Abstract In this paper, we have investigated the teleportation of quantum Fisher information (QFI) for a single qubit system using a class of X-states as resources influenced by decoherence channels with memory, including amplitude-damping, phase-damping and depolarizing channels. Using the QFI to quantify the quality of teleportation, we first derive the explicit analytical results of QFIs with respect to the weight parameter ( ) and phase parameter ( ) under these decoherence channels, and find that both and are strongly dependent on the initial state’s parameters c i , noisy channel parameters D and , as well as the teleported state’s parameters and . For comparison with the teleportation of the single qubit case, we have also addressed the teleportation of QFI for a two-qubit entanglement system. The results show that , for a single qubit state, is more robust against noisy channels than that for a two-qubit state. However, for a two-qubit state is more robust than that of a single qubit state against noisy channels.Abstract In this paper, we have investigated the teleportation of quantum Fisher information (QFI) for a single qubit system using a class of X-states as resources influenced by decoherence channels with memory, including amplitude-damping, phase-damping and depolarizing channels. Using the QFI to quantify the quality of teleportation, we first derive the explicit analytical results of QFIs with respect to the weight parameter ( ) and phase parameter ( ) under these decoherence channels, and find that both and are strongly dependent on the initial state’s parameters c i , noisy channel parameters D and , as well as the teleported state’s parameters and . For comparison with the teleportation of the single qubit case, we have also addressed the teleportation of QFI for a two-qubit entanglement system. The results show that , for a single qubit state, is more robust against noisy channels than that for a two-qubit state. However, for a two-qubit state is more robust than that of a single qubit state against noisy channels.

Laser Physics LettersAug 1, 201913 citations

Limitations of the dissipative quantum Fisher information in Liouville space

Tatiana Iakovleva, Ruvi Lecamwasam, Jason Twamley

Open quantum system dynamics traditionally described by a quantum master equation can be effectively reformulated in the Liouville space of vectorised density matrices. Despite an extensive use of the Liouville space framework to describe quantum states evolution, its application to quantum metrology is not well explored. Several papers have studied a Liouville-space generalisation of the quantum Fisher information, called the dissipative quantum Fisher information (DQFI). We perform a comparative study between the quantum Fisher information (QFI) in Hilbert space and DQFI, deriving an explicit relation between the two quantities for qubit, qudit, and harmonic oscillator systems. The derived relations are nontrivial, and depend on the state's purity. We show that for a single qubit, the QFI can be efficiently recovered from the DQFI via a simple mapping, while in higher dimensions the expression becomes convoluted and does not convert to a compact form. We find examples where the DQFI is neither an upper nor lower bound for the Hilbert space QFI, and suggest that the informational content of the DQFI itself cannot be straightforwardly interpreted. Our results clarify the limitations of the Liouville space based approach and structural differences with the QFI in the context of quantum parameter estimation problem.Open quantum system dynamics traditionally described by a quantum master equation can be effectively reformulated in the Liouville space of vectorised density matrices. Despite an extensive use of the Liouville space framework to describe quantum states evolution, its application to quantum metrology is not well explored. Several papers have studied a Liouville-space generalisation of the quantum Fisher information, called the dissipative quantum Fisher information (DQFI). We perform a comparative study between the quantum Fisher information (QFI) in Hilbert space and DQFI, deriving an explicit relation between the two quantities for qubit, qudit, and harmonic oscillator systems. The derived relations are nontrivial, and depend on the state's purity. We show that for a single qubit, the QFI can be efficiently recovered from the DQFI via a simple mapping, while in higher dimensions the expression becomes convoluted and does not convert to a compact form. We find examples where the DQFI is neither an upper nor lower bound for the Hilbert space QFI, and suggest that the informational content of the DQFI itself cannot be straightforwardly interpreted. Our results clarify the limitations of the Liouville space based approach and structural differences with the QFI in the context of quantum parameter estimation problem.

Scientific ReportsJun 22, 20260 citations

Quantum Fisher Information in the Symmetric Pure Three-Qubit State

Desheng Liu, Juan Du, Guoqiang Huang

International Journal of Theoretical PhysicsFeb 12, 20124 citations

Coherence and quantum Fisher information in general single-qubit parameter estimation processes

Jun‐Long Zhao, Dong‐Xu Chen, Yu Zhang +4 more

Quantum metrology is superior to classical metrology in parameter estimation. This is because quantum states have coherence that, however, does not exist in classical states. Previous works were limited to the study of the relationship between quantum Fisher information (QFI) and coherence of the initial probe state only for a specific single-qubit parameter estimation process (e.g., a process described by a single-qubit spin angular momentum operator ${J}_{z}$ ). Here, we consider a more general case and study the relationship between QFI and coherence of the initial probe state for a single-qubit general parameter estimation process, which is described by a single-qubit spin angular momentum operator ${J}_{\stackrel{P\vec}{n}}$ with a general unit vector $\stackrel{P\vec}{n}$. We find that the QFI is proportional to the square of coherence of the initial probe state, when the single-qubit bases are eigenstates of the spin angular momentum operator ${J}_{\stackrel{P\vec}{n}}$ describing the parametrization process. We also design and conduct a linear optical experiment to support our theory. The experimental results are in good agreement with the theoretical ones. This work provides an important guideline for enhancing the precision of parameter estimation.Quantum metrology is superior to classical metrology in parameter estimation. This is because quantum states have coherence that, however, does not exist in classical states. Previous works were limited to the study of the relationship between quantum Fisher information (QFI) and coherence of the initial probe state only for a specific single-qubit parameter estimation process (e.g., a process described by a single-qubit spin angular momentum operator ${J}_{z}$). Here, we consider a more general case and study the relationship between QFI and coherence of the initial probe state for a single-qubit general parameter estimation process, which is described by a single-qubit spin angular momentum operator ${J}_{\stackrel{P\vec}{n}}$ with a general unit vector $\stackrel{P\vec}{n}$. We find that the QFI is proportional to the square of coherence of the initial probe state, when the single-qubit bases are eigenstates of the spin angular momentum operator ${J}_{\stackrel{P\vec}{n}}$ describing the parametrization process. We also design and conduct a linear optical experiment to support our theory. The experimental results are in good agreement with the theoretical ones. This work provides an important guideline for enhancing the precision of parameter estimation.

Physical Review ADec 8, 20216 citations

Quantum Fisher Information of a Two-Qubit System in Non-Markovian Environment

Yao-Hua Hu, Yong-Gang Tan, Haifeng Yang +1 more

International Journal of Theoretical PhysicsNov 20, 20194 citations

{J}_{z}

). Here, we consider a more general case and study the relationship between QFI and coherence of the initial probe state for a single-qubit general parameter estimation process, which is described by a single-qubit spin angular momentum operator ${J}_{\stackrel{P\vec}{n}}$ with a general unit vector $\stackrel{P\vec}{n}$. We find that the QFI is proportional to the square of coherence of the initial probe state, when the single-qubit bases are eigenstates of the spin angular momentum operator ${J}_{\stackrel{P\vec}{n}}$ describing the parametrization process. We also design and conduct a linear optical experiment to support our theory. The experimental results are in good agreement with the theoretical ones. This work provides an important guideline for enhancing the precision of parameter estimation.