Entanglement and nonclassicality for multi-mode radiation field states

Nonclassicality in the sense of quantum optics is a prerequisite for entanglement in multi-mode radiation states. In this work we bring out the possibilities of passing from the former to the latter, via action of classicality preserving systems like beamsplitters, in a transparent manner. For single mode states, a complete description of nonclassicality is available via the classical theory of moments, as a set of necessary and sufficient conditions on the photon number distribution. We show that when the mode is coupled to an ancilla in any coherent state, and the system is then acted upon by a beamsplitter, these conditions turn exactly into signatures of NPT entanglement of the output state. Since the classical moment problem does not generalize to two or more modes, we turn in these cases to other familiar sufficient but not necessary conditions for nonclassicality, namely the Mandel parameter criterion and its extensions. We generalize the Mandel matrix from one-mode states to the two-mode situation, leading to a natural classification of states with varying levels of nonclassicality. For two--mode states we present a single test that can, if successful, simultaneously show nonclassicality as well as NPT entanglement. We also develop a test for NPT entanglement after beamsplitter action on a nonclassical state, tracing carefully the way in which it goes beyond the Mandel nonclassicality test. The result of three--mode beamsplitter action after coupling to an ancilla in the ground state is treated in the same spirit. The concept of genuine tripartite entanglement, and scalar measures of nonclassicality at the Mandel level for two-mode systems, are discussed. Numerous examples illustrating all these concepts are presented.Comment: Latex, 46 page

Multiphoton Quantum Optics and Quantum State Engineering

We present a review of theoretical and experimental aspects of multiphoton quantum optics. Multiphoton processes occur and are important for many aspects of matter-radiation interactions that include the efficient ionization of atoms and molecules, and, more generally, atomic transition mechanisms; system-environment couplings and dissipative quantum dynamics; laser physics, optical parametric processes, and interferometry. A single review cannot account for all aspects of such an enormously vast subject. Here we choose to concentrate our attention on parametric processes in nonlinear media, with special emphasis on the engineering of nonclassical states of photons and atoms. We present a detailed analysis of the methods and techniques for the production of genuinely quantum multiphoton processes in nonlinear media, and the corresponding models of multiphoton effective interactions. We review existing proposals for the classification, engineering, and manipulation of nonclassical states, including Fock states, macroscopic superposition states, and multiphoton generalized coherent states. We introduce and discuss the structure of canonical multiphoton quantum optics and the associated one- and two-mode canonical multiphoton squeezed states. This framework provides a consistent multiphoton generalization of two-photon quantum optics and a consistent Hamiltonian description of multiphoton processes associated to higher-order nonlinearities. Finally, we discuss very recent advances that by combining linear and nonlinear optical devices allow to realize multiphoton entangled states of the electromnagnetic field, that are relevant for applications to efficient quantum computation, quantum teleportation, and related problems in quantum communication and information.Comment: 198 pages, 36 eps figure

Realistic continuous-variable quantum teleportation using a displaced Fock state channel

We investigate ideal and non-ideal continuous-variable quantum teleportation protocols realized by using an entangled displaced Fock state resource. The characteristic function formulation is applied to measure the relative performance of displaced Fock state for teleporting squeezed and coherent states. It is found that for such single-mode input fields, the average fidelity remains at the classical threshold, suggesting that the displaced Fock states are not advantageous for teleportation. We also discuss the major decoherence effects, caused by the inaccuracy in Bell measurements and photon losses for the propagation of optical fields via fibre channels. The changes in the teleportation fidelity are described by adjusting the gain factor ($g$), reflectivity ($R$), mode damping ($\tau$), and the number of thermal photons ($n_\mathrm{th}$). The possibility of successful teleportation can be optimized by fixing these realistic parameters.Comment: 16 pages, 9 figure

Wigner negativity on the sphere

The rise of quantum information theory has largely vindicated the long-held belief that Wigner negativity is an indicator of genuine nonclassicality in quantum systems. This thesis explores its manifestation in spin-j systems using the spherical Wigner function. Common symmetric multi-qubit states are studied and compared. Spin coherent states are shown to never have vanishing Wigner negativity. Pure states that maximize negativity are determined and analyzed using the Majorana stellar representation. The relationship between negativity and state mixedness is discussed, and polytopes characterizing unitary orbits of lower-bounded Wigner functions are studied. Results throughout are contrasted with similar works on symmetric state entanglement and other forms of phase-space nonclassicality