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arXiv:2002.12684 · Physical Review A

Distributing memory effects in an open two-qubit system

Olli Siltanen, Tom Kuusela, Jyrki Piilo

Published Aug 25, 2020• 5 citations
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Abstract

We introduce a method to distribute memory effects among different subspaces of an open two-qubit system's state space. Within the linear optical framework, our system of interest is the polarization of two photons, while the environment consists of their frequency degrees of freedom. By exploiting initially correlated frequency distributions and initial frequency-dependent phase factors, we are able to control all the four decoherence functions for polarization---corresponding to different open-system subspace divisions---almost independently of each other. Hence, our results demonstrate how, in a multipartite dephasing system, Markovian and non-Markovian dynamics can be arbitrarily divided between the subsystems, giving rise to the concept of memory partitions. We also discuss further implications the results have, e.g., on the dynamics of purity and entropy within the two-qubit system.

DOI
10.1103/physreva.102.022225

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Photons are useful quantum systems for investigating the fundamental and practical aspects of dephasing, decoherence, and other types of open quantum dynamics. However, descriptions of open dynamics of photonic systems are usually in terms of decoherence functions and in many cases an explicit master-equation-based description is not available. This is particularly true when considering multipartite photonic open systems having possibly correlated environments. We obtain generic master equations for the reduced dephasing dynamics of a two-photon polarization state coupled to respective frequency degrees of freedom when the frequency degrees of freedom that form the environment are initially correlated. Our results show the explicit dependence of the operator form of the master equation and the decay rates on these correlations as well as on various types of frequency distributions. Furthermore, we use the recently developed bath-positive decomposition method to treat an initially correlated polarization-frequency state of a photon and demonstrate how this allows us to gain new insight and detailed information on how the contributions of different origins influence the photonic dephasing.
In this Thesis various aspects of memory effects in the dynamics of open quantum systems are studied. We develop a general theoretical framework for open quantum systems beyond the Markov approximation which allows us to investigate different sources of memory effects and to develop methods for harnessing them in order to realise controllable open quantum systems. \n \nIn the first part of the Thesis a characterisation of non-Markovian dynamics in terms of information flow is developed and applied to study different sources of memory effects. Namely, we study nonlocal memory effects which arise due to initial correlations between two local environments and further the memory effects induced by initial correlations between the open system and the environment. \n \nThe last part focuses on describing two all-optical experiment in which through selective preparation of the initial environment states the information flow between the system and the environment can be controlled. In the first experiment the system is driven from the Markovian to the non- Markovian regime and the degree of non-Markovianity is determined. In the second experiment we observe the nonlocal nature of the memory effects and provide a novel method to experimentally quantify frequency correlations in photonic environments via polarisation measurements.
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.
Quantum mechanics has both deepened our understanding of the physical reality and allowed development of quantum technologies beating their classical counterparts in efficiency, security, and sensitivity. As a major downside, the quantum properties behind these technologies are very sensitive to the effects the system’s interaction with its environment. The theory of open quantum systems describes how such interaction influences the system, and as a consequence, how the quantum features are lost, controlled, and possibly returned by manipulating the environment. This thesis begins with a short description of the most relevant features and results of the open quantum system theory. We continue by presenting some commonly used measures to quantify the information encoded in quantum systems and the correlations between spatially or temporally separated parties. The literature review ends with discussion of non-Markovianity and memory effects which combine the fields of open quantum systems and quantum information in a natural way. The rest of the thesis presents the main results of Publications I – VII. We study the memory effects and physicality conditions of open system dynamics described by the vast family of phase-covariant master equations. We show how the open quantum system picture can be exploited to design probing protocols to extract information without knowing how the probe and system interact. Such protocols are considered also from the point-of view of efficiently obtaining the information required in the probing, both in theory and by experimental implementation. The experiment serves also as evidence for applicability of recently developed geometric tools to design informationally incomplete measurements for solving so-called membership problems. We present and experimentally realize a protocol where control over intial correlations between polarization and frequency gives full freedom to implement any dephasing dynamics in the open system polarization, thus dictating how its information content changes in time. We study the two-qubit memory effects of dephasing dynamics and compare them to the effect of such noise in the transmission efficiency in superdense coding. Optimal noise configurations in different situations are found. Finally, we characterize the families of initial states for which the decay of quantum correlations depends or does not depend on the noise location.
We explore the possibility to generate nonlocal dynamical maps of an open quantum system through local system-environment interactions. Employing a generic decoherence process induced by a local interaction Hamiltonian, we show that initial correlations in a composite environment can lead to nonlocal open system dynamics which exhibit strong memory effects, although the local dynamics is Markovian. In a model of two entangled photons interacting with two dephasing environments, we find a direct connection between the degree of memory effects and the amount of correlation in the initial environmental state. The results demonstrate that, contrary to conventional wisdom, enlarging an open system can change the dynamics from Markovian to non-Markovian.
We combine the dynamics of open quantum systems with interferometry and interference, introducing the concept of an open system interferometer. By considering a single photon in a Mach-Zehnder interferometer, where the polarization (open system) and frequency (environment) of the photon interact, we theoretically show that inside the interferometer, pathwise polarization dephasing dynamics is Markovian while the joint dynamics displays non-Markovian features. Outside the interferometer and due to interference, the open system displays rich dynamical features with distinct alternatives: only one path displays non-Markovian memory effects, both paths individually display them, or no memory effects appear at all. The scheme allows one to (1) probe the optical path difference inside the interferometer by studying pathwise non-Markovianity outside the interferometer, and (2) introduce pathwise dissipative features for the open system dynamics even though the system-environment interaction itself contains only dephasing. Due to the path dependencies, our results are tightly connected to quantum erasure. In general, our results open up alternative ways to control open system dynamics and for fundamental studies of quantum physics.