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Laser Physics

Quantum Fisher information and its super additivity in an anisotropic quantum Rabi model

Bo Jiang, Jin‐Hui Wu, Zhihai Wang

Published Jul 20, 2021• 0 citations
Publisher

Abstract

Abstract In this paper, we study the additivity of quantum Fisher information (QFI) in a coupled system composed by a two-level system and a bosonic mode, which is described by an anisotropic Rabi model. Utilizing a unitary transformation approach, we obtain the approximate ground state for the global state and the reduced density matrix for each subsystem. We find the additivity of QFI, that is, the summation of QFI for two subsystems is always larger than that of the global system. We hope our work will stimulate the studies of quantum metrology in hybrid system.

DOI
10.1088/1555-6611/ac1277

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Abstract In this paper, we study the additivity of quantum Fisher information (QFI) in a coupled system composed by a two-level system and a bosonic mode, which is described by an anisotropic Rabi model. Utilizing a unitary transformation approach, we obtain the approximate ground state for the global state and the reduced density matrix for each subsystem. We find the additivity of QFI, that is, the summation of QFI for two subsystems is always larger than that of the global system. We hope our work will stimulate the studies of quantum metrology in hybrid system.
How quantum information encoded into a quantum state is lost, or transferred when an interest quantum system is coupled to its environment, is a fundamental issue in quantum information processing. In this paper, we systematically investigate the dynamics of Quantum Fisher Information (QFI) transfer and QFI flow in a hybrid quantum system composed of a three-level atom located in a cavity interacting with its own reservoir. Our analysis demonstrates that the phase (amplitude)-encoded QFI, initially localized in the atomic subsystem is completely transferred into the reservoir subsystem, as the cavity is as a bridge connecting atom to reservoir. Extending our investigation to two individual subsystems case where the QFI transfer and distribution are studied. Crucially, the relationship between the sum of the locally accessible QFI and the global QFI exhibits subadditivity, additivity, or superadditivity strongly depending on the initial entanglement configuration of the atomic states. Furthermore, the amount of information flowing from the environment (cavity plus reservoir) back into the system is also explicitly revealed by QFI flow which provides an indicator to characterizes the non-Markovianity of the open systems’ dynamics.
Famously, the quantum Fisher information -- the maximum Fisher information over all physical measurements -- is additive for independent copies of a system and the optimal measurement acts locally. We are left to wonder: does the same hold when the set of accessible measurements is constrained? Such constraints are necessary to account for realistic experimental restrictions. Here, we consider a fully Gaussian scenario focusing on only Gaussian measurements. We prove that the optimal Gaussian measurement protocol remains local, if the information is encoded in either the displacement or the covariance matrix. However, when the information is imprinted on both, this no longer holds true: we construct a simple global Gaussian measurement where the Fisher information becomes super additive. These results can improve parameter estimation tasks via feasible tools. Namely, in quantum optical platforms our proposed global operation requires only passive global operations and single mode Gaussian measurements. We demonstrate this in two examples where we estimate squeezing and losses. While in the former case there is a significant gap between the Fisher information of the optimal Gaussian measurement and the quantum Fisher information for a single copy, this gap can be reduced with joint Gaussian measurements and closed in the asymptotic limit of many copies.
Abstract The quantum Fisher information (QFI) plays a crucial role in quantum information theory and in many practical applications such as quantum metrology. However, computing the QFI is generally a computationally demanding task. In this work we analyze a lower bound on the QFI which we call the sub-quantum Fisher information (sub-QFI). The bound can be efficiently estimated on a quantum computer for an n -qubit state using 2 n qubits. The sub-QFI is based on the super-fidelity, an upper bound on Uhlmann’s fidelity. We analyze the sub-QFI in the context of unitary families, where we derive several crucial properties including its geometrical interpretation. In particular, we prove that the QFI and the sub-QFI are maximized for the same optimal state, which implies that the sub-QFI is faithful to the QFI in the sense that both quantities share the same global extrema. Based on this faithfulness, the sub-QFI acts as an efficiently computable surrogate for the QFI for quantum sensing and quantum metrology applications. Finally, we provide additional meaning to the sub-QFI as a measure of coherence, asymmetry, and purity loss.
Towards the statistical distinguishability about parameters encoded in the bipartite quantum state, we mainly investigate the distribution and transformation of quantum Fisher information over composite systems in spin channel. The relationship between the global quantum Fisher information and the sum of the locally accessible quantum Fisher information are studied, which can be subadditivity, additivity, or superadditivity. The transfer among them under the unitary operation is illustrated. We find that the quantum Fisher information can not only flow between the reduced systems, but also between the different types of distribution.
We study the energy-level crossing behavior in a two-dimensional quantum well with the Rashba and Dresselhaus spin-orbit couplings (SOCs). By mapping the SOC Hamiltonian onto an anisotropic Rabi model, we obtain the approximate ground state and its quantum Fisher information (QFI) via performing a unitary transformation. We find that the energy-level crossing can occur in the quantum well system within the available parameters rather than in cavity and circuit quantum eletrodynamics systems. Furthermore, the influence of two kinds of SOCs on the QFI is investigated and an intuitive explanation from the viewpoint of the stationary perturbation theory is given.
The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory. It can in particular be used as a witness to establish the degree of multiparticle entanglement in quantum many-body systems. In this work, we use polynomials of the density matrix to construct monotonically increasing lower bounds that converge to the QFI. Using randomized measurements we propose a protocol to accurately estimate these lower bounds in state-of-the-art quantum technological platforms. We estimate the number of measurements needed to achieve a given accuracy and confidence level in the bounds, and present two examples of applications of the method in quantum systems made of coupled qubits and collective spins.