Entanglement Distribution
Via
Quantum Communication
Anindita Banerjee
Department of Physics
Centre of Astroparticle Physics and Space Science
Bose Institute
Outline
 Basic Definitions
 Introduction
 Motivation
 Results
Entanglement

 
AB
 
A
00  11
2

B
AB
  
A
B
  a b
Source: perimeterinstitute.ca/videos/alice-and-bob
Entanglement measures
Log Negativity:
 (  )  log
N

2

TA
1
TA
Trace norm is the sum of the absolute
values of the eigen value of the density matrix

1
TA
Partial transpose of the bipartite mixed state
Entanglement is a resource
Dense Coding [Bennett, C.; Wiesner, S. Phys. Rev. Lett. 69 (20): 2881 (1992)].
Teleportation [C. H. Bennett et al., Phys. Rev. Lett. 70, 1895 (1993)].
Alice’s Lab
Bob’s Lab
QUANTUM
CHANNEL
A
A
B
B
Initial Entanglement between Alice’s Lab and
Bob’s Lab =0
Alice sends entangled particle B to Bob
Final entanglement is same as the
communicated entanglement
A
B
No entanglement is necessary to distribute entanglement
C
A
B
Theory: T.S. Cubitt, F. Verstraete, W. Dür, J.I. Cirac. "Separable
States can be used to distribute entanglement". Physical Review
Letters, 91, 037902 (2003).
Experiment: Christina E. Vollmer et al., Experimental
Entanglement Distribution by Separable States, Phys. Rev. Lett. 111,
230505 (2013).
Alice’s Lab
Bob’s Lab
QUANTUM
QUANTUM
CHANNEL
CHANNEL

C
ABC
C
A
0
(A vsvsBC)
 (C
(AC
AB)=0
B)=0
C
B
Entanglement Distribution
Direct Distribution
Indirect Distribution
C
A
A
B
B
A
B
A
B
C
A
B
Indirect Distribution protocol
Initial Entanglement (

INITIAL
) =

AC/B
 ) =
Final Entanglement (
) =
Entanglement change
 ==   
 

 COM non excessive
 
 COM excessive
Communicated entanglement (
FINAL
COM
AB/C
A/BC
FINAL
INITIAL
A/BC
AC/B

INITIAL

COM

FINAL
-

ZERO
ZERO
INCREASE
NON ZERO
ZERO
INCREASE
ZERO
NON ZERO
?
NON ZERO
NON ZERO
?
INITIAL

CASE 1
12345
IS SUBJECTED TO PARAMETER q
 
  00
 
123/ 45
1245
123//345
Alice
FINAL
FINAL
COM
INITIAL
COM
Bob
Initial Entanglement (

INITIAL
)
=

Final Entanglement (
) =
Entanglement change
 
Communicated entanglement (
FINAL
Log
negativity
q

COM
Init
0
) =
0
12/345
123/45
COM
3/1245


FINAL
123/45




INITIAL
12/345
COM
3/1245
CASE 2



   00
 
13 / 245
Alice
3 /11245
/ 2345
FINAL
FINAL
INITIAL
COM
COM
Bob
Initial Entanglement (

INITIAL
)
=

Final Entanglement (
) =
Entanglement change
 
Communicated entanglement (
FINAL
Log
negativity
q

COM
0
) =
0
3/1245
1/2345
Init
13/245
COM


FINAL
13/245




INITIAL
COM
3/1345
1/2345
CASE 3
 
   00
 
23 / 145
23/1345
/1245
Alice
FINAL
FINAL
INITIAL
COM
COM
Bob
Initial Entanglement (

INITIAL
)
=

Final Entanglement (
) =
Entanglement change
 
Communicated entanglement (
FINAL
Log
negativity
q

COM
Init
0
) =
0
2/1345
23/245
COM
3/1245


FINAL
23/245




INITIAL
COM
2/1345
3/1245

INITIAL

COM

FINAL
-

ZERO
ZERO
INCREASE
NON ZERO
ZERO
INCREASE
ZERO
NON ZERO
NON ZERO
NON ZERO
?
?
INITIAL
COLLABORATORS
Somshubhro Bandyopadhyay
Saronath Haldar
Prasnjit Deb
Tomasz Paterek
Kavan Modi
Margherita Zuppardo
Thank you
Absolutely Maximally Entangled state
AME(n,d) is a pure state of n qudits in d dimension
such that every bipartition of the system is strictly
maximally entangled state .
AME(5,2)
 00000  10010  01001  10100  01010  11011  00110  11000
0  1 / 4
  11101  00011  11110  01111  10001  01100  10111  00101





 11111  01101  10110  01011  10101  00100  11001  00111
1  1 / 4
  00010  11100  00001  10000  01110  10011  01000  11010





1 ebit
2 ebit
Deporalizing channel
The depolarizing channel is a model of a
decohering qubit with probability p the qubit
remains intact, while with probability 1- p an
“error” occurs. If an error occurs, then evolves to
an ensemble of the three states all occurring with
equal likelihood. (Bit flip + Phase Flip + Both)
'
1 p 
p1  
( 1   2   3 )
 3 
One parameter family q
Cavity QED where ancilla is the cavity mode