Talk delivered at the CAMEL 10 conference in Nessebar, Bulgaria, 22-27 June 2014. The talk presents recent results on entanglement witnesses for hybrid systems, with applications to quantum technologies and specifically quantum simulations

1. ENTANGLEMENT
Witnessing
in hybrid systems

2. “I would not call that one
but rather the characteristic
trait of quantum mechanics,
the one that enforces its
entire departure from
classical lines of thought.”

3. Entanglement is a resource

5. ?
NP hard

6. ENTANGLEMENT
Witnessing
Hermitian operator

7. detects entanglement of if
for any separable state

8. 3 Examples
1
2
3

9. 2 criteria
C2
Use of local measurements
Assumption on the form of the microscopic
Hamiltonian and/or the Hilbert space of the
system
C1

10. 1
Up to 6entangled qubits

11. C1
C2

12. C2
CROSSTALK

13. C1
C2

14. C1
C2

15. PROBLEM
WITH C1 and C2
Quantum simulations
Manybody systems

16. ENTANGLEMENT
Global Witnesses of
P. Krammer et al. “Multipartite Entanglement Detection via Structure Factors”, PRL 103, 100502 (2009)
Structure factor
M. Cramer et al. “Measuring Entanglement in Condensed Matter Systems”, PRL 106, 020401 (2011)

17. Structure factor
ri rj
light/neutrons
scattered light/neutrons

18. Witness
Structure factors

19. Witness
C2
C1
Independent of the form of the
microscopic Hamiltonian
Requires only global measurements

20. Great!

21. Experiments

22. Experiments

23. Trapped ions
Bragg scattering
Pump-probe experiment
PROBE
D
⌦1 ⌦0
PUMP LASER PAIR
C. Macchiavello and G. Morigi “Entanglement detection via Bragg scattering”, PRA 87, 044301 (2013)

24. What if the positions
are quantized ?

25. Q Witness
forTrapped ions
position operators
quantized motion

27. How does a quantum environment
affect spin entanglement detection
by ?

28. Can we define a generalised
witness and use it to detect
entanglement in hybrid systems ?

29. ENTANGLEMENT
Witnessing
in hybrid systems
Massimo Borrelli, Matteo Rossi, Chiara
Macchiavello, S.M.
arXiv:1404.6083

30. Q Witness
?

32. Q Witness
forTrapped ions
N spins factorised state collective vibrational state
For

33. Q Witness
forTrapped ions
normal modes decomposition

34. How does a quantum environment
affect spin entanglement detection
by ?

35. Q Witness
forTrapped ions
sinusoidal modulation of the collective
vibrational state characteristic function
if

36. Q Witness
forTrapped ions
Example 1
One collective vibrational mode in a
thermal state
2 effective spins

37. Optimal Q Witness
forTrapped ions
cx = 1, cy = 1, cz = 1

38. Optimal Q Witness
q’
= ~⌫/kBT
= 100
lowT
= 1
= 100 highT

39. Can we define a generalised
witness and use it to detect
entanglement in hybrid systems ?

40. Q Witness
forTrapped ions
Example 2 2 spins
One collective vibrational mode

41. state 1
↵ = 1
↵ = 0
state 2
state 3

42. Optimal Q Witness
q’
↵ = 0

43. Optimal Q Witness
q’
↵ = 1

44. Optimal Q Witness
q’
|↵| > 1
? ?

45. Optimal Q Witness
q’

46. Optimal Q Witness
q’
hybrid entanglement

48. short summary
spin detection:
the cooler the better!
spin detection:
shit happens!
witnessing hybrid entanglement!

49. what next ?
ENTANGLEMENT
Witnessing
in hybrid systems
Hybrid entanglement witness

50. what next ?
ENTANGLEMENT
Witnessing
in hybrid systems

51. ...one more minute ???

52. www.dscien.com

53. www.dscien.com

54. CAMEL 10