) material. This is based on a microscopic Hamiltonian describing both radiative and vibrational processes quantum mechanically. Phonon sidebands in an ordinary electromagnetic reservoir are recaptured in a simple model of optical phonons using a mean-field factorization of the atomic and lattice displacement operators. Our formalism is then used to treat the non-Markovian dynamics of the same system within the structured electromagnetic density of states of a photonic crystal. We elucidate the extent to which phonon-assisted decay limits the lifetime of a single photon-atom bound state and derive the modified spontaneous emission dynamics due to coupling to various phonon baths. We demonstrate that coherent interaction with undamped phonons can lead to enhanced lifetime of a photon-atom bound state in a PBG by (i) dephasing and reducing the transition electric dipole moment of the atom and (ii) reducing the quantum mechanical overlap of the state vectors of the excited and ground state (polaronic shift). This results in reduction of the steady-state atomic polarization but an increase in the fractionalized upper state population in the photon-atom bound state. We demonstrate, on the other hand, that the lifetime of the photon-atom bound state in a PBG is limited by the lifetime of phonons due to lattice anharmonicities (break-up of phonons into lower energy phonons) and purely nonradiative decay. We demonstrate how these additional damping effects limit the extent of the polaronic (Franck-Condon) shift of the atomic excited state. We also derive the modified polarization decay and dephasing rates in the presence of such damping. This leads to a microscopic, quantum theory of the optical absorption lineshapes. Our model and formalism provide a starting point for describing dephasing and relaxation in the presence of external coherent fields and multiple quantum dot interactions in electromagnetic reservoirs with radiative memory effects.
6

Quantum Theory of Phonon-mediated Decoherence and Relaxation of Two-level Systems in a Structured Electromagnetic Reservoir

Roy, Chiranjeeb 02 March 2010 (has links)
In this thesis we study the role of nonradiative degrees of freedom on quantum optical properties of mesoscopic quantum dots placed in the structured electromagnetic reservoir of a photonic crystal. We derive a quantum theory of the role of acoustic and optical phonons in modifying the optical absorption lineshape, polarization dynamics, and population dynamics of a two-level atom (quantum dot) in the ``colored" electromagnetic vacuum of a photonic band gap (PBG) material. This is based on a microscopic Hamiltonian describing both radiative and vibrational processes quantum mechanically. Phonon sidebands in an ordinary electromagnetic reservoir are recaptured in a simple model of optical phonons using a mean-field factorization of the atomic and lattice displacement operators. Our formalism is then used to treat the non-Markovian dynamics of the same system within the structured electromagnetic density of states of a photonic crystal. We elucidate the extent to which phonon-assisted decay limits the lifetime of a single photon-atom bound state and derive the modified spontaneous emission dynamics due to coupling to various phonon baths. We demonstrate that coherent interaction with undamped phonons can lead to enhanced lifetime of a photon-atom bound state in a PBG by (i) dephasing and reducing the transition electric dipole moment of the atom and (ii) reducing the quantum mechanical overlap of the state vectors of the excited and ground state (polaronic shift). This results in reduction of the steady-state atomic polarization but an increase in the fractionalized upper state population in the photon-atom bound state. We demonstrate, on the other hand, that the lifetime of the photon-atom bound state in a PBG is limited by the lifetime of phonons due to lattice anharmonicities (break-up of phonons into lower energy phonons) and purely nonradiative decay. We demonstrate how these additional damping effects limit the extent of the polaronic (Franck-Condon) shift of the atomic excited state. We also derive the modified polarization decay and dephasing rates in the presence of such damping. This leads to a microscopic, quantum theory of the optical absorption lineshapes. Our model and formalism provide a starting point for describing dephasing and relaxation in the presence of external coherent fields and multiple quantum dot interactions in electromagnetic reservoirs with radiative memory effects.
7

