1. Institute of Physics (IOP), Bhubaneswar
2017/3/21
ISCQI-2016
Institute of Physics (IOP), Bhubaneswar 
Symmetric and Asymmetric
Multiparty Quantum Communication
Anindita Banerjee
Department of Physics
Centre of Astroparticle Physics and Space Science
Bose Institute 1
QUANTUM CHANNEL
QUANTUM CHANNEL
AQD with G3 4C 1C 6C 6C
16 OPERATORS
2 OPERATORS
64 OPERATORS
64 OPERATORS
CASE 4
CASE 5
CASE 6
CASE 1
CASE 2
CASE 3
QUANTUM CHANNEL
QUANTUM CHANNEL 6C 5C 6C 2C
4 OPERATORS
32 OPERATORS
QUANTUM CHANNEL
QUANTUM CHANNEL 6C 6C 6C 3C
8 OPERATORS
64 OPERATORS
QUANTUM CHANNEL
QUANTUM CHANNEL
MAX QD

2. Quantum communication
2017/3/21
Quantum communication
Insecure
(Teleportation,
RSP and their controlled versions)
Secure
(QSS, QSDC , DSQC, QD)
and its controlled versions 2

3. Secure quantum communication
2017/3/21
Secure quantum communication
Quantum key distribution (QKD)
Charles Bennett and Gilles Brassard 1984
A. K. Ekert 1991
L. Goldenberg and L. Vaidman 1995
Kak 3-stage protocol quantum cryptography 2006
Quantum key agreement (QKA)
Weaker notion
Stronger notion 3

4. Secure Direct quantum communication
2017/3/21
Secure Direct quantum communication
Pong
Ping
Information flow
QSDC
Ping Pong Two way two step
Bostrom and Felbinger in 2002
Cai and Li in (more efficient )
LM (no entangled state)
DLL One way two step
Shukla C., Banerjee A.,
Pathak A., One way one step
Int. J. Theor. Phys., vol. 52,
pp , 2013
DSQC
Long and Liu (2002)
Banerjee A., Pathak A.,
Phys. Lett. A, vol. 376,
pp , 2012.
Shukla C., Banerjee A.,
And Pathak A.,
Int. J. Theor. Phys., vol. 52,
pp , 2013 QD 4

5. Quantum world Information flow Quantum telephone Quantum Dialogue
2017/3/21
Information flow
Quantum world
Quantum telephone
Quantum Dialogue
Quantum Conference

6. Quantum Dialogue Classical channel Quantum channel Bob’s Lab
2017/3/21
Quantum Dialogue
B. A. Nguyen, Phys. Lett. A 328 (2004) 6.
intercept-resend attack
Classical
channel
Ba An 2005
Quantum
channel
Bob’s Lab
Home photon
Bob’s Lab
measurement
Alice’s Lab
Travel photon
time
Source (Pics of Alice And Bob):

7. Generalized structure of QD
2017/3/21
Group-theoretic
Approach
& on
Appropriate Quantum states
Sufficient Condition
Results
Large no. of useful dense coding schemes
Shukla C., Kothari V., Banerjee A., Pathak A., “On the Group-Theoretic Structure of a Class of Quantum Dialogue Protocols”, Phys. Lett. A, vol. 377, pp , 2013. 7

8. How to form groups of unitary operators?
2017/3/21
Example: G2 is the group of order 16.
Group multiplication table 8 8

9. Subgroups of G2 , G3 Example: Following are order 8, subgroups of G2
2017/3/21
Example: Following are order 8, subgroups of G2
Example: Following are order 32 ,subgroups of G3 9 9

10. Bell state Cluster state Higher number of state higher the encoding
2017/3/21
I CAN ENCODE
2 BITS
I CAN ENCODE
2 BITS
Bell state
I CAN ENCODE
4 BITS
I CAN ENCODE
4 BITS
Cluster state
Higher number of state higher the encoding

