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

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

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

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 2004 (more efficient ) LM05 2005 (no entangled state) DLL 2003 One way two step Shukla C., Banerjee A., Pathak A., One way one step Int. J. Theor. Phys., vol. 52, pp. 1914-1924, 2013 DSQC Long and Liu (2002) Banerjee A., Pathak A., Phys. Lett. A, vol. 376, pp. 2944-2950, 2012. Shukla C., Banerjee A., And Pathak A., Int. J. Theor. Phys., vol. 52, pp. 1914-1924, 2013 QD 4

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

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):http://perimeterinstitute.ca/videos/alice-and-bob

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. 518-527, 2013. 7

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

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

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

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

2017/3/21 Noise 12

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

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

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

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

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

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.

2017/3/21 Disjoint set

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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

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

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

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

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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 10.1007/s11128-014-0784-0 26

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

Collaborators 2017/3/21

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