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 Introduction Open quantum system approach Using Geometric phase corrections to understand thermal nature of de Sitter space-time Optimal quantum estimation of Unruh effect Further works

Relativistic Quantum Information 1. Introduction Relativistic quantum information: Quantum Fields Theory Relativity Theory . Relativistic Quantum Information Information Theory Quantum Information Quantum Mechanics

Resources/Tasks of QI well known: 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 Environment Atom Master equation: Accelerated In curved spacetime In thermal bath Other cases Phys. Rev. A 79, 052109 (2009)

Initial state: Evolving state: Eigenvalues: Eigenvectors:

3. Using geometric phase corrections to understand thermal nature of de Sitter space-time 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: Environment Atom 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 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)

Zehua Tian and Jiliang Jing,JHEP 04. 109 (2013). Geometric phase of a freely falling atom in de Sitter spacetime Geometric phase: Inertial Thermal Pure phase correction : Zehua Tian and Jiliang Jing,JHEP 04. 109 (2013).

Zehua Tian and Jiliang Jing,JHEP 04. 109 (2013). Geometric phase of a static atom in de Sitter spacetime Proper acceleration： Geometric phase: Inertial Thermal Pure phase correction : Zehua Tian and Jiliang Jing,JHEP 04. 109 (2013).

Conclusions

4. Optimally quantum estimation of Unruh effect Minkowski vacuum No particles T=a/2π Rindler particles

Some questions of estimating Unruh effect: No linear operator that acts as an observable for temperature Unruh temperature Directly detect? Quantum estimation theory Indirectly detect (probe) Other parameters (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.

Quantum Fisher information: Optimal condition: Quantum Fisher information: (1) best probe state? (2) the optimal measurement? Population measurement (3) the attainable precision?

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? .

Thank you for your attention