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

AbstractWe introduce and study a quantum channel that arises from the structure of the vacuum state of Dirac fields propagating in a Garfinkle–Horowitz–Strominger ($$\mathrm {GHS}$$GHS) dilation black hole spacetime. We put forward the concept of quantum information divergence, which is a new measure for relativistic parameter estimation. We employ quantum metrology to estimate the amplitude and relative phase of a Dirac field state using the quantum Fisher information and information divergence. The decoherence of quantum parameter estimation is studied through the evolution of the Bloch vector for arbitrary initial states subjected to the quantum channel and external noises. We find that the quantum information divergence decreases more than the quantum Fisher information as a function of the radiation temperature. Due to the Pauli exclusion principle and Dirac statistics, the estimation precision will gradually decrease to a non-zero value. In order to study the decoherence in the dilation black hole, we obtain the monotonic decrease of quantum coherence when an initial field evolves from the highly correlated state to the current cosmic background. The external noises can further suppress the decoherence effect from the black hole.

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Remote State Design for Efficient Quantum Metrology with Separable and Non-Teleporting States

Quantum Reports ◽

10.3390/quantum3010013 ◽

2021 ◽

Vol 3 (1) ◽

pp. 228-241

Author(s):

Rahul Raj ◽

Shreya Banerjee ◽

Prasanta K. Panigrahi

Keyword(s):

Parameter Estimation ◽

Quantum Information ◽

Fisher Information ◽

Quantum Information Processing ◽

Quantum Fisher Information ◽

Quantum Correlations ◽

Quantum States ◽

Quantum Metrology ◽

High Quantum ◽

Non Local

Measurements leading to the collapse of states and the non-local quantum correlations are the key to all applications of quantum mechanics as well as in the studies of quantum foundation. The former is crucial for quantum parameter estimation, which is greatly affected by the physical environment and the measurement scheme itself. Its quantification is necessary to find efficient measurement schemes and circumvent the non-desirable environmental effects. This has led to the intense investigation of quantum metrology, extending the Cramér–Rao bound to the quantum domain through quantum Fisher information. Among all quantum states, the separable ones have the least quantumness; being devoid of the fragile non-local correlations, the component states remain unaffected in local operations performed by any of the parties. Therefore, using these states for the remote design of quantum states with high quantum Fisher information can have diverse applications in quantum information processing; accurate parameter estimation being a prominent example, as the quantum information extraction solely depends on it. Here, we demonstrate that these separable states with the least quantumness can be made extremely useful in parameter estimation tasks, and further show even in the case of the shared channel inflicted with the amplitude damping noise and phase flip noise, there is a gain in Quantum Fisher information (QFI). We subsequently pointed out that the symmetric W states, incapable of perfectly teleporting an unknown quantum state, are highly effective for remotely designing quantum states with high quantum Fisher information.

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Quantum Fisher Information and Tomographic Entropy of a Single Qubit in Excited Binomial and Negative Binomial Distributions

Journal of Russian Laser Research ◽

10.1007/s10946-019-09806-3 ◽

2019 ◽

Vol 40 (4) ◽

pp. 313-320 ◽

Cited By ~ 2

Author(s):

Abdullah M. Almarashi ◽

Ali Algarni ◽

S. Abdel-Khalek ◽

Hon Keung Tony Ng

Keyword(s):

Fisher Information ◽

Negative Binomial ◽

Quantum Fisher Information ◽

Single Qubit ◽

Binomial Distributions ◽

Tomographic Entropy

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Quantum Fisher information of two atoms with dipole–dipole interaction under the environment of phase noise lasers

Scientific Reports ◽

10.1038/s41598-021-99449-9 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Yu Chen ◽

Zheng-wen Long ◽

Zhi He ◽

Shen-tong Ji

Keyword(s):

Parameter Estimation ◽

Phase Noise ◽

Fisher Information ◽

Quantum Fisher Information ◽

Dipole Interaction ◽

Estimation Problems ◽

Calculation Results ◽

Numeric Solution ◽

Atom System ◽

General Method

AbstractWe investigate the parameter estimation problems of two-atom system driven by the phase noise lasers (PNLs) environment. And we give a general method of numeric solution to handle the problems of atom system under the PNLs environment. The calculation results of this method on Quantum Fisher Information (QFI) are consistent with our former results. Moreover, we consider the dipole–dipole (d–d) interaction between the atoms under PNLs environment with the collective decay, and the results show that larger d–d interaction and smaller collective decay rate lead to larger QFI of the two-atom system. So the collective decay will destroy the QFI while the d–d interaction will preserve the QFI, these results can be used to protect the QFI of two-atom system driven by the PNLs environment.

