Jyrki Piilo

Measure for the degree of non-Markovian behavior of quantum processes in open systems

We construct a general measure for the degree of non-Markovian behavior in open quantum systems. This measure is based on the trace distance which quantifies the distinguishability of quantum states. It represents a functional of the dynamical map describing the time evolution of physical states, and can be interpreted in terms of the information flow between the open system and its environment. The measure takes on nonzero values whenever there is a flow of information from the environment back to the open system, which is the key feature of non-Markovian dynamics.

Sudden transition between classical and quantum decoherence.

We study the dynamics of quantum and classical correlations in the presence of nondissipative decoherence. We discover a class of initial states for which the quantum correlations, quantified by the quantum discord, are not destroyed by decoherence for times t<[symbol: see text]. In this initial time interval classical correlations decay. For t>[symbol: see text], on the other hand, classical correlations do not change in time and only quantum correlations are lost due to the interaction with the environment. Therefore, at the transition time [symbol: see text] the open system dynamics exhibits a sudden transition from classical to quantum decoherence regime.

Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems

An open quantum system loses its ‘quantumness’ when information about the state leaks into its surroundings. Researchers now control this so-called decoherence in a single photon. By rotating an optical filter, the information flow between the photon and its environment can be tuned. This concept could be harnessed for future quantum technologies.

Measure for the non-Markovianity of quantum processes

Recently, a measure for the non-Markovian behavior of quantum processes in open systems has been developed, which is based on the quantification of the flow of information between the open system and its environment [Phys. Rev. Lett. 103, 210401 (2009)]. The information flow is connected to the rate of change of the trace distance between quantum states, which can be interpreted in terms of the distinguishability of these states. Here, we elaborate the mathematical details of this theory, present applications to specific physical models, and discuss further theoretical and experimental implications as well as relations to alternative approaches proposed recently.

Non-Markovian Quantum Jumps

Open quantum systems that interact with structured reservoirs exhibit non-Markovian dynamics. We present a quantum jump method for treating the dynamics of such systems. This approach is a generalization of the standard Monte Carlo wave function (MCWF) method for Markovian dynamics. The MCWF method identifies decay rates with jump probabilities and fails for non-Markovian systems where the time-dependent rates become temporarily negative. Our non-Markovian quantum jump approach circumvents this problem and provides an efficient unraveling of the ensemble dynamics.

Sudden death and sudden birth of entanglement in common structured reservoirs

We study the exact entanglement dynamics of two qubits in a common structured reservoir. We demonstrate that for certain classes of entangled states, entanglement sudden death occurs, while for certain initially factorized states, entanglement sudden birth takes place. The backaction of the non-Markovian reservoir is responsible for revivals of entanglement after sudden death has occurred, and also for periods of disentanglement following entanglement sudden birth.

Statistically Validated Networks in Bipartite Complex Systems

Many complex systems present an intrinsic bipartite structure where elements of one set link to elements of the second set. In these complex systems, such as the system of actors and movies, elements of one set are qualitatively different than elements of the other set. The properties of these complex systems are typically investigated by constructing and analyzing a projected network on one of the two sets (for example the actor network or the movie network). Complex systems are often very heterogeneous in the number of relationships that the elements of one set establish with the elements of the other set, and this heterogeneity makes it very difficult to discriminate links of the projected network that are just reflecting systems heterogeneity from links relevant to unveil the properties of the system. Here we introduce an unsupervised method to statistically validate each link of a projected network against a null hypothesis that takes into account system heterogeneity. We apply the method to a biological, an economic and a social complex system. The method we propose is able to detect network structures which are very informative about the organization and specialization of the investigated systems, and identifies those relationships between elements of the projected network that cannot be explained simply by system heterogeneity. We also show that our method applies to bipartite systems in which different relationships might have different qualitative nature, generating statistically validated networks in which such difference is preserved.

Witness for initial system-environment correlations in open-system dynamics

We study the evolution of a general open quantum system when the system and its environment are initially correlated. We show that the trace distance between two states of the open system can increase above its initial value, and derive tight upper bounds for the growth of the distinguishability of open-system states. This represents a generalization of the contraction property of quantum dynamical maps. The obtained inequalities can be interpreted in terms of the exchange of information between the system and the environment, and lead to a witness for system-environment correlations which can be determined through measurements on the open system alone.

Measuring non-Markovianity of processes with controllable system-environment interaction

Non-Markovian processes have recently become a central topic in the study of open quantum systems. We realize experimentally non-Markovian decoherence processes of single photons by combining time delay and evolution in a polarization-maintaining optical fiber. The experiment allows the identification of the process with strongest memory effects as well as the determination of a recently proposed measure for the degree of quantum non-Markovianity based on the exchange of information between the open system and its environment. Our results show that an experimental quantification of memory in quantum processes is indeed feasible which could be useful in the development of quantum memory and communication devices.

Identification of Clusters of Investors from Their Real Trading Activity in a Financial Market

We use statistically validated networks, a recently introduced method to validate links in a bipartite system, to identify clusters of investors trading in a financial market. Specifically, we investigate a special database allowing to track the trading activity of individual investors of the stock Nokia. We find that many statistically detected clusters of investors show a very high degree of synchronization in the time when they decide to trade and in the trading action taken. We investigate the composition of these clusters and we find that several of them show an over-expression of specific categories of investors.