Download Using Quantum Means to Understand and Estimate Relativistic Effects

Using Quantum Means to Understand and Estimate
Relativistic Effects
报告人： 田泽华
指导老师：荆继良 教授
湖南师范大学
Outline
1. Introduction
2.
Open quantum system approach
3. Using Geometric phase corrections to understand thermal
nature of de Sitter space-time
4.
Optimal quantum estimation of Unruh effect
5.
Further works
1. Introduction
Relativistic quantum information:
Relativity Theory
Information Theory
Quantum
Information
Relativistic Quantum
Information
Quantum Mechanics
Quantum Fields
Theory
.
.
.
Motivations:

Resources/Tasks of QI well known:
How are they (entanglement, quantum correlation, quantum teleportation . . . )
affected by Relativity?
Are effects degraded/enhanced?

Connection between QFT and QI
Unruh effect, Hawking effect, Casimir effect

New ways to . . . create, store, transmit, process QI
Our aim here . . .
Utilizing quantum means to understand, detect and estimate relativistic effects
2. Open quantum system approach
Hamiltonian:
Detector
Atom
Master equation:
Atom
Accelerated
In curved
spacetime
Environment
In thermal
bath
Phys. Rev. A 79, 052109 (2009)
Other cases
Initial state:
Evolving state:
Eigenvalues:
Eigenvectors:
3. Using geometric phase corrections to understand
thermal nature of de Sitter space-time
Geometric phase:
1. The Hamiltonian H(R) depends on
a set of parameters R
2. The external parameters are time
dependent, R(T)= R(0)
3. Adiabatic approximation holds
M. Berry, Proc. Roy. Soc. A 392, 45 (1984).
Geometric phase in an open quantum system:
Atom
Environment
Geometric phase of the two-level atom:
D. M. Tong, E. Sjoqvist, L. C. Kwek, and C. H. Oh, PRL 93.080405 (2004).
Geometric phase of a two-level atom in de Sitter spacetime
de Sitter spacetime:
Freely falling atom:
Static atom:
N. D. Birrell and P.C. W. Davies, Quantum Fields Theory in Curved Space (Cambridge, University
Press,Cambridge, England, 1982)
Geometric phase of a freely falling atom in de Sitter spacetime
Geometric phase:
Pure phase correction :
Inertial
Zehua Tian and Jiliang Jing,JHEP 04. 109 (2013).
Thermal
Geometric phase of a static atom in de Sitter spacetime
Proper acceleration：
Geometric phase:
Inertial
Pure phase correction :
Zehua Tian and Jiliang Jing,JHEP 04. 109 (2013).
Thermal
Conclusions
4. Optimally quantum estimation of Unruh effect
Minkowski vacuum
No
particles
Rindler particles
T=a/2π
Some questions of estimating Unruh effect:
Unruh temperature
Indirectly detect
(probe)
Directly detect?
Other parameters
No linear
operator that
acts as an
observable for
temperature
Quantum estimation theory
(1) Which is the best probe state?
(2) Which is the optimal measurement that should be performed at the output?
(3) Which is the attainable precision?
(4) Can the precision be improved?
Quantum estimation
 Optimal measurements
 Ultimate bounds to precision
 Cramer-Rao bound (unbiased estimators)
 Variance of unbiased estimators
 M  number of measurements
 F Fisher information
 Optimal measurement  maximum
Fisher information
 Optimal estimator  saturation of
CR inequality
In quantum mechanics:
Exact form of Fisher information
Classical:
Quantum:
SLD operator
Mix:
Pure:
Quantum Cramer-Rao inequality:
 Optimal measurement  maximum quantum Fisher infromation
 Optimal estimator  saturation of quantum CR inequality
Accelerated atom:
Correlation function:
M. G. A. Paris, International Journal of Quantum Information 7，(2009) 125-137.
Optimally quantum estimation of Unruh effect
Fisher information based on population
measurement:
Zehua Tian, Jieci Wang, Heng Fan, and Jiliang Jing, Relativistic quantum metrology in open system dynamics.
Optimally quantum estimation of Unruh effect
Quantum Fisher information based on
all possible POVM:
Zehua Tian, Jieci Wang, Heng Fan, and Jiliang Jing, Relativistic quantum metrology in open system dynamics.
Optimal condition:
Quantum Fisher information:
(1) best probe state?
(2) the optimal measurement?
(3) the attainable precision?
Population measurement
Conclusions
1. The maximum Fisher information for population measurement is obtained
when
and it is independent of any initial preparations of the probe.
2. The same configuration is also corresponding to the maximum of the quantum
Fisher information, i.e., the ultimate bound allowed by quantum mechanics to
the sensitivity of the Unruh temperature estimation can be achieved based on
the population measurement.
5. Further works
1. Can we distinguish different spacetime by quantum means?
2. Can the precision be improved by entanglement, quantum discord
and other quantum resources?
3. Experimentally feasible?
.
.
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