Quantum fidelity of Gaussian states in open systems

Using the expression of the fidelity for the most general Gaussian quantum states, the behaviour of the quantum fidelity is described for the states of a harmonic oscillator interacting with an environment, in particular with a thermal bath. By taking a correlated squeezed Gaussian state as initial state, we calculate the quantum fidelity for both kinds of undisplaced and displaced states, and for different values of the squeezing and correlation parameters and of the environment temperature.     

Two-mode Gaussian states as resource of secure quantum teleportation in open systems

For secure quantum teleportation (SQT) of coherent states two conditions are necessary to be fulfilled: Gaussian-state resources with two-way steering and teleportation fidelity higher than 2/3. We investigate and compare squeezed thermal states and squeezed vacuum states as initial resource states for SQT in an open quantum system, consisting of two uncoupled harmonic oscillators interacting with a thermal environment. The evolution of the open system is obtained in terms of the covariance matrix, by using the Gorini-Kossakowski-Lindblad-Sudarshan master equation. The SQT conditions are satisfied in a longer period of time in the case of initial squeezed vacuum states, therefore these states are better resource states for SQT than squeezed thermal states. We show that the admissible time for SQT decreases by increasing temperature, dissipation coefficient and average number of thermal photons, while for greater values of the squeezing parameter, SQT conditions are satisfied in a longer period of time.     

Quantum key distillation from Gaussian states by Gaussian operations

We study the secrecy properties of Gaussian states under Gaussian operations. Although such operations are useless for quantum distillation, we prove that it is possible to distill a secret key secure against any attack from sufficiently entangled Gaussian states with nonpositive partial transposition. Moreover, all such states allow for key distillation, when Eve is assumed to perform finite-size coherent attacks before the reconciliation process.     

一个描述金融投资项目演化的量子力学状态方程

本文提出了一个描述金融投资项目演化的量子力学状态方程,该方程的参数比较好地模拟了金融市场的基本要素,包括投资(输入)、资产损耗(缩水)、资产增益、和收益(输出)等,方程中的量子力学算符也能够反映该项目的动力学过程与特征,所以能代表一类金融投资项目(其状态用Dirac符号表示)在市场中的演化模式.通过引入纠缠态表象得出了该方程的量子解(算符之和形式),该量子解给出了初态与终态的联系,也就给出了投资项目的动态过程.作为例子,求出单一投资项目在金融市场中的演化,不但得出了符合市场演化趋势的解,而且提出了二项-负二项纠缠态.在推导过程中,充分利用了Dirac符号和有序算符内的积分技术(IWOP).     

Markovian evolution of Gaussian states in the semiclassical limit

We derive an approximate Gaussian solution of the Lindblad equation in the semiclassical limit, given a general Hamiltonian and linear coupling with the environment. The theory is carried out in the chord representation and describes the evolved quantum characteristic function, which gives direct access to the Wigner function and the position representation of the density operator by Fourier transforms. The propagation is based on a system of non-linear equations taking place in a double phase space, which coincides with Heller's theory of unitary evolution of Gaussian wave packets when the Lindbladian part is zero. The example of a double well is worked out.     

Testing the fidelity of Gaussian processes for cosmography

The dependence of implications from observations on cosmological models is an intractable problem not only in cosmology, but also in astrophysics. Gaussian processes(GPs), a powerful nonlinear interpolating tool without assuming a model or parametrization, have been widely used to directly reconstruct functions from observational data(e.g., expansion rate and distance measurements) for cosmography. However, the fidelity of this reconstructing method has never been checked. In this study, we test the fidelity of GPs for cosmography by mocking observational data sets comprising different number of events with various uncertainty levels. These factors are of great importance for the fidelity of reconstruction. That is, for the expansion rate measurements, GPs are valid for reconstructing the functions of the Hubble parameter versus redshift when the number of observed events is as many as 256 and the uncertainty of the data is ～3%. Moreover, the distance-redshift relation reconstructed from the observations of the upcoming Dark Energy Survey type la supernovae is credible.     

Preferred states of open electronic systems

System-environment interaction may introduce dynamic destruction of quantum coherence, resulting in a special representation named as pointer states. In this work, pointer states of an open electronic system are studied. The decoherence effect is taken into account through two different ways which are Büttiker's virtual probe model and strong electron-phonon interaction in the polaron picture. The pointer states of the system with different coupling strength are investigated. The pointer states are identified by tracking the eigenstates of the density matrix in real-time propagation. It is found that the pointer states can emerge for arbitrary coupling strength. And the pointer states deform to the eigenstates of the system in the strong coupling limit, which indicates the vanish of quantumness in the strong coupling limit.     

