Elsi-Mari Laine

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.

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.

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.

Markovianity and non-Markovianity in quantum and classical systems

We discuss the conceptually different definitions used for the non-Markovianity of classical and quantum processes. The well-established definition of non-Markovianity of a classical stochastic process represents a condition on the Kolmogorov hierarchy of the n-point joint probability distributions. Since this definition cannot be transferred to the quantum regime, quantum non-Markovianity has recently been defined and quantified in terms of the underlying quantum dynamical map, using either its divisibility properties or the behavior of the trace distance between pairs of initial states. Here, we investigate and compare these definitions and their relations to the classical notion of non-Markovianity by employing a large class of non-Markovian processes, known as semi-Markov processes, which admit a natural extension to the quantum case. A number of specific physical examples are constructed that allow us to study the basic features of the classical and the quantum definitions and to evaluate explicitly the measures of quantum non-Markovianity. Our results clearly demonstrate several fundamental differences between the classical and the quantum notion of non-Markovianity, as well as between the various quantum measures of non-Markovianity. In particular, we show that the divisibility property in the classical case does not coincide with Markovianity and that the non-Markovianity measure based on divisibility assigns equal infinite values to different dynamics, which can be distinguished by exploiting the trace distance measure. A simple exact expression for the latter is also obtained in a special case.

Optimal state pairs for non-Markovian quantum dynamics

We study a recently proposed measure for the quantification of quantum non-Markovianity in the dynamics of open systems which is based on the exchange of information between the open system and its environment. This measure relates the degree of memory effects to certain optimal initial state pairs featuring a maximal flow of information from the environment back to the open system. We rigorously prove that the states of these optimal pairs must lie on the boundary of the space of physical states and that they must be orthogonal. This implies that quantum memory effects are maximal for states which are initially distinguishable with certainty, having a maximal information content. Moreover, we construct an explicit example which demonstrates that optimal quantum states need not be pure states.

Nonlocal memory effects allow perfect teleportation with mixed states

One of the most striking consequences of quantum physics is quantum teleportation – the possibility to transfer quantum states over arbitrary distances. Since its theoretical introduction, teleportation has been demonstrated experimentally up to the distance of 143 km. In the original proposal two parties share a maximally entangled quantum state acting as a resource for the teleportation task. If, however, the state is influenced by decoherence, perfect teleportation can no longer be accomplished. Therefore, one of the current major challenges in accomplishing teleportation over long distances is to overcome the limitations imposed by decoherence and the subsequent mixedness of the resource state. Here we show that, in the presence of nonlocal memory effects, perfect quantum teleportation can be achieved even with mixed photon polarisation states. Our results imply that memory effects can be exploited in harnessing noisy quantum systems for quantum communication and that non-Markovianity is a resource for quantum information tasks.

Photonic realization of nonlocal memory effects and non-Markovian quantum probes

The study of open quantum systems is important for fundamental issues of quantum physics as well as for technological applications such as quantum information processing. Recent developments in this field have increased our basic understanding on how non-Markovian effects influence the dynamics of an open quantum system, paving the way to exploit memory effects for various quantum control tasks. Most often, the environment of an open system is thought to act as a sink for the system information. However, here we demonstrate experimentally that a photonic open system can exploit the information initially held by its environment. Correlations in the environmental degrees of freedom induce nonlocal memory effects where the bipartite open system displays, counterintuitively, local Markovian and global non-Markovian character. Our results also provide novel methods to protect and distribute entanglement, and to experimentally quantify correlations in photonic environments.

Correlations in quantum states and the local creation of quantum discord

Quantum discord is usually referred to as a measure for quantum correlations. In the search of the fundamental resource to gain a quantum advantage in quantum information applications, quantum discord is considered a promising candidate. In this paper we present an alternative view on quantum correlations in terms of the rank of the correlation matrix as introduced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105, 190502 (2010)]. According to our analysis, information about the quantum discord does not necessarily determine the amount of quantum correlations but rather the quantumness of the state. Nonzero quantum discord is only a necessary but not a sufficient condition for correlations above the classically achievable limit. This becomes clear when we consider states of nonzero discord, which can be created from zero discord states only by a single local operation. We further show that the set of these states has measure zero.