1. Q UANTUM C OMMUNICATION P ART 2 Aditi Harish-Chandra Research Institute, India

2. O UTLINE Communication Secure Communication Quantum Cryptography Communication Without security Classical info transmission Classical info transmission Quantum state transmission

3. DC C APACITY : K NOWN /U NKNOWN Single Sender – Single Receiver Many Senders – Single Receiver Solved

4. Dense Coding Network 3

5. D ISTRIBUTED DC: T WO RECEIVERS Alice (A 1 ) Alice (A 2 ) Bob (B 1 ) Bob (B 2 )

6. D ISTRIBUTED DC: T WO RECEIVERS Alice (A 1 ) Alice (A 2 ) Bob (B 1 ) Bob (B 2 ) LOCC i1i1 i2i2

7. D ISTRIBUTED DC: T WO RECEIVERS Alice (A 1 ) Alice (A 2 ) Bob (B 1 ) Bob (B 2 )

8. D ISTRIBUTED DC: T WO RECEIVERS Alice (A 1 ) Alice (A 2 ) Bob (B 1 ) Bob (B 2 ) Alices send her particles to Bobs

9. D ISTRIBUTED DC: T WO RECEIVERS Bob (B 1 ) Bob (B 2 ) Bobs task: gather info abt i k by LOCC

10. D ISTRIBUTED DC: T WO RECEIVERS Bob (B 1 ) Bob (B 2 ) Bobs task: gather info abt i k by LOCC LOCC

11. C = Max D ISTRIBUTED DC: T WO RECEIVERS

12. C = Max Max LOCC Holevo bound Maximization over all encodings i.e. over all {p i, U i } D ISTRIBUTED DC: T WO RECEIVERS

13. C = Max Max LOCC Holevo bound Maximization over all encodings i.e. over all {p i, U i } Badziag, Horodecki, ASD, Sen, PRL’03 D ISTRIBUTED DC: T WO RECEIVERS

14. C = Max Max LOCC Holevo bound Maximization over all encodings i.e. over all {p i, U i } Bruss, D’Ariano, Lewenstein, Macchiavello, ASD, Sen, PRL’ 04 D ISTRIBUTED DC: T WO RECEIVERS

15. DC C APACITY : K NOWN /U NKNOWN Single Sender – Single Receiver Many Senders – Single Receiver Solved

16. DC C APACITY : K NOWN /U NKNOWN Single Sender – Single Receiver Many Senders – Single Receiver Solved Many Senders – Two Receivers

17. DC C APACITY : K NOWN /U NKNOWN Single Sender – Single Receiver Many Senders – Single Receiver Solved Many Senders – Two Receivers Partially Solved

18. DC C APACITY : K NOWN /U NKNOWN Single Sender – Single Receiver Many Senders – Single Receiver Solved Many Senders – Two Receivers Partially Solved Many Senders – Many Receivers Not Solved 

19. O UTLINE Communication Secure Communication Quantum Cryptography Communication Without security Classical info transmission Classical info transmission Quantum state transmission

20. Quantum Dense Coding Task: Classical info transmission Quantum Dense Coding Task: Classical info transmission Quantum Dense Coding

21. Task: Classical info transmission Medium: Quantum State Quantum Dense Coding Task: Classical info transmission Medium: Quantum State Quantum Dense Coding

22. Task: Classical info transmission Medium: Quantum State Quantum Dense Coding Task: Classical info transmission Medium: Quantum State Task: quantum state/info transmission Task: quantum state/info transmission Task: Quantum state/info transmission Task: Quantum state/info transmission Quantum Dense Coding

23. Task: Classical info transmission Medium: Quantum State Quantum Dense Coding Task: Classical info transmission Medium: Quantum State Task: Quantum state/info transmission Medium: Quantum State Task: Quantum state/info transmission Medium: Quantum State Quantum Dense Coding

