Entanglement on demand: Time reordering

1. Entanglement on demand: Time reordering Bisker, Gershoni, Lindner, Meirom, Warburton

2. \documentclass{article}\pagestyle{empty} \usepackage[usenames]{color} \newcommand{\braket}[2]{\langle #1 | #2 \rangle} \newcommand{\average}[1]{\left\langle #1 \right\rangle} \newcommand{\ket}[1]{\left| #1 \right\rangle} \newcommand{\bra}[1]{\left\langle #1 \right|} \newcommand{\dbar}{\kern-.1em{\raise.8ex\hbox{ -}}\kern-.6em{d}} \newcommand{\mbf}[1]{\mathbf #1}\begin{document} \color{cyan} $$ \ket{0}=\ket{H},\quad \ket{1}=\ket{V} $$ \end{document} Bell states Maximally entangled Good for Quantum information

3. Qubits Flying quabits: Photons Storage qubits: Nuclear spin Working qubits: Electronic states Photons: encode qubit in polarization

4. Down conversion Nonlinear optics: Which path ambiguity

5. On demand Entangled piece junk

6. P S S P Quantum dots Can one entangle the pair?

7. H V H H V V Which path and entanglement Entanglement: A 2 photon analog of interference

8. H V H V H V H V Color monitors the cascade Monitored by color Un-monitored Monitoring: Kills ambiguity and entanglement

9. What is entanglement? Classical vs quantum probabilities independence Correlations due to common preparation

10. Classical probabilities Any probability distribution is a weighted sum of independent Independent (sure) events Common preparation

11. Quantum probabilities Quantum independence Correlations due to common preparation Separable states States that are not separable are entangled

12. Entangled states Separable states Independent up to common preparation There are states, r > 0, that are not separable! Definition:States that are not separable are entangled

13. Separable and entangled states Octahedron=separable Tetrahedron=all states Horodecki’s,Leinaas Myrheim Uvrom, Kenneth Avron, Bisker

14. Entanglement (Peres) test If transform has negative eigenvalue state is entangled Example: Bell state Negative eigenvalue is a measure of entanglement

15. H V H V g f is a measure of entanglment How monitoring kills entanglement

16. Monitoring: Energy scales Entanglement needs G > D

17. D Field Why making D small is hard Principle of level repulsion 1eV Spin-Orbit: Protected subspace Forcing degeneracy: Stevenson et. al. , Hafenbrak et. al.

18. Life in protected subspace D is due to spin orbit interaction - Relativistic effect In principle easy In principle hard

19. t V H Detector Detector Ambiguity up to order Space time diagrams: Lindenr H V Order Monitors the path J. Finley

20. t t V H V H Detector Detector Reordering Reimer et. al. Detector Detector Forcing ambiguity Fixing the order How much entanglement? Can reordering be done on demand,i.e. unitary?

21. E e e e E Photon field from cascade E f

22. E ev eh Photon field for 2 paths Coincidence of colors: E eh ev ev eh E

23. How much entanglement? Entanglment small By phase cancellation not by lack of overlap manifestly unitary Not small

24. How much overlap ? Large overlap Little overlap

25. Setup

26. Concluding remarks • Test: Make the experiment • Dephasing • Fight Wigner von Neuman Special thanks to Jonathan Finely