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Fisher information of accelerated two-qubit system in the presence of the color and white noisy channels

International Journal of Modern Physics B ◽

10.1142/s0217979220500277 ◽

2020 ◽

Vol 34 (05) ◽

pp. 2050027

Author(s):

N. Metwally ◽

F. Ebrahim

Keyword(s):

Fisher Information ◽

Quantum Fisher Information ◽

Entangled State ◽

Acceleration Process ◽

Noise Strength ◽

Initial State ◽

Noisy Channels ◽

Noise Effect ◽

Single Qubit ◽

Qubit System

In this paper, an accelerated two-qubit system initially prepared in maximum or partial entangled state, which interacts locally with white/color or white-color noises, is considered. Due to the acceleration process and the noise effect, the entanglement degraded. Therefore, the effect of noise strength, initial state settings and the acceleration on the survival entanglement are investigated by means of the concurrence. Moreover, the initial parameters that describe this system are estimated by using the quantum Fisher information, where two forms are considered, namely by using a single and two-qubit forms. It is shown that, by using the two-qubit form, the estimation degree of these parameters is larger than that displayed by using a single-qubit form.

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Effects of partial measurements on quantum resources and quantum Fisher information of a teleported state in a relativistic scenario

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2020.0378 ◽

2020 ◽

Vol 476 (2239) ◽

pp. 20200378

Author(s):

M. Jafarzadeh ◽

H. Rangani Jahromi ◽

M. Amniat-Talab

Keyword(s):

Fisher Information ◽

Quantum Coherence ◽

Quantum Fisher Information ◽

Optimal Estimation ◽

Dirac Field ◽

Unruh Effect ◽

Single Qubit ◽

Maximum Value ◽

Phase Parameter ◽

The One

We address the teleportation of single- and two-qubit quantum states, parametrized by weight θ and phase ϕ parameters, in the presence of the Unruh effect experienced by a mode of a free Dirac field. We investigate the effects of the partial measurement (PM) and partial measurement reversal (PMR) on the quantum resources and quantum Fisher information (QFI) of the teleported states. In particular, we discuss the optimal behaviour of the QFI, quantum coherence (QC) as well as fidelity with respect to the PM and PMR strength and examine the effect of the Unruh noise on optimal estimation. It is found that, in the single-qubit scenario, the PM (PMR) strength at which the optimal estimation of the phase parameter occurs is the same as the PM (PMR) strength with which the teleportation fidelity and the QC of the teleported single-qubit state reaches its maximum value. On the other hand, generalizing the results to two-qubit teleportation, we find that the encoded information in the weight parameter is better protected against the Unruh noise in two-qubit teleportation than in the one-qubit scenario. However, extraction of information encoded in the phase parameter is more efficient in single-qubit teleportation than in the two-qubit version.

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Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied

Quantum ◽

10.22331/q-2021-07-01-489 ◽

2021 ◽

Vol 5 ◽

pp. 489

Author(s):

Karol Gietka ◽

Friederike Metz ◽

Tim Keller ◽

Jing Li

Keyword(s):

Parameter Estimation ◽

Fisher Information ◽

Quantum Fisher Information ◽

Quantum Metrology ◽

Zener Model ◽

Heisenberg Limit ◽

Shortcuts To Adiabaticity ◽

Adiabatic Approach ◽

Rabi Model ◽

Quantum Parameter Estimation

We show that the quantum Fisher information attained in an adiabatic approach to critical quantum metrology cannot lead to the Heisenberg limit of precision and therefore regular quantum metrology under optimal settings is always superior. Furthermore, we argue that even though shortcuts to adiabaticity can arbitrarily decrease the time of preparing critical ground states, they cannot be used to achieve or overcome the Heisenberg limit for quantum parameter estimation in adiabatic critical quantum metrology. As case studies, we explore the application of counter-diabatic driving to the Landau-Zener model and the quantum Rabi model.

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