24. Task: Classical info transmission Medium: Quantum State Task: Classical info transmission Medium: Quantum State Task: Quantum state/info transmission Medium: Quantum State Task: Quantum state/info transmission Medium: Quantum State Quantum Dense Coding Quantum Teleportation

25. Bennett, Brassard, Crepeau, Jozsa, Peres, Wootters, PRL 1993

26. Q UANTUM T ELEPORTATION Task: Sending arbitrary quantum state

27. Q UANTUM T ELEPORTATION Task: Sending

28. Q UANTUM T ELEPORTATION Task: Sending

29. Q UANTUM T ELEPORTATION Task: Sending Classical: Infinite communication

30. Q UANTUM T ELEPORTATION Task: Sending Classical: Infinite communication

31. Q UANTUM T ELEPORTATION A in B Alice Bob

32. Q UANTUM T ELEPORTATION A in B Alice Bob Alice performs measurements on “in’’ and A

33. Q UANTUM T ELEPORTATION A in B Alice Bob After measurement

34. Q UANTUM T ELEPORTATION A in B Alice Bob After measurement 2 bits of classical comm. sent by Alice to Bob

35. Q UANTUM T ELEPORTATION A in B Alice Bob After measurement Bob performs unitary

36. Q UANTUM T ELEPORTATION A in B Alice Bob After measurement State is with Bob

37. M ORAL Classical Quantum Vs. Task: sending arbitrary quantum state Infinite classical comm 2 bits of classical comm

38. M ORAL Classical Quantum Task: sending arbitrary quantum state Infinite classical comm 2 bits of classical comm Vs.

39. I S IT MAGIC ?

40. Of course not!

41. I S IT MAGIC ? Ingredient: Quantum Mechanics

42. I S IT MAGIC ? Entangled states

43. W HAT IS ENTANGLEMENT ? Unentangled/Useless states : Entangled/Useful states :

44. W HAT IS ENTANGLEMENT ? Unentangled/Useless states : Entangled/Useful states :

45. W HAT IS ENTANGLEMENT ? Unentangled/Useless states : Entangled/Useful states :

46. Is it just theory ?

47. Experiments

48. P HOTONS

49. 143 Km Teleportation

50. ~100KM

51. E NTANGLEMENT S WAPPING Zukowski, Zeilinge, Horne, Ekert, PRL 71, 4287 (’93)

52. E NTANGLEMENT S WAPPING Zukowski, Zeilinge, Horne, Ekert, PRL 71, 4287 (’93)

53. P HOTONS Photons

54. P HOTONS Photons

55. IONS

56. IONS 14 ions entangled

57. ION E NTANGLED S TATES Phys. Rep. 2008

58. Quantum Teleportation between Light and Matter

59. Quantum Teleportation between Light and Matter

60. Quantum Teleportation between Light and Matter Polzik’s group, Nature 443, 557 (’06)

61. Quantum Teleportation between Light and Matter Polzik’s group, Nature 443, 557 (’06)

62. IONS: T ELEPORTATION

66. NMR Entangled states in NMR

67. T ELEPORTATION BY NMR

68. Nielsen, Knill, Laflamme, Nature 395 (’98)

69. O PTICAL L ATTICES

70. Entangled states in Optical lattices

71. O PTICAL L ATTICES Entangled states in Optical lattices

72. O PTICAL L ATTICES Resonating valence bond states in Optical lattices

73. T ELEPORTATION : N EUTRAL A TOMS Wu, Yang, Shen, Zheng, J. Phys. B: At. Mol. Opt. Phys. 46, 185502 (’13)

74. T ELEPORTATION : S PIN CHAIN 1. Initially the spin chain is in the ground state:

75. T ELEPORTATION : S PIN CHAIN 1. Initially the spin chain is in the ground state: 2. Alice places an arbitrary state at her end:

76. T ELEPORTATION : S PIN CHAIN 1. Initially the spin chain is in the ground state: 2. Alice places an arbitrary state at her end: 3. The state evolves according to some Hamiltonian:

