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 investigated the entropic uncertainty relation under the relativistic motion and showed that the quantum channel can be modeled as a quantum memory, which can be altered by considering a particle as quantum memory.
Abstract: The uncertainty principle is the most important feature of quantum mechanics, which can be called the heart of quantum mechanics. This principle sets a lower bound on the uncertainties of two incompatible measurement. In quantum information theory, this principle is expressed in terms of entropic measures. Entropic uncertainty bound can be altered by considering a particle as a quantum memory. In this work we investigate the entropic uncertainty relation under the relativistic motion. In relativistic uncertainty game Alice and Bob agree on two observables, $ \widehat{Q}$
and $ \widehat{R}$
, Bob prepares a particle constructed from the free fermionic mode in the quantum state and sends it to Alice, after sending, Bob begins to move with an acceleration a, then Alice does a measurement on her particle A and announces her choice to Bob, whose task is then to minimize the uncertainty about the measurement outcomes. we will have an inevitable increase in the uncertainty of the Alic’s measurement outcome due to information loss which was stored initially in B. In this work we look at the Unruh effect as a quantum noise and we will characterize it as a quantum channel.
11 citations
TL;DR: This work derives an OSD representation for a two-qubit amplitude-damping channel and applies it to general Hermitian-sum maps and can be extended to the more general, linear maps.
Abstract: When a model for quantum noise is exactly solvable, a Kraus (or operator-sum) representation can be derived from the spectral decomposition of the Choi matrix for the channel. More generally, a Kraus representation can be obtained from any positive-sum (or ensemble) decomposition of the matrix. Here we extend this idea to any Hermitian-sum decomposition. This yields what we call the "operator-sum-difference" (OSD) representation, in which the channel can be represented as the sum and difference of "subchannels." As one application, the subchannels can be chosen to be analytically diagonalizable, even if the parent channel is not (on account of the Abel-Galois irreducibility theorem), though in this case the number of the OSD representation operators may exceed the channel rank. Our procedure is applicable to general Hermitian (completely positive or non-completely positive) maps and can be extended to the more general, linear maps. As an illustration of the application, we derive an OSD representation for a two-qubit amplitude-damping channel.
10 citations
TL;DR: 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: 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 entirely 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.
10 citations
TL;DR: In this article, the authors study various facets of non-Markovian evolution in the context of coined quantum walks, with particular stress on disambiguating the internal vs. environmental contributions to non-markovian backflow.
Abstract: Quantum non-Markovianity of a quantum noisy channel manifests typically as information backflow, characterized by the departure of the intermediate map from complete positivity, though we indicate certain noisy channels that don't exhibit this behavior. In complex systems, non-Markovianity becomes more involved on account of subsystem dynamics. Here we study various facets of non-Markovian evolution, in the context of coined quantum walks, with particular stress on disambiguating the internal vs. environmental contributions to non-Markovian backflow. For the above problem of disambiguation, we present a general power-spectral technique based on a distinguishability measure such as trace-distance or correlation measure such as mutual information. We also study various facets of quantum correlations in the transition from quantum to classical random walks, under the considered non-Markovian noise models. The potential for the application of this analysis to the quantum statistical dynamics of complex systems is indicated.
9 citations
TL;DR: In this article, it was shown that mixing channels with a singularity can lead to the elimination of singularities in the resultant channel and the connection to non-Markovianity (in the sense of completely positive indivisibility) was pointed out.
Abstract: Quantum non-Markovianity of channels can be produced by mixing Markovian channels, as observed recently by various authors. We consider an analogous question of whether singularities of the channel can be produced by mixing nonsingular channels, i.e., ones that lack them. Here we answer the question in the negative in the context of qubit Pauli channels. On the other hand, mixing channels with a singularity can lead to the elimination of singularities in the resultant channel. We distinguish between two types of singular channels, which lead under mixing to broadly quite different properties of the singularity in the resultant channel. The connection to non-Markovianity (in the sense of completely positive indivisibility) is pointed out. These results impose nontrivial restrictions on the experimental realization of noninvertible quantum channels by a process of channel mixing.
9 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