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Qatar Foundation Annual Research Forum Volume 2012 Issue 1

Information aspects of quantum systems

Mahmoud Abdel‐Aty

Published Jan 1, 2012• 0 citations
Publisher

Abstract

Information dynamics of different quantum systems under influence of both a phonon bath in contact with the resonator and irreversible decay of the qubits is considered. The focus of our analysis is devoted to multilevel atoms and the effects arising from the coupling to the reservoir. Even in the presence of the reservoirs, the inherent entanglement is found to be rather robust. Due to this fact, together with control of system parameters, the system may therefore be especially suited for quantum information processing. Information entropy, entropy squeezing and wehrl entropy are discussed as indicators of entanglement. Our findings also shed light on the evolution of open quantum many-body systems.

DOI
10.5339/qfarf.2012.csp2

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Information dynamics of different quantum systems under influence of both a phonon bath in contact with the resonator and irreversible decay of the qubits is considered. The focus of our analysis is devoted to multilevel atoms and the effects arising from the coupling to the reservoir. Even in the presence of the reservoirs, the inherent entanglement is found to be rather robust. Due to this fact, together with control of system parameters, the system may therefore be especially suited for quantum information processing. Information entropy, entropy squeezing and wehrl entropy are discussed as indicators of entanglement. Our findings also shed light on the evolution of open quantum many-body systems.
The dynamics of charge qubits coupled to a nanomechanical resonator under influence of both a phonon bath in contact with the resonator and irreversible decay of the qubits is considered. The focus of our analysis is devoted to multi partite entanglement and the effects arising from the coupling to the reservoir. It is shown that despite losses, entanglement formation may still persist for relatively long times and it is especially robust against temperature dependence of the reservoir. Together with control of system parameters, the system may therefore be especially suited for quantum information processing. Furthermore, our results shed light on the evolution of open quantum many-body systems. For instance, due to intrinsic qubit-qubit couplings our model is related to a driven XY spin model.
We present a theoretical discussion of various aspects of the dynamics of information in quantum systems of qubits. We begin by reviewing ideas about entanglement and information in systems of qubits, different models for realistic qubits coupled to an external environment, how this causes the loss of information stored in qubits, and some practical designs for qubits that have been created. Then we study how the state of many-body systems can be decomposed in terms of its different subsystems and derived a hierarchy of equations describing the motion of these different parts. We show that in a qubit system, the central objects in this hierarchy are correlators between different components of different qubits. Systems where the environment coupled to a central qubit is a "spin bath'' of environmental qubits are then considered in detail and we find that information lost by the central qubit is transferred via a cascade to higher and higher order correlations with the environment. We discuses this process in the realistic example of an "Fe₈'' magnetic molecule qubit. Finally we discuss simple models of the dynamics of many entangled qubits.
The notion of Shannon entropy is crucial for the theory of classical information. In quantum information theory, an analogous key role is played by the von Neumann entropy: quantum information processing is closely related to entropy dynamics. This reveals a direct link with the theory of quantum chaotic systems, which can be characterized by a positive entropy production. Furthermore, noise, which inevitably affects any quantum system, can be modeled by a random quantum operation or by coupling to an environment in a generic chaotic state. In this contribution, we emphasize the universality of quantum chaotic dynamics and discuss its implications for quantum information processing.
Wehrl entropy and its density are used to investigate the dynamics of loss of coherence and information in a phase space for an atomic model of two-photon two-level atom coupled to different radiation reservoirs (namely, normal vacuum (NV), thermal field (TF) and squeezed vacuum (SV) reservoirs). Particularly, quantum interference (QI) effect, due to the 2-photon transition decay channels, has a paramount role in: (i) the atomic inversion decay in the NV case, which behaves as quantum Zeno and anti-Zeno decay effect; (ii) the coherence and information loss in the phase space; and (iii) identifying temporal information entropy squeezing. Results are also sensitive to the initial atomic state.
Squeezed reservoirs provide a powerful means of engineering nonclassical noise and controlling irreversible dynamics in open quantum systems. Here we develop a comprehensive analysis of two coupled harmonic oscillators driven by independent squeezed baths, focusing on the emergence of coherence-driven entropy flow and the structure of exceptional points (EPs) in the corresponding Lindblad dynamics. Working entirely within the Gaussian formalism, we derive closed-form evolution equations for the covariance matrix and show that squeezing induces entropy generation only at *second order* in the anomalous correlations, a nonlinear mechanism absent in thermal environments. This entropy flow is accompanied by a rich non-Hermitian structure: by scanning the squeezing parameters we uncover a characteristic "exceptional-point fan" in the (M1, M2) plane, which separates a narrow PT-unbroken region of oscillatory dynamics from broad PT-broken sectors in which one normal mode becomes purely overdamped. This geometric organization of EPs reveals that PT symmetry survives only when the two reservoirs squeeze opposite quadratures, and is generically broken for in-phase squeezing. Our analysis establishes squeezed reservoirs as a natural setting where information-bearing noise drives irreversible behavior through coherent pathways, and lays the groundwork for experimentally accessible probes of entropy flow and critical mode behavior in more complex open systems.
This work explores the dynamics of quantum Fisher information (QFI) in open quantum systems coupled to squeezed reservoirs, providing a mathematical framework for analyzing parameter estimation precision under decoherence. We analyze QFI in two-qubit systems undergoing pure dephasing, considering the effects of squeezing parameter, phase difference, and coupling strength within an Ohmic spectral density model. The decoherence factor shows how reservoir engineering influences coherence loss. Numerical results demonstrate that optimal squeezing and local bath configurations enhance QFI preservation, while collective couplings accelerate decay. We also examine the interplay with von Neumann entropy, highlighting their inverse correlation, where increased mixedness reduces metrological sensitivity.