Experimental investigation of the evolution of gaussian quantum discord in an open system

Gaussian quantum discord is a measure of quantum correlations in Gaussian systems. Using Gaussian discord, we quantify the quantum correlations of a bipartite entangled state and a separable two-mode mixture of coherent states. We experimentally analyze the effect of noise addition and dissipation on Gaussian discord and show that the former noise degrades the discord, while the latter noise for some states leads to an increase of the discord. In particular, we experimentally demonstrate the near death of discord by noisy evolution and its revival through dissipation.     

General-dyne unravelling of a thermal master equation

We analyze the unravelling of the quantum optical master equation at finite temperature due to direct, continuous, general-dyne detection of the environment. We first express the general-dyne Positive Operator Valued Measure (POVM) in terms of the eigenstates of a non-Hermitian operator associated to the general-dyne measurement. Then we derive the stochastic master equation obtained by considering the interaction between the system and a reservoir at thermal equilibrium, which is measured according to the POVM previously determined. Finally, we present a feasible measurement scheme, which reproduces general-dyne detection for any value of the parameter characterizing the stochastic master equation.     

Dynamics of a qubit as a classical stochastic process with time-correlated noise: minimal measurement invasiveness

So far it has been shown that the quantum dynamics cannot be described as a classical Markov process unless the number of classical states is uncountably infinite. In this Letter, we present a stochastic model with time-correlated noise that exactly reproduces any unitary evolution of a qubit and requires just four classical states. The invasive updating of only 1 bit during a measurement accounts for the quantum violation of the Leggett-Garg inequalities. Unlike in a pilot-wave theory, the stochastic forces governing the jumps among the four states do not depend on the quantum state but only on the unitary evolution. This model is used to derive a local hidden variable model, augmented by 1 bit of classical communication, for simulating entangled Bell states.     

Some exact results on discrete noisy maps

Using the Chapman-Kolmogorov type equation introduced by H. Haken and G. Mayer-Kress for discrete time processes we derive forward and backward equations for the corresponding transition probability and obtain an integral equation for the conditional first passage time. In the case of linear dynamics with Gaussian noise we present the exact solution of the Chapman-Kolmogorov equation.     

Quantum Dynamics in Noisy Backgrounds: from Sampling to Dissipation and Fluctuations

We investigate the dynamics of a quantum system coupled linearly to Gaussian white noise using functional methods. By performing the integration over the noisy field in the evolution operator, we get an equivalent non-Hermitian Hamiltonian, which evolves the quantum state with a dissipative dynamics. We also show that if the integration over the noisy field is done for the time evolution of the density matrix, a gain contribution from the fluctuations can be accessed in addition to the loss one from the non-hermitian Hamiltonian dynamics. We illustrate our study by computing analytically the effective non-Hermitian Hamiltonian, which we found to be the complex frequency harmonic oscillator, with a known evolution operator. It leads to space and time localisation, a common feature of noisy quantum systems in general applications.     

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.     

Noise dephasing in edge states of the integer quantum Hall regime

An electronic Mach-Zehnder interferometer is used in the integer quantum Hall regime at a filling factor 2 to study the dephasing of the interferences. This is found to be induced by the electrical noise existing in the edge states capacitively coupled to each other. Electrical shot noise created in one channel leads to phase randomization in the other, which destroys the interference pattern. These findings are extended to the dephasing induced by thermal noise instead of shot noise: it explains the underlying mechanism responsible for the finite temperature coherence time tau_{phi}(T) of the edge states at filling factor 2, measured in a recent experiment. Finally, we present here a theory of the dephasing based on Gaussian noise, which is found to be in excellent agreement with our experimental results.     

Disentanglement Dynamics in Nonequilibrium Environments

We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.     

