Dynamics of decoherence without dissipation in a squeezed thermal bath
TL;DR: In this article, a generic open quantum system where the coupling between the system and its environment is of an energy-preserving quantum nondemolition (QND) type is studied.
Abstract: We study a generic open quantum system where the coupling between the system and its environment is of an energy-preserving quantum nondemolition (QND) type. We obtain the general master equation for the evolution of such a system under the influence of a squeezed thermal bath of harmonic oscillators. From the master equation it can be seen explicitly that the process involves decoherence or dephasing without any dissipation of energy. We work out the decoherence-causing term in the high- and zero-temperature limits and check that they match with known results for the case of a thermal bath. The decay of the coherence is quantified as well by the dynamics of the linear entropy of the system under various environmental conditions. We make a comparison of the quantum statistical properties between QND and dissipative types of evolution using a two-level atomic system and a harmonic oscillator.
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TL;DR: In this article, the authors study the dynamics of the quantum phase distribution associated with the reduced density matrix of a system for a number of situations of practical importance, as the system evolves under the influence of its environment, interacting via a quantum non-deletion type of coupling, such that there is decoherence without dissipation, as well as when it interacts via a dissipative interaction, resulting in decocherence and dissipation.
Abstract: We study the dynamics of the quantum phase distribution associated with the reduced density matrix of a system for a number of situations of practical importance, as the system evolves under the influence of its environment, interacting via a quantum nondemolition type of coupling, such that there is decoherence without dissipation, as well as when it interacts via a dissipative interaction, resulting in decoherence as well as dissipation. The system is taken to be either a two-level atom (or, equivalently, a spin-1/2 system) or a harmonic oscillator, and the environment is modeled as a bath of harmonic oscillators, starting out in a squeezed thermal state. The impact of the different environmental parameters on the dynamics of the quantum phase distribution for the system starting out in various initial states is explicitly brought out. An interesting feature that emerges from our work is that the relationship between squeezing and temperature effects depends on the type of system-bath interaction. In the case of a quantum nondemolition type of interaction, squeezing and temperature work in tandem, producing a diffusive effect on the phase distribution. In contrast, in the case of a dissipative interaction, the influence of temperature can be counteracted by squeezing, whichmore » manifests as a resistance to randomization of phase. We make use of the phase distributions to bring out a notion of complementarity in atomic systems. We also study the variance of the phase using phase distributions conditioned on particular initial states of the system.« less
30 citations
TL;DR: In this paper, the authors studied the non-Markovian entanglement dynamics of two qubits in a common squeezed bath and showed a remarkable difference between their non-markovian dynamics and its Markovian counterpart.
Abstract: We study the non-Markovian entanglement dynamics of two qubits in a common squeezed bath. We see a remarkable difference between the non-Markovian entanglement dynamics and its Markovian counterpart. We show that a non-Markovian decoherence-free state is also decoherence free in the Markovian regime, but all the Markovian decoherence-free states are not necessarily decoherence free in the non-Markovian domain. We extend our calculation from a squeezed vacuum bath to a squeezed thermal bath, where we see the effect of finite bath temperatures on the entanglement dynamics.
29 citations
TL;DR: In this paper, a generalized phase gate on a line is used to generate a quantum walk on a unitary unitary transformation, which is a symmetry for both noisy and noiseless quantum walks.
Abstract: Augmenting the unitary transformation which generates a quantum walk by a generalized phase gate $G$ is a symmetry for both noisy and noiseless quantum walk on a line, in the sense that it leaves the position probability distribution invariant. However, this symmetry breaks down in the case of a quantum walk on an $n$ cycle, and hence can be regarded as a probe of the walk topology. Noise, modeled here as phase flip and generalized amplitude damping channels, tends to restore the symmetry because it classicalizes the walk. However, symmetry restoration happens even in the regime where the walker is not entirely classical, because noise also has the effect of desensitizing the operation $G$ to the walk topology. We discuss methods for physical implementation, and talk about the wider implications to condensed matter systems.
28 citations
TL;DR: In this paper, the dynamics of entanglement in a two-qubit system interacting with an initially squeezed thermal environment via aquantum non-demolition system-reservoir interaction was analyzed.
Abstract: We analyze the dynamics of entanglement in a two-qubit system
interacting with an initially squeezed thermal environment via a
quantum nondemolition system-reservoir interaction, with the system
and reservoir assumed to be initially separable. We compare and
contrast the decoherence of the two-qubit system in the case where
the qubits are mutually close-by (`collective regime’) or distant
(`localized regime’) with respect to the spatial variation of the
environment. Sudden death of entanglement (as quantified by
concurrence) is shown to occur in the localized case rather than in
the collective case, where entanglement tends to `ring down’.
A consequence of the QND character of the interaction is that the
time-evolved fidelity of a Bell state never falls below $1/\sqrt{2}$
,
a fact that is useful for quantum communication applications
like a quantum repeater. Using
a novel quantification of mixed state entanglement, we show that
there are noise regimes where even though entanglement
vanishes, the state is still available for
applications like NMR quantum computation, because of the presence
of a pseudo-pure component.
28 citations
TL;DR: In this paper, two non-Markovian models: random telegraph noise and non-markovian dephasing are considered from the perspective of quantum Fisher information flow and the quantum coherence and its balance with mixedness is studied.
Abstract: We consider two non-Markovian models: random telegraph noise and non-Markovian dephasing. The memory in these models is studied from the perspective of quantum Fisher information flow. This is found to be consistent with the other well-known witnesses of non-Markovianity. The two noise channels are characterized quantum information theoretically by studying their gate and channel fidelities. Further, the quantum coherence and its balance with mixedness is studied. This helps to put in perspective the role that the two noise channels can play in various facets of quantum information processing and quantum communication.
26 citations
References
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Book•
01 Jan 2000
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
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
25,929 citations
Book•
29 Aug 2002
TL;DR: Probability in classical and quantum physics has been studied in this article, where classical probability theory and stochastic processes have been applied to quantum optical systems and non-Markovian dynamics in physical systems.
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
6,325 citations
TL;DR: In this article, the authors considered a radiating gas as a single quantum-mechanical system, and the energy levels corresponding to certain correlations between individual molecules were described, where spontaneous emission of radiation in a transition between two such levels leads to the emission of coherent radiation.
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.
5,672 citations
TL;DR: In this paper, 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.
2,288 citations