Shaking Entanglement: Teleportation in Relativistic Motion

1. Shaking Entanglement:Teleportation in Relativistic Motion Antony Richard Lee In collaboration with RQI Group University of Nottingham LOOPS 13 – Perimeter Institute – July 2013

2. Shaking Entanglement: Teleportation in Relativistic Motion • Introduction • Motivation • RQI • Objectives • Framework • QFT • Bogoliubov transformations • Gaussian states • Teleportation • Method • Result • Conclusions • Outlook • Future directions • Summary • Introduction • Motivation, relativistic quantum information, experiments • Framework • QFT, Bogoliubov transformations, Gaussian QI, motion in spacetime • Teleportation • Description, our angle, results • Conclusions • Brief recap and future directions Antony Richard Lee – UoN – Loops 13

3. Shaking Entanglement: Teleportation in Relativistic Motion • Introduction • Motivation • RQI • Objectives • Framework • QFT • Bogoliubov transformations • Gaussian states • Teleportation • Method • Result • Conclusions • Outlook • Future directions • Introduction • Motivation • How does relativistic principles and quantum information influence each other? • Relativistic Quantum Information • Current attempt at implementing QI protocols and tools in a QFT setting • Objectives • Produce a framework which can guide us to new protocols which cannot exist without both relativity and QI. Antony Richard Lee – UoN – Loops 13

4. Shaking Entanglement: Teleportation in Relativistic Motion • Introduction • Motivation • RQI • Objectives • Framework • QFT • Bogoliubov transformations • Gaussian states • Teleportation • Method • Result • Conclusions • Outlook • Future directions • Canonical Quantum Field Theory • Field equation (1+1 scalar field) • Second Quantisation • Commutation and inner product relations • Different basis? Antony Richard Lee – UoN – Loops 13

5. Shaking Entanglement: Teleportation in Relativistic Motion • Introduction • Motivation • RQI • Objectives • Framework • QFT • Bogoliubov transformations • Gaussian states • Teleportation • Method • Result • Conclusions • Outlook • Future directions • Bogoliubov transformations • Field expansion • Relation between mode bases • Bogoliubov coefficients Antony Richard Lee – UoN – Loops 13

6. Shaking Entanglement: Teleportation in Relativistic Motion • Introduction • Motivation • RQI • Objectives • Framework • QFT • Bogoliubov transformations • Gaussian states • Teleportation • Method • Result • Conclusions • Outlook • Future directions • Bogoliubov Transformations • Compactly written as • Satisfy the symplectic group definition • Link to quantum information? Antony Richard Lee – UoN – Loops 13

7. Shaking Entanglement: Teleportation in Relativistic Motion • Introduction • Motivation • RQI • Objectives • Framework • QFT • Bogoliubov transformations • Gaussian states • Teleportation • Method • Result • Conclusions • Outlook • Future directions • Gaussian State Quantum Information • Define the vector of mode operators • Quantum state fully characterised by 1st and 2nd moments • Uses? • Experimental access, elegant mathematical description, underpinned by symplectic geometry Antony Richard Lee – UoN – Loops 13

8. Shaking Entanglement: Teleportation in Relativistic Motion • Introduction • Motivation • RQI • Objectives • Framework • QFT • Bogoliubov transformations • Gaussian states • Teleportation • Method • Result • Conclusions • Outlook • Future directions • Gaussian State Quantum Information • State transformation under Bogoliubov transformation • 1st and 2nd moments • Example of a Gaussian state is the vacuum Antony Richard Lee – UoN – Loops 13

9. Shaking Entanglement: Teleportation in Relativistic Motion • Introduction • Motivation • RQI • Objectives • Framework • QFT • Bogoliubov transformations • Gaussian states • Teleportation • Method • Result • Conclusions • Outlook • Future directions • Model the motion of a cavity via Bogoliubov transformations • quantifies proper acceleration • quantifies proper time Change back to previous type of observer Evolution under free Hamiltonian Change from one type of observer to another Antony Richard Lee – UoN – Loops 13

10. Shaking Entanglement: Teleportation in Relativistic Motion • Introduction • Motivation • RQI • Objectives • Framework • QFT • Bogoliubov transformations • Gaussian states • Teleportation • Method • Result • Conclusions • Outlook • Future directions Revert back to previous type of observer Acceleration Evolution under free Hamiltonian Inertial Change to new type of observer Antony Richard Lee – UoN – Loops 13

11. Shaking Entanglement: Teleportation in Relativistic Motion • Introduction • Motivation • RQI • Objectives • Framework • QFT • Bogoliubov transformations • Gaussian states • Teleportation • Method • Result • Conclusions • Outlook • Future directions Antony Richard Lee – UoN – Loops 13

12. Shaking Entanglement: Teleportation in Relativistic Motion • Introduction • Motivation • RQI • Objectives • Framework • QFT • Bogoliubov transformations • Gaussian states • Teleportation • Method • Result • Conclusions • Outlook • Future directions Alice – Bob entangled state Bob’s state Unknown state Antony Richard Lee – UoN – Loops 13

13. Shaking Entanglement: Teleportation in Relativistic Motion • Introduction • Motivation • RQI • Objectives • Framework • QFT • Bogoliubov transformations • Gaussian states • Teleportation • Method • Result • Conclusions • Outlook • Future directions • Result • Fidelity • Perturbative result in • Periodic dependence on Antony Richard Lee – UoN – Loops 13

14. Shaking Entanglement: Teleportation in Relativistic Motion • Introduction • Motivation • RQI • Objectives • Framework • QFT • Bogoliubov transformations • Gaussian states • Teleportation • Method • Result • Conclusions • Outlook • Future directions • Result • Fidelity • Non-uniform motion of Bob implies • Reduction in usable entanglement • Reduction in teleportation efficiency • Implications for communication technologies Antony Richard Lee – UoN – Loops 13

15. Shaking Entanglement: Teleportation in Relativistic Motion • Introduction • Motivation • RQI • Objectives • Framework • QFT • Bogoliubov transformations • Gaussian states • Teleportation • Method • Result • Conclusions • Outlook • Future directions • Outlook • Flexible framework within symplectic geometry • Can give a concrete setting to analyse quantum information within QFT • Has possible implications for communication over long distances and in a gravitational field • Papers • D. E. Bruschi, I. Fuentes and J. Louko, Phys. Rev. D 85, 061701(R) (2012) • N. Friis, A. R. L, K. Truong, C. Sabín, E. Solano, G. Johansson and I. Fuentes, Phys. Rev. Lett. 110, 113602 (2013) Antony Richard Lee – UoN – Loops 13

16. Shaking Entanglement: Teleportation in Relativistic Motion • Introduction • Motivation • RQI • Objectives • Framework • QFT • Bogoliubov transformations • Gaussian states • Teleportation • Method • Result • Conclusions • Outlook • Future directions • Future Directions • Use of symplectic geometry in QG + QI? • Information, entropy, correlations and LQG? • Black hole information paradox, firewall problem? Antony Richard Lee – UoN – Loops 13

17. Thanks!