Theory of Ultrafast Electron Diffraction

Michalik, Anna Maria 17 July 2009 (has links)
Ultrafast electron diffraction (UED) is a method of directly imaging system dynamics at the atomic scale with picosecond time resolution. In this thesis I present theoretical analyses of the experimental processes, and construct models in order to better understand UED experiments and to guide future refinements. In particular, I derive a model of electron bunch propagation and a model of electron bunch diffraction, where both models take into account all bunch parameters. To analyse the propagation of electron bunches, I present a mean-field analytic Gaussian (AG) model. I derive a system of ordinary differential equations that are solved quickly and easily to give the bunch dynamics. The AG model is compared to N -body numerical simulations of initially Gaussian bunches, and I demonstrate excellent agreement between the two result sets. I also present a comparison of the AG model with numerical simulations of quasi-Gaussian and non-Gaussian distributions, extending the applicability of the AG model to the propagation of ``real-world'' bunches. During propagation, electron bunches can be shaped by electron-optic devices, which are necessary to attain high brightness, sub-100 fs bunches. I investigate two types of electron-optic devices: one is a magnetic lens used for collimating or focusing bunches, the other is a bunch compressor. I derive bunch parameter transformations for each of the electron-optic devices, and present numerical calculations using these transformations along with the AG model showing the effects of the devices on the evolution of the bunch parameters. To analyse electron bunch diffraction in UED experiments, I present a general scattering formalism. Using single-scattering and far-field approximations, I derive an expression for the diffracted signal that depends on the electron bunch properties just before scattering. Using this expression I identify the transverse and longitudinal coherence lengths and discuss the importance of these length scales in diffraction pattern formation. I also discuss the effects of different bunch parameters on the measured diffracted flux, and present sample numerical calculations for scattering by nanosize particles based on this model. This simulation demonstrates the cumulative effects of the bunch parameters, and shows the complex interplay of the bunch and target properties on the diffracted signal.
8

Coherent Two-dimensional Infrared Spectroscopy of Vibrational Excitons in Hydrogen-bonded Liquids

Paarmann, Alexander 21 April 2010 (has links)
The structure and structural dynamics of hydrogen bonded liquids were studied experimentally and theoretically with coherent two-dimensional infrared (2DIR) spectroscopy. The resonant intermolecular interactions within the fully resonant hydrogen bond networks give access to spatial correlations in the dynamics of the liquid structures. New experimental and theoretical tools were developed that significantly reduced the technical challenges of these studies. A nanofluidic flow device was designed and manufactured providing sub-micron thin, actively stabilized liquid sample layers between similarly thin windows. A simulation protocol for nonlinear vibrational response calculations of disordered fluctuating vibrational excitons was developed that allowed for the first treatment of resonant intermolecular interactions in the 2DIR response of liquid water. The 2DIR spectrum of the O-H stretching vibration of pure liquid water was studied experimentally at different temperatures. At ambient conditions the loss of frequency correlations is extremely fast, and is attributed to very efficient modulations of the two-dimensional O-H stretching vibrational potential through librational motions in the hydrogen bond network. At temperatures near freezing, the librational motions are significantly reduced leading to a pronounced slowing down of spectral diffusion dynamics. Comparison with energy transfer time scales revealed the first direct proof of delocalization of the vibrational excitations. This work establishes a fundamentally new view of vibrations in liquid water by providing a spatial length scale of correlated hydrogen-bond motions. The linear and 2DIR response of the amide I mode in neat liquid formamide was found to be dominated by excitonic effects due to largely delocalized vibrational excitations. The spectral response and dynamics are very sensitive to the excitonic mode structure and infrared activity distributions, leading to a pronounced asymmetry of linear and 2DIR line shapes. This was attributed to structurally different species in the liquid characterized by their degree of medium range structural order. The response is dominated by energy transfer effects, sensitive to time-averaged medium range structural order, while being essentially insensitive to structural dynamics. This work is the first to recognize the importance of energy transfer contributions to the 2DIR response in a liquid, and provides additional proof of the well-structured character of liquid formamide.
9