11. SYMMETRIC COMMUNICATION
2017/3/21
3 words
How are you
I am fine
3 words
ASSYMMETRIC COMMUNICATION
ASSYMMETRIC COMMUNICATION
3 words
How are you
fine
1 word

12. 2017/3/21
Noise 12

13. 2017/3/21
Bell state 2C 1C
QUANTUM CHANNEL 1C 2C
QUANTUM CHANNEL

14. 4-qubit cluster state and Ω state 1C 4C 1C 4C QUANTUM QUANTUM CHANNEL
2017/3/21 1C 1C 4C 4C
QUANTUM
CHANNEL
QUANTUM
CHANNEL 14

15. AQD with G2 4C 1C 4C 2C 4C 3C 4C 4C CASE 1 CASE 2 CASE 3 2 OPERATORS
2017/3/21
AQD with G2 4C
2 OPERATORS 1C
CASE 1
CASE 2
CASE 3
16 OPERATORS
QUANTUM CHANNEL 4C 2C
4 OPERATORS
QUANTUM CHANNEL 4C 3C
8 OPERATORS
QUANTUM CHANNEL 4C 4C
16 OPERATORS
QUANTUM CHANNEL
MAX QD

16. AQD with G3 6C 1C 6C 2C 6C 3C 4C 6C 6C 5C 6C 6C CASE 1 CASE 2 CASE 3
2017/3/21 6C 1C
2 OPERATORS
64 OPERATORS
CASE 1
CASE 2
CASE 3
QUANTUM CHANNEL 6C 2C
4 OPERATORS
QUANTUM CHANNEL 6C
AQD
with G3 3C
8 OPERATORS
QUANTUM CHANNEL 4C 6C
16 OPERATORS
CASE 4
CASE 5
CASE 6
64 OPERATORS
QUANTUM CHANNEL 6C 5C
32 OPERATORS
QUANTUM CHANNEL 6C 6C
64 OPERATORS
QUANTUM CHANNEL
MAX QD

17. Direct QUANTUM communication
2017/3/21
So far ALL
Direct QUANTUM communication
Schemes USE
COMMUNIATION!

18. Multi party communication
2017/3/21
Multi party communication
A conference is a meeting of people to exchange ideas on a topic.
Quantum conference (QC) is a multiparty secure quantum communication.
Here the conversations by all the parties stays in the channel until the final measurement
is done on the channel.

19. 2017/3/21
Disjoint set

20. 2017/3/21

21. Quantum conference -1 UA UA UB....UZ UA UB UA UB UC 2017/3/21 qd 21 UA
UA UB UC......UZ qd
UA UB
UA UB UC
UA UB UC 21

22. Leakage Success Probability of Eve = 1 / 2k
2017/3/21
Leakage
For sending K bit by each party
Operators required by each party = 2k
Success Probability of Eve = 1 / 2k
If we increase k then success probability will fall asymptotically
Eve’s success probability rate can be reduced by (n = number of qubits) using multipartite entangled states.
This leakage is not there in scheme 2. However the efficiency is reduced in scheme 2

23. 2017/3/21
Quantum conference-2
Passing the parcel
Qsdc based 23

24. INITIAL INFORMATION CAN BE SENT THROUGH QSDC
2017/3/21
Scheme 3
INITIAL INFORMATION CAN BE SENT THROUGH QSDC

25. 2017/3/21

26. All QD can be converted to QKA
2017/3/21
All QD can be converted to QKA
Following our sufficiency condition to construct Ba An-type protocol of QD, if we just encode the random sequence of bits in place of meaningful information on the quantum state, then we can convert all QD to QKA protocols.
Quantum Inf. Process., (2014) DOI /s 26

27. If i can send messages securely
2017/3/21
If i can send messages securely
why do i need to send key instead? Why QKA
Sending few bits securely is different (in practice) than sending lots of bits securely 27

28. Collaborators
2017/3/21

29. Thank you for your attention
2017/3/21
Thank you for your attention 29