Quantum decoherence in the theory of open systems

Within the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We also calculate the decoherence time scale and analyze the transition from quantum to classical behavior of the considered system. The text was submitted by the author in English.     

Quantum entanglement and nonlocality properties of two-mode Gaussian squeezed states

Quantum entanglement and nonlocality properties of a family of two-mode Gaussian pure states have been investigated. The results show that the entanglement of these states is determined by both the two-mode squeezing parameter and the difference of the two single-mode squeezing parameters. For the same two-mode squeezing parameter, these states show larger entanglement than the usual two-mode squeezed vacuum state. The violation of Bell inequality depends strongly on all the squeezing parameters of these states and disappears completely in the limit of large squeezing. In particular, these states can exhibit much stronger violation of local realism than two-mode squeezed vacuum state in the range of experimentally available squeezing values.     

Quantum and classical correlations in tripartite Gaussian states of light

We demonstrate an optical scheme involving two interlinked nonlinear interactions taking place simultaneously in a second-order nonlinear crystal. The three-mode output state is fully inseparable and endowed with perfect photon-number correlations among the generated fields. In order to discriminate between classical and quantum correlations we evaluate the quantum noise reduction, i.e. compare the fluctuations of the difference photocurrent between one mode and the sum of the other two with those coming from three uncorrelated coherent states. Preliminary results indicate that our scheme may achieve three-mode sub-shot noise correlations with current technology.     

Quasistationary states in open disordered systems

Institute of Radiophysics and Electronics, Academy of Sciences of the Ukrainian SSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 33, No. 1, pp. 61–64, January, 1990.     

Quantum states and potentialities of quantum systems

In a previous article it was shown that in general quantum states represent perspectives on the potentialities of quantum systems, rather than the potentialities themselves. In the present paper the following questions are investigated in the context of this result: (1) How do quantum states which undergo collapse transform under pure translations? (2) Under what conditions do quantum states represent the potentialities themselves? Two alternatives are presented in response to the first question: (1) Quantum states are scalars under translations. (2) The collapse of a quantum state propagates between frames of reference at the speed of light. The advantages and disadvantages of the two alternatives are discussed. The response to the second question is shown to depend on the chosen alternative. In addition, the second alternative is shown to lead to a consistent view of quantum states as “potential perspectives on potentialities.”     

Quantum transport from the perspective of quantum open systems

By viewing the non-equilibrium transport setup as a quantum open system, we propose a reduced-density-matrix based quantum transport formalism. At the level of self-consistent Born approximation, it can precisely account for the correlation between tunneling and the system internal many-body interaction, leading to certain novel behavior such as the non-equilibrium Kondo effect. It also opens a new way to construct time-dependent density functional theory for transport through large-scale complex systems.     

Quantum fidelity in the thermodynamic limit

We study quantum fidelity, the overlap between two ground states of a many-body system, focusing on the thermodynamic regime. We show how a drop in fidelity near a critical point encodes universal information about a quantum phase transition. Our general scaling results are illustrated in the quantum Ising chain for which a remarkably simple expression for fidelity is found.     

Quantum kinetic equations in systems with bound states

Starting from the quantum mechanical BBGKY-hierarchy kinetic equations in systems with two particles bound states are given in this paper. With this equation it is possible to consider transport properties in nonideal gases with three particles reactions.     

Quantum freeze of fidelity decay for chaotic dynamics

We show that the mechanism of quantum freeze of fidelity decay for perturbations with a zero time average, recently discovered for a specific case of integrable dynamics [New J. Phys. 5, 109 (2003)], can be generalized to arbitrary quantum dynamics. We work out explicitly the case of a chaotic classical counterpart, for which we find semiclassical expressions for the value and the range of the plateau of fidelity. After the plateau ends, we find explicit expressions for the asymptotic decay, which can be exponential or Gaussian depending on the ratio of the Heisenberg time to the decay time. Arbitrary initial states can be considered; e.g., we discuss coherent states and random states.     

Quantum games in open systems using biophysical Hamiltonians

We analyze the necessary physical conditions to model an open quantum system as a quantum game. By applying the formalism of quantum operations on a particular system, we use Kraus operators as quantum strategies. The physical interpretation is a conflict among different configurations of the environment. The resolution of the conflict displays regimes of minimum loss of information.