77. T ELEPORTATION : S PIN CHAIN 1. Initially the spin chain is in the ground state: 2. Alice places an arbitrary state at her end: 3. The state evolves according to some Hamiltonian: 4. Bob receives the state after some time. Bose, PRL(’03), Subrahmanyam, PRA (’03)

78. Many other systems …….

79. Teleportation for arbitrary states

80. AB Alice & Bob share a state

81. AB

82. A in B Task: To send to Bob single copy of is available CdCd

83. A in B Allowed operations: LOCC

84. A in B Not allowed operations: exchange qubits

85. A in B Alice & Bob perform some LOCC, T,

86. A in B Alice & Bob perform some LOCC, T, and create at Bob’s side

87. A in B Alice & Bob perform some LOCC, T, and create at Bob’s side Check its closeness with

88. A in B Quantify closeness: integration over all inputs Teleportation fidelity

89. Singlet Fraction: : max singlet fraction from by LOCC Bennett, Divincenzo, Smolin, Wootters, PRA 54, 3824 (’97) MPR Horodeccy, PRA 60, 1888 (’99) M.A. Nielsen, quant-ph/0205035

90. Singlet Fraction: : max singlet fraction from by LOCC Horodeccy, PRA 60, 1888 (’99) Nielsen, arXiv: 0205035 Verstreate, Verschele, PRL 90, 097901 (’03)

91. Popescu, PRL 72, 797 (’94) Alice & Bob share separable state, then f max =2/3

92. T ELE C APACITY : K NOWN /U NKNOWN Single Sender – Single Receiver d  d Solved

93. Teleportation Network 1

94. T ELEPORTATION : M ONOGAMY Alice Debu Charu Nitu........ Bob SendersReceiver

95. T ELEPORTATION : M ONOGAMY Alice Debu Charu Nitu........ Bob SendersReceiver Teleportation monogamy Faithful teleportation cannot be freely performed

96. T ELEPORTATION : M ONOGAMY Tele mono ineq: Lee and Park, PRA 79, 054309(’09)

97. T ELEPORTATION : M ONOGAMY Holds for pure states: Lee and Park, PRA 79, 054309(’09)

98. T ELEPORTATION : M ONOGAMY Holds for pure states: Lee and Park, PRA 79, 054309(’09) Follows from monogamy of concurrence squared in 2  d

99. T ELEPORTATION : M ONOGAMY Does Not hold for mixed states: Lee and Park, PRA 79, 054309(’09)

100. Teleportation Network 2

101. T ELEPORTATION N ETWORK Alice (A 1 ) Alice (A 2 ) Bob (B 1 ) Bob (B 2 ) ASD, U. Sen, PRA 81, 012308 (’01)

102. T ELEPORTATION N ETWORK Alice (A 1 ) Alice (A 2 ) Bob (B 1 ) Bob (B 2 ) ASD, U. Sen, PRA 81, 012308 (’01)

103. T ELEPORTATION N ETWORK Alice (A 1 ) Alice (A 2 ) Bob (B 1 ) Bob (B 2 ) ASD, U. Sen, PRA 81, 012308 (’01) Establish relation between capacity & entanglement

104. T ELE C APACITY : K NOWN /U NKNOWN Single Sender – Single Receiver d  d Solved

105. T ELE C APACITY : K NOWN /U NKNOWN Single Sender – Single Receiver d  d Solved Many Senders – single Receiver Not Solved 

106. T ELE C APACITY : K NOWN /U NKNOWN Single Sender – Single Receiver d  d Solved Many Senders – single Receiver Not Solved  Many Senders – many Receiver Not Solved 

107. Single Sender – Single Receiver Many Senders – Single Receiver Solved Many Senders – Two Receivers Many Senders – Many Receivers Partially Solved Not Solved  Classical info transmit known/Unknown known/Unknown Quantum info transmission Single Sender – Single Receiver d  d Solved Many Senders – Single Receiver Not Solved  Many Senders – Many Receivers Not Solved 

108. QIC@HRI