We devise and examine two procrustean entanglement concentration schemes using Quantum Non- Demolition (QND) interaction Hamiltonians in the continuous variable regime, applicable for light, for atomic ensembles or in a hybrid setting. We thus expand the standard entanglement distillation toolbox to the use of a much more general, versatile and experimentally feasible interaction class. The first protocol uses Gaussian ancillary modes and a non-Gaussian post-measurement, the second a non-Gaussian ancillary mode and a Gaussian post-measurement. We explicitly calculate the density matrix elements of the non-Gaussian mixed states resulting from these protocols using an elegant Wigner-function based method in a numerically efficient manner. We then quantify the entanglement increase calculating the Logarithmic Negativity of the output state and discuss and compare the performance of the protocols.
We devise and examine two procrustean entanglement concentration schemes using Quantum Non- Demolition (QND) interaction Hamiltonians in the continuous variable regime, applicable for light, for atomic ensembles or in a hybrid setting. We thus expand the standard entanglement distillation toolbox to the use of a much more general, versatile and experimentally feasible interaction class. The first protocol uses Gaussian ancillary modes and a non-Gaussian post-measurement, the second a non-Gaussian ancillary mode and a Gaussian post-measurement. We explicitly calculate the density matrix elements of the non-Gaussian mixed states resulting from these protocols using an elegant Wigner-function based method in a numerically efficient manner. We then quantify the entanglement increase calculating the Logarithmic Negativity of the output state and discuss and compare the performance of the protocols.
We devise and examine two procrustean entanglement concentration schemes using quantum nondemolition (QND) interaction Hamiltonians in the continuous variable regime, applicable for light, for atomic ensembles or in a hybrid setting. We thus expand the standard entanglement distillation toolbox for use of a much more general, versatile, and experimentally feasible interaction class. The first protocol uses Gaussian ancillary modes and a non-Gaussian postmeasurement, the second a non-Gaussian ancillary mode and a Gaussian postmeasurement. We explicitly calculate the density matrix elements of the non-Gaussian mixed states resulting from these protocols using an elegant Wigner-function-based method in a numerically efficient manner. We then quantify the entanglement increase calculating the logarithmic negativity of the output state and discuss and compare the performance of the protocols.
This thesis explores the role of non-classical correlations in bipartite continuous variable quantum systems, and the approach taken is three-fold. We show that given two initially entangled atomic ensembles, it is possible to probabilistically increase the entanglement between them using a beamsplitter-like interaction formed from two quantum non-demolition (QND) interactions with auxiliary polarised light modes. We then develop an elegant method to calculate density matrix elements of non-Gaussian bipartite quantum states and use this to show that the entanglement in a two mode squeezed vacuum can be distilled using QND interactions and non-Gaussian elements. \n Secondly, we introduce a potential new measure of quantum entanglement in bipartite Gaussian states. This measure has an operational meaning in quantum cryptography and provides an upper bound on the amount of a secret key that can be distilled from a Gaussian probability distribution shared by two conspirators, Alice and Bob, given the presence of an eavesdropper, Eve. \n Finally, we go beyond the realm of quantum entanglement to explore other non-classical correlations in continuous variable systems. We provide solutions for a number of these measures on two mode Gaussian states and introduce the Gaussian Ameliorated Measurement Induced Disturbance (GAMID). The interplay between these different measures and quantum entanglement is examined. We then attempt to take small steps into the non-Gaussian regime by computing these non-classicality measures on the three-parameter continuous variable Werner states.
We present an effort to find a measure of non-Gaussianity of non-Gaussian states. We compute the difference between the logarithmic negativities of a non-Gaussian state and its Gaussified form as a non-Gaussian entanglement resource. We use the latter to assess the resource content of non-Gaussianity of experimentally relevant state - two- mode squeezed vacuum with a subtracted photon. We also used symplectic analysis to discard the Gaussian entanglement. Therefore the measure is reduced to the logarithmic negativity of a non-Gaussian state only. We compare the measure with the Wigner distribution and its negativity and discuss the results. 1
Quantum entanglement is the key property that makes quantum information theory different from its classical counterpart and is also a valuable physical resource with massive potential for technological applications. However, our understanding of entanglement is still far from complete despite intense research activities. Like other physical resources, the first step towards exploiting them fully is to know how to quantify. There are many reasons to focus on the entanglement of continuous-variable states since the underlying degrees of freedom of physical systems carrying quantum information are frequently continuous, rather than discrete. Much of the effort has been concentrated on Gaussian states, because these are common as the ground or \nthermal states of optical modes. Within this framework, many interesting topics have been studied and some significant progress made. Nevertheless, non-Gaussian states are also extremely important; this is especially so in condensed-phase systems, where harmonic behaviour in any \ndegree of freedom is likely to be only an approximation. So far, there is little knowledge about the quantification of entanglement in non-Gaussian states. \nThis thesis aims to contribute to the active field of research in quantum entanglement by introducing a new approach to the analysis of entanglement, especially in continuous-variable states, and shows that it leads to the first systematic quantification of the (local) entanglement \nin arbitrary bipartite non-Gaussian states. By applying this local approach, many new insights can be gained. Notably, local entanglements of systems with smooth wavefunctions are fully characterised by the derived simple expressions, provided the wavefunction is known. The local (logarithmic) negativity of any two-mode mixed states can be directly computed from the closed-form formulae given. For multi-mode mixed states, this approach provides a scheme that \npermits much simpler numerical computation for quantifying entanglement than is generally possible from directly computing the full entanglement of the system.
In the present PhD work, we focus on a specific class of quantum states of light: the non-Gaussian states. These states have the particularity of exhibiting Wigner functions with some negative values. This quantum feature is a necessary condition to perform some quantum computation task; furthermore it is also useful for various other applications, including quantum communication and metrology. Different strategies can be used to generate these states. Here, we start from Gaussian states produced by optical parametric oscillators in the continuous wave regime, (i.e. single-mode and two-mode squeezed vacuum states). The non-Gaussian feature can only be obtained by non-linear phenomena (over-quadratic Hamiltonian). In our case, the non-linearity is induced by photon-counting-based measurements (also called non-Gaussian measurements). This study is mainly divided into two parts. First, the generation of non-classical states associated with two types of qubit encoding: the single-photon state, used for quantum information with discrete variables, and the coherent state superposition (the so-called optical Schrodinger cat state), used for quantum information with continuous variables. These two states have then been used to perform some quantum information protocols. The first one addresses the problem of single-photon entanglement witness, and the other the generation of entanglement between the two encodings (also called hybrid entanglement).
In the present PhD work, we focus on a specific class of quantum states of light: the non-Gaussian states. These states have the particularity of exhibiting Wigner functions with some negative values. This quantum feature is a necessary condition to perform some quantum computation task; furthermore it is also useful for various other applications, including quantum communication and metrology. Different strategies can be used to generate these states. Here, we start from Gaussian states produced by optical parametric oscillators in the continuous wave regime, (i.e. single-mode and two-mode squeezed vacuum states). The non-Gaussian feature can only be obtained by non-linear phenomena (over-quadratic Hamiltonian). In our case, the non-linearity is induced by photon-counting-based measurements (also called non-Gaussian measurements). This study is mainly divided into two parts. First, the generation of non-classical states associated with two types of qubit encoding: the single-photon state, used for quantum information with discrete variables, and the coherent state superposition (the so-called optical Schrödinger cat state), used for quantum information with continuous variables. These two states have then been used to perform some quantum information protocols. The first one addresses the problem of single-photon entanglement witness, and the other the generation of entanglement between the two encodings (also called hybrid entanglement).