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arXiv:2103.11994 · Laser & Photonics Review

Tracing Information Flow from Open Quantum Systems

Jan Dziewior, Leonardo Ruscio, Lukas Knips, Eric Meyer, Alexander Szameit, Jasmin D. A. Meinecke

Published Feb 16, 2025• 1 citation
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Abstract

Abstract Open quantum systems are highly relevant, both for practical applications as well as for fundamental questions about the nature of information and its transfer, encompassing for example decoherence and memory effects. Quantum mechanics introduces additional complexity to the transfer of information, e.g., storage of information in non‐classical correlations. Yet, some of these aspects tend to be neglected by the usual framework of open system research. In this work, photons are used in a waveguide array to implement a quantum simulation of the coupling of a qubit with a low‐dimensional discrete environment. Using the trace distance between quantum states as a measure of information, different types of information transfer are analyzed. Extending the usual perspective which is focused on the system alone, the presence of information is also investigated in the environment.

DOI
10.1002/lpor.202400737

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Abstract Open quantum systems are highly relevant, both for practical applications as well as for fundamental questions about the nature of information and its transfer, encompassing for example decoherence and memory effects. Quantum mechanics introduces additional complexity to the transfer of information, e.g., storage of information in non‐classical correlations. Yet, some of these aspects tend to be neglected by the usual framework of open system research. In this work, photons are used in a waveguide array to implement a quantum simulation of the coupling of a qubit with a low‐dimensional discrete environment. Using the trace distance between quantum states as a measure of information, different types of information transfer are analyzed. Extending the usual perspective which is focused on the system alone, the presence of information is also investigated in the environment.
Quantum simulation is one of the core areas in the development of quantum technologies. Among the various simulation platforms, integrated waveguides have proven to be a powerful and versatile tool. One important aspect of quantum simulation is the analysis of open quantum systems. In most practical applications it is in fact essential to understand and control the dynamics between the quantum system and its environment. Typical effects of interest for example involve decoherence or memory effects, which lead to non-Markovian behavior. In this work we establish integrated waveguides as a tool for the simulation of open quantum systems. Using polarization as well as a photon's path degree of freedom, we implement the coupling of a qubit with a low dimensional discrete environment. Based on a measure of non-Markovianity, we define and quantify specific types of information and information transfer between system and environment. Experimentally we implement and verify non-Markovian evolution in an optical waveguide array and analyze types of information flow between system and environment realizable through integrated photonics.
Quantum information science is a rapidly growing research area for that it provides new insights to the fundamentals of quantum mechanics and offers a platform for the architecture of novel quantum technologies. The successfulness and practicality of this important scientific field rely on the controllability of a quantum system subject to a realistic noisy environment. The environment always leads to unintended dynamics of the system, and thus destroys its coherence and limits its applications. It is therefore important to understand these decoherence mechanisms from first principles, in order to minimize, or even remove, its adverse effect on the quantum system. The study of this open quantum system problem is usually based on some effective paradigms, where the environment is assumed to be "large", such that it can affect the quantum system without any back action. However, due to the demand for a high precision in quantum computation, such an approximate framework becomes questionable. We provide a new theoretical approach to treat this type of open quantum system problem, including the correlated dynamics between the system and the environment, by using a diagrammatic technique in the same spirit as the Keldysh non-equilibrium Green's function. In this formalism, both the environment and the photonic control are quantized. The dynamics of the system can be evaluated accurately for a time scale of small decoherence, but arbitrary quantum control, relevant to the need for quantum technologies. This offers a way of precise quantum noise calculations. We find how fundamental quantum correlations between the quantum control and quantum environment can arise, and are missing in the existing Master equation approximations. On the other hand, the study of the environment not only provides a better understanding of the decoherence, it also allows applicable designs of quantum operations between different qubit systems. In particular, we engineer a new protocol to entangle two qubits at a distance by projection measurements of their environments, the resonance fluorescence photons. We find exceptional improvements on the probability of success and the rate of entanglement based on the multiphoton environment approach, in comparison with the existing single photon entanglement scheme
The exchange of information between an open quantum system and its environment allows us to discriminate among different kinds of dynamics, in particular detecting memory effects to characterize non-Markovianity. Here, we investigate the role played by the system-environment correlations and the environmental evolution in the flow of information. First, we derive general conditions ensuring that two generalized dephasing microscopic models of the global system-environment evolution result exactly in the same open-system dynamics, for any initial state of the system. Then, we use the trace distance to quantify the distinct contributions to the information inside and outside the open system in the two models. Our analysis clarifies how the interplay between system-environment correlations and environmental-state distinguishability can lead to the same information flow from and toward the open system, despite significant qualitative and quantitative differences at the level of the global evolution.
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 exchange of information between an open quantum system and its environment, especially the backflow of information from the environment to the open system associated with quantum notions of non-Markovianity, is a widely discussed topic for years now. This information flow can be quantified by means of the trace distance of pairs of quantum states which provides a measure for the distinguishability of the states. The same idea can also be used to characterize the information flow in classical open systems through a suitable distance measure for their probability distributions on phase space. Here, we investigate the connection between the trace distance based quantum measure and the Kolmogorov distance for differently ordered quasiprobability distributions on phase space. In particular, we show that, for any pair of quantum states, one can find a unique quasiprobability distribution for which the Kolmogorov distance coincides with the trace distance. We further study the quantum-to-classical transition of the distance measures. By employing the Caldeira-Leggett model of quantum Brownian motion as a prototypical example, numerical simulations indicate a particularly rapid convergence of the Kolmogorov distance of the Wigner functions to the trace distance in the classical uncertainty limit, which establishes the Wigner function distance as an optimal tool for measuring semi-classical information backflow and for quantifying non-Markovianity in open continuous variable quantum systems.
We study in detail the decoherence process of a quantum register, coupled to a composite environment. We use recently developed methods of information transfer study in open quantum systems to analyze information flow between the register and its environment. We show that there are regimes when not only the register decoheres effectively to a classical bit string, but this bit string is redundantly encoded in the environment, making it available to multiple observers. This process is more subtle and in general qualitatively different than in the case of a single qubit due to the presence of various protected subspaces: decoherence-free subspaces and so-called orthogonalization-free subspaces. We show that this leads to a rich structure of coherence loss or protection in the asymptotic state of the register and a part of its environment. We formulate a series of examples illustrating these structures.