Estimating Quantum Mutual Information of Continuous-Variable Quantum States by Measuring Purity and Covariance Matrix

We derive accessible upper and lower bounds for continuous-variable (CV) quantum states on quantum mutual information. The derivations are based on the observation that some functions of purities bound the difference between quantum mutual information of a quantum state and its Gaussian reference. The bounds are efficiently obtainable by measuring purities and the covariance matrix without multimode quantum state reconstruction. We extend our approach to the upper and lower bounds for the quantum total correlation of CV multimode quantum states. Furthermore, we investigate the relations of the bounds for the quantum mutual information with the bounds for the quantum conditional entropy.     

Quantum fidelity for Gaussian states describing the evolution of open systems

Using the expression of the fidelity for the most general Gaussian quantum states, the quantum fidelity is studied for the states of a harmonic oscillator interacting with an environment, in particular with a thermal bath. The time evolution of the considered system is described in the framework of the theory of open systems based on quantum dynamical semigroups. By taking a correlated squeezed Gaussian state as initial state, we calculate the quantum fidelity for both undisplaced and displaced states. The time evolution of the quantum fidelity is analyzed depending on the squeezing and correlation parameters characterizing the initial Gaussian state and on the dissipation constant and temperature of the thermal bath.     

Redundancy and Synergy of an Entangling Cloner in Continuous-Variable Quantum Communication

We address minimization of information leakage from continuous-variable quantum channels. It is known, that regime of minimum leakage can be accessible for the modulated signal states with variance equivalent to a shot noise, i.e., vacuum fluctuations, in the case of collective attacks. Here we derive the same condition for the individual attacks and analytically study the properties of the mutual information quantities in and out of this regime. We show that in such regime a joint measurement on the modes of a two-mode entangling cloner, being the optimal individual eavesdropping attack in a noisy Gaussian channel, is no more effective that independent measurements on the modes. Varying variance of the signal out of this regime, we observe the nontrivial statistical effects of either redundancy or synergy between the measurements of two modes of the entangling cloner. The result reveals the non-optimality of entangling cloner individual attack for sub-shot-noise modulated signals. Considering the communication between the cloner modes, we show the advantage of knowing the residual noise after its interaction with the cloner and extend the result to a two-cloner scheme.     

Hopping Transport and Stochastic Dynamics of Electrons in Plasma Layers

We investigate the stochastic dynamics and the hopping transfer of electrons embedded into two‐dimensional atomic layers. First we formulate the quantum statistics of general atom ‐ electron systems based on the tight‐binding approximation and express ‐ following linear response transport theory ‐ the quantum‐mechanical time correlation functions and the conductivity by means of equilibrium time correlation functions. Within the relaxation time approach an expression for the effective collision frequency is derived in Born approximation, which takes into account quantum effects and dynamic effects of the atom motion through the dynamic structure factor of the lattice and the quantum dynamics of the electrons. In the last part we derive Pauli equations for the stochastic electron dynamics including nonlinear excitations of the atomic subsystem. We carry out Monte Carlo simulations and show that mean square displacements of electrons and transport properties are in a moderate to high temperature regime strongly influenced by by soliton‐type excitations and demonstrate the existence of percolation effects (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the theory of Brownian motion with the Alder-Wainwright effect

The Stokes-Boussinesq-Langevin equation, which describes the time evolution of Brownian motion with the Alder-Wainwright effect, can be treated in the framework of the theory of KMO-Langevin equations which describe the time evolution of a real, stationary Gaussian process withT-positivity (reflection positivity) originating in axiomatic quantum field theory. After proving the fluctuation-dissipation theorems for KMO-Langevin equations, we obtain an explicit formula for the deviation from the classical Einstein relation that occurs in the Stokes-Boussinesq-Langevin equation with a white noise as its random force. We are interested in whether or not it can be measured experimentally.     