Theory of Ultrafast Electron Diffraction

Michalik, Anna Maria 17 July 2009 (has links)
Ultrafast electron diffraction (UED) is a method of directly imaging system dynamics at the atomic scale with picosecond time resolution. In this thesis I present theoretical analyses of the experimental processes, and construct models in order to better understand UED experiments and to guide future refinements. In particular, I derive a model of electron bunch propagation and a model of electron bunch diffraction, where both models take into account all bunch parameters. To analyse the propagation of electron bunches, I present a mean-field analytic Gaussian (AG) model. I derive a system of ordinary differential equations that are solved quickly and easily to give the bunch dynamics. The AG model is compared to N -body numerical simulations of initially Gaussian bunches, and I demonstrate excellent agreement between the two result sets. I also present a comparison of the AG model with numerical simulations of quasi-Gaussian and non-Gaussian distributions, extending the applicability of the AG model to the propagation of ``real-world'' bunches. During propagation, electron bunches can be shaped by electron-optic devices, which are necessary to attain high brightness, sub-100 fs bunches. I investigate two types of electron-optic devices: one is a magnetic lens used for collimating or focusing bunches, the other is a bunch compressor. I derive bunch parameter transformations for each of the electron-optic devices, and present numerical calculations using these transformations along with the AG model showing the effects of the devices on the evolution of the bunch parameters. To analyse electron bunch diffraction in UED experiments, I present a general scattering formalism. Using single-scattering and far-field approximations, I derive an expression for the diffracted signal that depends on the electron bunch properties just before scattering. Using this expression I identify the transverse and longitudinal coherence lengths and discuss the importance of these length scales in diffraction pattern formation. I also discuss the effects of different bunch parameters on the measured diffracted flux, and present sample numerical calculations for scattering by nanosize particles based on this model. This simulation demonstrates the cumulative effects of the bunch parameters, and shows the complex interplay of the bunch and target properties on the diffracted signal.
10

Coherent Two-dimensional Infrared Spectroscopy of Vibrational Excitons in Hydrogen-bonded Liquids

Paarmann, Alexander 21 April 2010 (has links)
The structure and structural dynamics of hydrogen bonded liquids were studied experimentally and theoretically with coherent two-dimensional infrared (2DIR) spectroscopy. The resonant intermolecular interactions within the fully resonant hydrogen bond networks give access to spatial correlations in the dynamics of the liquid structures. New experimental and theoretical tools were developed that significantly reduced the technical challenges of these studies. A nanofluidic flow device was designed and manufactured providing sub-micron thin, actively stabilized liquid sample layers between similarly thin windows. A simulation protocol for nonlinear vibrational response calculations of disordered fluctuating vibrational excitons was developed that allowed for the first treatment of resonant intermolecular interactions in the 2DIR response of liquid water. The 2DIR spectrum of the O-H stretching vibration of pure liquid water was studied experimentally at different temperatures. At ambient conditions the loss of frequency correlations is extremely fast, and is attributed to very efficient modulations of the two-dimensional O-H stretching vibrational potential through librational motions in the hydrogen bond network. At temperatures near freezing, the librational motions are significantly reduced leading to a pronounced slowing down of spectral diffusion dynamics. Comparison with energy transfer time scales revealed the first direct proof of delocalization of the vibrational excitations. This work establishes a fundamentally new view of vibrations in liquid water by providing a spatial length scale of correlated hydrogen-bond motions. The linear and 2DIR response of the amide I mode in neat liquid formamide was found to be dominated by excitonic effects due to largely delocalized vibrational excitations. The spectral response and dynamics are very sensitive to the excitonic mode structure and infrared activity distributions, leading to a pronounced asymmetry of linear and 2DIR line shapes. This was attributed to structurally different species in the liquid characterized by their degree of medium range structural order. The response is dominated by energy transfer effects, sensitive to time-averaged medium range structural order, while being essentially insensitive to structural dynamics. This work is the first to recognize the importance of energy transfer contributions to the 2DIR response in a liquid, and provides additional proof of the well-structured character of liquid formamide.

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