Measure of the density of quantum states in information geometry and quantum multiparameter estimation

@article{Xing2020MeasureOT,
  title={Measure of the density of quantum states in information geometry and quantum multiparameter estimation},
  author={Haijun Xing and Libin Fu},
  journal={Physical Review A},
  year={2020}
}
Recently, there is a growing interest in study quantum mechanics from the information geometry perspective, where a quantum state is depicted with a point in the projective Hilbert space. By taking quantum Fisher information (QFI) as the metric of projective Hilbert spaces, estimating a small parameter shift is equivalent to distinguishing neighboring quantum states along a given curve. Henceforth, information geometry plays a significant role in the single parameter estimation. However, the… 

Figures from this paper

Incorporating Heisenberg's Uncertainty Principle into Quantum Multiparameter Estimation.
TLDR
This work finds a correspondence relationship between the inaccuracy of a measurement for estimating the unknown parameter with the measurement error in the context of measurement uncertainty relations and incorporates Heisenberg's uncertainty principle into quantum multiparameter estimation by giving a trade-off relation between the measurement inaccuracies for estimating different parameters.
Generalization of Rayleigh's Curse on Parameter Estimation with Incoherent Sources
The basic idea behind Rayleigh’s criterion on resolving two incoherent optical point sources is that the overlap between the spatial modes from different sources would reduce the estimation precision
Generalization of Rayleigh's criterion on parameter estimation with incoherent sources
The basic idea behind Rayleigh's criterion on resolving two incoherent optical point sources is that the overlap between the spatial modes from different sources would reduce the estimation precision
Measure of quantum Fisher information flow in multi-parameter scenario
We generalize the quantum Fisher information flow proposed by Lu et al. [Phys. Rev. A 82, 042103 (2010)] to the multi-parameter scenario from the information geometry perspective. A measure named the

References

SHOWING 1-10 OF 91 REFERENCES
Quantum Fisher information matrix and multiparameter estimation
Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cram\'{e}r-Rao bound in quantum parameter estimation. However,
Generalized Geometric Quantum Speed Limits
TLDR
This work establishes an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism, and provides instances of novel bounds which are tighter than any established one based on the conventional quantum Fisher information.
Determining the continuous family of quantum Fisher information from linear-response theory
The quantum Fisher information represents the continuous family of metrics on the space of quantum states and places the fundamental limit on the accuracy of quantum state estimation. We show that
Classifying and measuring geometry of a quantum ground state manifold
From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics, many physical processes depend on the Berry curvature. However, recent
Quantum information-geometry of dissipative quantum phase transitions.
TLDR
It is argued that the fidelity approach to quantum phase transitions to open systems whose steady state is a Gaussian fermionic state provides insights into dissipative quantum critical phenomena as well as a general and powerful strategy to explore them.
An information geometric viewpoint of algorithms in quantum computing
We show that quantum information geometry can be used to characterize Grover's searching algorithm. Specifically, quantifying the notion of quantum distinguishability between parametric density
Quantum critical scaling of the geometric tensors.
TLDR
This Letter shows that criticality is not a sufficient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible.
Geometry of quantum evolution.
TLDR
It is shown that the integral of the uncertainty of energy with respect to time is independent of the particular Hamiltonian used to transport the quantum system along a given curve in the projective Hilbert space, which gives a new time-energy uncertainty principle.
...
1
2
3
4
5
...