Dynamics of decoherence without dissipation in a squeezed thermal bath

Abstract: It is shown that a realistic controlled bidirectional remote state preparation is possible using a large class of entangled quantum states having a particular structure. Existing protocols of probabilistic, deterministic and joint remote state preparation are generalized to obtain the corresponding protocols of controlled bidirectional remote state preparation (CBRSP). A general way of incorporating the effects of two well-known noise processes, the amplitude-damping and phase-damping noise, on the probabilistic CBRSP process is studied in detail by considering that noise only affects the travel qubits of the quantum channel used for the probabilistic CBRSP process. Also indicated is how to account for the effect of these noise channels on deterministic and joint remote state CBRSP protocols.

Abstract: We study the dynamics of entanglement in a two-qubit system interacting with a squeezed thermal bath via a dissipative system–reservoir interaction with the system and reservoir assumed to be in a separable initial state. The resulting entanglement is studied by making use of concurrence as well as a recently introduced measure of mixed state entanglement via a probability density function which gives a statistical and geometrical characterization of entanglement by exploring the entanglement content in the various subspaces spanning the two-qubit Hilbert space. We also make an application of the two-qubit dissipative dynamics to a simplified model of quantum repeaters.

Abstract: The effect of noise on various protocols of secure quantum communication has been studied. Specifically, we have investigated the effect of amplitude damping, phase damping, squeezed generalized amplitude damping, Pauli type as well as various collective noise models on the protocols of quantum key distribution, quantum key agreement, quantum secure direct quantum communication and quantum dialogue. From each type of protocol of secure quantum communication, we have chosen two protocols for our comparative study: one based on single-qubit states and the other one on entangled states. The comparative study reported here has revealed that single-qubit-based schemes are generally found to perform better in the presence of amplitude damping, phase damping, squeezed generalized amplitude damping noises, while entanglement-based protocols turn out to be preferable in the presence of collective noises. It is also observed that the effect of noise depends upon the number of rounds of quantum communication involved in a scheme of quantum communication. Further, it is observed that squeezing, a completely quantum mechanical resource present in the squeezed generalized amplitude channel, can be used in a beneficial way as it may yield higher fidelity compared to the corresponding zero squeezing case.

Abstract: Single-qubit dissipative and non-dissipative channels, set in the general scenario of a system's interaction with a squeezed thermal bath, are compared in the Choi isomorphism framework, to bring out their contrasting rank and geometric properties. The equivalence of commutativity between the signal states and the Kraus operators to that between the system and interaction Hamiltonian, and thus to non-dissipativeness, is pointed out. Two distinct unitarily equivalent Kraus representations of the dissipative channel, one based on the Choi isomorphism, and the other based on an ansatz, are used to illustrate that the orthogonality of Kraus operators under the Hilbert---Schmidt inner product is not a unitary invariant. Unlike the non-dissipative (Pauli) channels, the dissipative (squeezed generalized amplitude damping) channels do not form a convex set. Further, whereas the rank of Pauli channels can be any positive integer up to 4, that of the amplitude damping ones is either 2 or 4. In the latter case, a noise range is identified where environmental squeezing counteracts the effect of thermal decoherence.

Abstract: We study nonclassical features in a number of spin-qubit systems including single, two and three qubit states, as well as an N qubit Dicke model and a spin-1 system, of importance in the fields of quantum optics and information. This is done by analyzing the behavior of the well known Wigner, P , and Q quasiprobability distributions on them. We also discuss the not so well known F function and specify its relation to the Wigner function. Here we provide a comprehensive analysis of quasiprobability distributions for spin-qubit systems under general open system effects, including both pure dephasing as well as dissipation. This makes it relevant from the perspective of experimental implementation.

Abstract: Part I Fundamental Concepts: 1 Introduction and overview 2 Introduction to quantum mechanics 3 Introduction to computer science Part II Quantum Computation: 4 Quantum circuits 5 The quantum Fourier transform and its application 6 Quantum search algorithms 7 Quantum computers: physical realization Part III Quantum Information: 8 Quantum noise and quantum operations 9 Distance measures for quantum information 10 Quantum error-correction 11 Entropy and information 12 Quantum information theory Appendices References Index

Abstract: PREFACE ACKNOWLEDGEMENTS PART 1: PROBABILITY IN CLASSICAL AND QUANTUM MECHANICS 1. Classical probability theory and stochastic processes 2. Quantum Probability PART 2: DENSITY MATRIX THEORY 3. Quantum Master Equations 4. Decoherence PART 3: STOCHASTIC PROCESSES IN HILBERT SPACE 5. Probability distributions on Hilbert space 6. Stochastic dynamics in Hilbert space 7. The stochastic simulation method 8. Applications to quantum optical systems PART 4: NON-MARKOVIAN QUANTUM PROCESSES 9. Projection operator techniques 10. Non-Markovian dynamics in physical systems PART 5: RELATIVISTIC QUANTUM PROCESSES 11. Measurements in relativistic quantum mechanics 12. Open quantum electrodynamics

Abstract: By considering a radiating gas as a single quantum-mechanical system, energy levels corresponding to certain correlations between individual molecules are described. Spontaneous emission of radiation in a transition between two such levels leads to the emission of coherent radiation. The discussion is limited first to a gas of dimension small compared with a wavelength. Spontaneous radiation rates and natural line breadths are calculated. For a gas of large extent the effect of photon recoil momentum on coherence is calculated. The effect of a radiation pulse in exciting "super-radiant" states is discussed. The angular correlation between successive photons spontaneously emitted by a gas initially in thermal equilibrium is calculated.

Abstract: A formalism has been developed, using Feynman's space-time formulation of nonrelativistic quantum mechanics whereby the behavior of a system of interest, which is coupled to other external quantum systems, may be calculated in terms of its own variables only. It is shown that the effect of the external systems in such a formalism can always be included in a general class of functionals (influence functionals) of the coordinates of the system only. The properties of influence functionals for general systems are examined. Then, specific forms of influence functionals representing the effect of definite and random classical forces, linear dissipative systems at finite temperatures, and combinations of these are analyzed in detail. The linear system analysis is first done for perfectly linear systems composed of combinations of harmonic oscillators, loss being introduced by continuous distributions of oscillators. Then approximately linear systems and restrictions necessary for the linear behavior are considered. Influence functionals for all linear systems are shown to have the same form in terms of their classical response functions. In addition, a fluctuation-dissipation theorem is derived relating temperature and dissipation of the linear system to a fluctuating classical potential acting on the system of interest which reduces to the Nyquist–Johnson relation for noise in the case of electric circuits. Sample calculations of transition probabilities for the spontaneous emission of an atom in free space and in a cavity are made. Finally, a theorem is proved showing that within the requirements of linearity all sources of noise or quantum fluctuation introduced by maser-type amplification devices are accounted for by a classical calculation of the characteristics of the maser.