Maximal Quantum Fisher Information Research Articles

Analysis of Entanglement Measures and LOCC Maximized Quantum Fisher Information of General Two Qubit Systems

Entanglement has been studied extensively for unveiling the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known measures for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. It was found that for sets of non-maximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we revisit the state ordering problem of general two qubit states. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with concurrence, REE and negativity and obtain new state orderings. We show that there are pairs of states having equal maximized QFI but different values for concurrence, REE and negativity and vice versa.

Dynamics of the quantum Fisher information in a spin-boson model

The quantum Fisher information characterizes the phase sensitivity of qubits in the spin-boson model with a finite bandwidth spectrum. In contrast with Markovian reservoirs, the quantum Fisher information flows from the environments to qubits after a number of times if the bath parameter s is larger than a critical value which is related to temperature. The sudden-change behavior will happen during the evolution of the quantum Fisher information of the maximal entanglement state in the non-Markovian environments. The sudden-change times can be varied with the change of the bath parameter s. For a very large number of entangled qubits, the sudden-change behavior of the maximal quantum Fisher information can be used to characterize the existence of the entanglement. The metrology strategy based on the quantum correlated state leads to a lower phase uncertainty when compared with the uncorrelated product state.

Phase Sensitivity in Bose–Einstein Condensates

We investigate the phase sensitivity of a collection of interacting spins with quantum Fisher information controlled by an external field. By adopting the frozen-spin approximation, we derive the approximate analytical expressions of the maximal quantum Fisher information and the phase sensitivity. It is shown that the maximal quantum Fisher information and the phase sensitivity depend on the strength of the external field. With the increases of the external field, the period of oscillation of quantum Fisher information and phase estimation decrease, while the values of quantum Fisher information and phase sensitivity increase because of the suppress by the external field.

Unbounded quantum Fisher information in two-path interferometry with finite photon number

The minimum error of unbiased parameter estimation is quantified by the quantum Fisher information in accordance to the Cramér–Rao bound. We indicate that only superposed NOON states by simultaneous measurements can achieve the maximum quantum Fisher information with form for a given photon number distribution by a POVM in linear two-path interferometer phase measurement. We present a series of specified superposed states with infinite quantum Fisher information but with finite average photon numbers. The advantage of this unbounded quantum Fisher information will be beneficial to many applications in quantum technology.

Quantum Fisher Information and Heisenberg Limit in Multi-qubit State

We investigate the quantum Fisher information and Heisenberg limit in multi-qubit pure state superposed by a GHZ state and two W states with a relative phase. Analytical expressions of quantum Fisher information and phase estimation sensitivity are derived. It is shown that the maximal quantum Fisher information occurs and the phase estimation is enhanced to the Heisenberg limit when the number of qubits is large.

Phase Sensitivity in Yurke-Like State

We investigate we investigate the quantum Fisher information and phase sensitivity in Yurke-like state superposed by two special multi-particle states and a symmetric state with relative phase. By studying the influences of superposition coefficients and relative phase on the maximal quantum Fisher information and phase sensitivity, we reveal some entanglement properties of Yurke-like state.

Quantum Fisher Information and the Heisenberg Limit in Superpositions of Two W States and Symmetric State

We investigate the quantum Fisher information and the Heisenberg limit in superposition of a four-qubit symmetric state and two W states. Numerical and analytical calculations for quantum Fisher information and the Heisenberg limit of the four-qubit state are driven. It is shown that quantum Fisher information of the four-qubit state depends on the superposition coefficients and the relative phase. It is also shown that under certain conditions, the maximal quantum Fisher information occurred; which leads to the estimation sensitivity beats the Heisenberg limit.

Dynamics of Quantum Fisher Information in Two Component Bose-Einstein Condensate

We investigate quantum Fisher information dynamics in two component Bose-Einstein condensate interacting spins with an external field. Approximate analytical expressions of quantum Fisher information is presented. Our analysis shows that quantum Fisher information is controlled by adjusting the strength of the external field and the total atomic number. It is shown that the maximal mean quantum Fisher information is occurred and the phase estimation is enhanced to the Heisenberg limit under some conditions.

Quantum Fisher Information of a Two Component Bose-Einstein Condensate in a Strong External Field

We investigate quantum Fisher information dynamics of a collection of interacting spins with a strong coupling. Approximate analytical expressions of quantum Fisher information is presented. Our analysis shows that the maximal quantum Fisher information always appears in the x direction with an extended period and it can be controlled by adjusting the coupling strength of the internal field and the total atomic number.

CORRELATION IDENTIFICATION IN BIPARTITE PAULI CHANNELS

The classical communication capacities of quantum Pauli channels with memory (correlation) are known to exhibit a transition effect. We revisit this phenomenon from the standpoint of the functionally analogous task of Pauli channel correlation identification. We treat the complete class of Pauli channels with correlation and determine the maximum quantum Fisher information achievable both with pure separable channel probe states and with maximally entangled bipartite probe states. A comparison of these Fisher informations reveals four distinct classes of Pauli channels and shows that only those channels that exceed a certain parametric threshold exhibit a transition effect. For those Pauli channels that exhibit this effect, the threshold at which it occurs has a simple analytic expression.

Quantum Fisher Information in the Generalized One-axis Twisting Model

We investigate the quantum Fisher information (QFI) of symmetric states for spin-s particles. We derive the maximal QFI, and find that quantum spin correlations are essential ingredients of the maximal QFI. We make applications to the generalized one-axis twisting model. The results show that the redistributions of uncertainties on the basis of the quantum correlations in the multiqubit system are useful for sub-shot-noise phase sensitivity. Furthermore, for high-spin (s>1/2) composite systems, we find a sufficient criterion for entanglement.

A fibre bundle over manifolds of quantum channels and its application to quantum statistics

A fibre bundle structure is introduced over manifolds of quantum channels. This structure has a close connection with the problem of estimating an unknown quantum channel Γθ specified by a parameter θ. It is shown that the quantum Fisher information of the family of output states maximized over all input states , which quantifies the ultimate statistical distinguishability of the parameter θ, is expressed in terms of a geometrical quantity on the fibre bundle. Using this formula, a criterion for the maximum quantum Fisher information of the nth extended channel (id ⊗ Γθ)⊗n to be O(n) is derived. This criterion further proves that for almost all quantum channels, the maximum quantum Fisher information increases in the order of O(n).