On the Classical Capacity of General Quantum Gaussian Measurement

In this paper, we consider the classical capacity problem for Gaussian measurement channels. We establish Gaussianity of the average state of the optimal ensemble in the general case and discuss the Hypothesis of Gaussian Maximizers concerning the structure of the ensemble. Then, we consider the case of one mode in detail, including the dual problem of accessible information of a Gaussian ensemble. Our findings are relevant to practical situations in quantum communications where the receiver is Gaussian (say, a general-dyne detection) and concatenation of the Gaussian channel and the receiver can be considered as one Gaussian measurement channel. Our efforts in this and preceding papers are then aimed at establishing full Gaussianity of the optimal ensemble (usually taken as an assumption) in such schemes.     

Large Deviations of Lattice Hamiltonian Dynamics Coupled to Stochastic Thermostats

We discuss the Donsker-Varadhan theory of large deviations in the framework of Hamiltonian systems thermostated by a Gaussian stochastic coupling. We derive a general formula for the Donsker-Varadhan large deviation functional for dynamics which satisfy natural properties under time reversal. Next, we discuss the characterization of the stationary states as the solution of a variational principle and its relation to the minimum entropy production principle. Finally, we compute the large deviation functional of the current in the case of a harmonic chain thermostated by a Gaussian stochastic coupling.     

Robustness and diffusion of pointer states

Classical properties of an open quantum system emerge through its interaction with other degrees of freedom (decoherence). We treat the case where this interaction produces a Markovian master equation for the system. We derive the corresponding distinguished local basis (pointer basis) by three methods. The first demands that the pointer states mimic as closely as possible the local nonunitary evolution. The second demands that the local entropy production be minimal. The third imposes robustness on the inherent quantum and emerging classical uncertainties. All three methods lead to localized Gaussian pointer states, their formation and diffusion being governed by well-defined quantum Langevin equations.     

Correlation Dynamics of Three-Qubit System Under a Classical Dephasing Environment

By starting from the stochastic Hamiltonian of the three correlated spins and modeling their frequency fluctuations as caused by dephasing noisy environments described by Ornstein-Uhlenbeck (OU) processes, we study the dynamics of quantum correlations, including entanglement and quantum discord. Of course, in this article, we use two definitions for the quantum discord (global quantum discord and quantum dissension). We prepared initially our open system with the Greenberger-Horne-Zeilinger (GHZ) and W states and present the exact solutions for evolution dynamics of entanglement and quantum discord between three spins under both Markovian and non-Markovian regime of this classical noise. By comparison the dynamics of entanglement with that of quantum discord we find that entanglement can be more robust than quantum discord against this noise. It is shown that by considering non-Markovian extensions the survival time of correlations prolong. Also, we compare the results of two definitions of the quantum discord and show that the quantum dissension is equal to the global quantum discord for GHZ state, but they are unequal for the W state.     

Squeezed vacuum as a universal quantum probe

We address local quantum estimation of bilinear Hamiltonians probed by Gaussian states. We evaluate the relevant quantum Fisher information (QFI) and derive the ultimate bound on precision. Upon maximizing the QFI we found that single- and two-mode squeezed vacuum represent an optimal and universal class of probe states, achieving the so-called Heisenberg limit to precision in terms of the overall energy of the probe. We explicitly obtain the optimal observable based on the symmetric logarithmic derivative and also found that homodyne detection assisted by Bayesian analysis may achieve estimation of squeezing with near-optimal sensitivity in any working regime.     

Projection operator techniques and Hilbert space averaging in the quantum theory of nonequilibrium systems

The development of efficient strategies for the treatment of the dynamics of relevant observables in complex quantum systems plays a decisive role in the theory of quantum relaxation and transport behavior. Here we discuss the most important tools that are based on the projection operator techniques of nonequilibrium statistical mechanics. For both the Nakajima-Zwanzig and the time-convolutionless projection operator technique we derive the equations of motion for a set of relevant observables and develop explicit expressions in second and fourth order of the corresponding perturbation expansions. We also discuss the Hilbert space average method which is based on the idea of a best guess of conditional quantum expectations determined by an average over a suitable region in the underlying Hilbert space, and relate this method to the projection operator technique.