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

Quantum ◽  
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.

scholarly journals Decoherence of quantum parameter estimation for open Dirac particle in Garfinkle–Horowitz–Strominger dilation black hole

2019 ◽  
Vol 79 (11) ◽  
Author(s):  
Yumeng Huang ◽  
Kai Yan ◽  
Yinzhong Wu ◽  
Xiang Hao
Keyword(s):  
Black Hole ◽  
Parameter Estimation ◽  
Quantum Information ◽  
Fisher Information ◽  
Quantum Channel ◽  
Quantum Fisher Information ◽  
Exclusion Principle ◽  
Quantum Parameter ◽  
Information Divergence ◽  
Quantum Parameter Estimation

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.

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

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.

Quantum Fisher information width in quantum metrology

2018 ◽  
Vol 62 (4) ◽  
Author(s):  
Bo Liu ◽  
GuoLong Li ◽  
YanMing Che ◽  
Jie Chen ◽  
XiaoGuang Wang
Keyword(s):  
Fisher Information ◽  
Quantum Fisher Information ◽  
Quantum Metrology

scholarly journals Multi-parameter estimation beyond quantum Fisher information

2020 ◽  
Vol 53 (36) ◽  
pp. 363001 ◽  
Author(s):  
Rafał Demkowicz-Dobrzański ◽  
Wojciech Górecki ◽  
Mădălin Guţă
Keyword(s):  
Parameter Estimation ◽  
Fisher Information ◽  
Quantum Fisher Information

scholarly journals Symmetric Logarithmic Derivative of Fermionic Gaussian States

2018 ◽  
Author(s):  
Angelo Carollo ◽  
Bernardo Spagnolo ◽  
Davide Valenti
Keyword(s):  
Fisher Information ◽  
Logarithmic Derivative ◽  
Quantum Fisher Information ◽  
Closed Form Expression ◽  
Quantum Metrology ◽  
Many Body ◽  
Form Expression ◽  
Gaussian States ◽  
Many Body Systems ◽  
Thermal States

In this article we derive a closed form expression for the symmetric logarithmic derivative of Fermionic Gaussian states. This provides a direct way of computing the quantum Fisher Information for Fermionic Gaussian states. Applications range from quantum Metrology with thermal states to non-equilibrium steady states with Fermionic many-body systems.

scholarly journals Quantum Fisher Information: Theory and Applications

2017 ◽  
Author(s):  
Volkan Erol
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Fisher Information ◽  
Quantum Fisher Information ◽  
Research Area ◽  
Quantum Metrology ◽  
Information Research ◽  
Active Research ◽  
Information Domain ◽  
Active Research Area

Entanglement is at the heart of quantum technologies such as quantum information and quantum metrology. Providing larger quantum Fisher information (QFI), entangled systems can be better resources than separable systems in quantum metrology. QFI topic is a very active research area and it has many possible usage areas in quantum information domain. In this study, we review quantum Fisher information research with both from theoritical and application perspective.

scholarly journals Taming singularities of the quantum Fisher information

2021 ◽  
Author(s):  
Aaron Z. Goldberg ◽  
José L. Romero ◽  
Ángel S. Sanz ◽  
Luis L. Sánchez-Soto
Keyword(s):  
Density Matrix ◽  
Fisher Information ◽  
Statistical Models ◽  
Probability Distributions ◽  
Quantum Fisher Information ◽  
Quantum Metrology ◽  
Quantum Statistical ◽  
Information Matrices ◽  
Parameter Dependent ◽  
Ultimate Limit

Quantum Fisher information matrices (QFIMs) are fundamental to estimation theory: they encode the ultimate limit for the sensitivity with which a set of parameters can be estimated using a given probe. Since the limit invokes the inverse of a QFIM, an immediate question is what to do with singular QFIMs. Moreover, the QFIM may be discontinuous, forcing one away from the paradigm of regular statistical models. These questions of nonregular quantum statistical models are present in both single- and multiparameter estimation. Geometrically, singular QFIMs occur when the curvature of the metric vanishes in one or more directions in the space of probability distributions, while QFIMs have discontinuities when the density matrix has parameter-dependent rank. We present a nuanced discussion of how to deal with each of these scenarios, stressing the physical implications of singular QFIMs and the ensuing ramifications for quantum metrology.

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

2021 ◽  
Vol 104 (6) ◽  
Author(s):  
Jun-Long Zhao ◽  
Dong-Xu Chen ◽  
Yu Zhang ◽  
Yu-Liang Fang ◽  
Ming Yang ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Fisher Information ◽  
Quantum Fisher Information ◽  
Single Qubit
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