Multiparticle Quantum Correlationschep.iisc.ac.in/Meetings/CQIQC/ICQIQC/talks/Jan09_SenDe.pdf · Multiparticle Quantum Correlations & its application in Quantum Communication Aditi

Multiparticle Quantum Correlations

& its application in Quantum Communication

Aditi Sen (De)

Harish-Chandra Research Institute, Allahabad

Multiparticle Quantum Correlations

& its application in Quantum Communication

Aditi Sen (De)

Harish-Chandra Research Institute, Allahabad

Collaborators: Utkarsh Mishra, R. Prabhu, Ujjwal Sen

Outline Entanglement

Two-party Multi-party

Macroscopic Schrödinger Cat

More resistant to noise

Quantum Communication

Utkarsh Mishra, ASD, Ujjwal Sen, arXiv:1207.5239

Complementarity between

quantum communication & entanglement measures

R. Prabhu, ASD, Ujjwal Sen, arXiv:1208.6535

http://arxiv.org/abs/1207.5239










































quantum communication & entanglement















Entanglement : 2 Party

Entanglement of a pure state is

A = trB(| AB|)

S() = - tr (log2 ) von Neumann entropy

E(|AB) = S(A) = S(B)

Is it entangled?

How much?

For 2 spin-1/2 particles,

Entanglement: well – understood

qualitatively, quantitatively

Entanglement : 2 Party

Entanglement of a pure state is

A = trB(| AB|)

S() = - tr (log2 ) von Neumann entropy

E(|AB) = S(A) = S(B)

Is it entangled?

How much?

For 2 spin-1/2 particles,

Entanglement: well – understood

qualitatively, quantitatively

Entanglement Measures: 2 Party

The negativity of :

the absolute value of the sum of the negative

eigenvalues of

Logarithmic Negativity

G. Vidal, R.F. Werner, PRA’01

Entanglement Measures: 2 Party

The negativity of :

the absolute value of the sum of the negative

eigenvalues of

Logarithmic Negativity

G. Vidal, R.F. Werner, PRA’01












E.g., the factorization of a 200-digit number requires about 3,500 qubits

Why Multiparty important?

• Quantum computer is powerful than classical

one: ~ 1000 qubits

• Many-body system: realization of quantum

communication and computation



one: ~ 1000 qubits




J.I. Cirac, P. Zoller, Nature’00



one: ~ 1000 qubits




Preparation of multi-party state in Lab

14 ion trapped linearly, R. Blatt’s Group, Innsbruck, 2011

Preparation of multi-party state in Lab

14 ion trapped linearly, R. Blatt’s Group, Innsbruck, 2011

Experiments demand immediate investigation

of multiparty state












Schrödinger Cat

Schrödinger Cat

Schrödinger Cat

Schrödinger Cat

Schrödinger Cat



Proposing a new macroscopic Schrödinger Cat

N Particles


Proposing a new macroscopic Schrödinger Cat Why they r macroscopically different?


Proposing a new macroscopic Schrödinger Cat Why they r macroscopically different?

Ans: violation of local realism



More resistant to local decoherence and particle loss

U. Mishra, ASD, U. Sen, arXiv: 1207:5239

New Schrödinger Cat under Particle Loss


More resistant to local decoherence and particle loss.










Particle Loss No Entanglement

New Schrödinger Cat under Local Decoherence


More resistant to local decoherence and particle loss. Decoherence parameter




New Cat state is better than others in the market




New Cat state is better than others in the market

Utkarsh

Mishra’s

Poster












Communication Network

Ali (A)

Bebo(B) Charu (C) Damu (D)

ABCD


Ali (A)


ABCD


Ali (A)


ABCD

Individually

communicate


Ali (A)


ABCD

A individually performs dense

coding with B, C, & D

R.Prabhu’s

Poster

Capacity of Dense Coding

A (sender) & B (receiver) share :

Capacity of sending classical information

from A to B is

Coherent Information

S = von Neumann entropy

dA :dimension of A ASD, U. Sen, Physics News (arXiv:1105:2412)



Capacity of sending classical information via

quantum channel from A to B is


S = von Neumann entropy

dA :dimension of A ASD, U. Sen, Physics News (arXiv:1105:2412)





dA :dimension of A





Classical protocol










Coherent Information > 0

densecodeable



Quantum advantage in dense coding:

Quantum advantage in network:

Communication Network:

Advantage in capacity

Ali (A)


Goal

• Connect

Capacity of quantum communication

with

multiparty entanglement

Goal

• Connect

Capacity of quantum communication

with

multiparty entanglement measures














one: ~ 1000 qubits



E.g., the factorization of a 200-digit number requires about 3,500 qubits Important to quantify

multipartite entanglement

Relative Entropy of Entanglement

V. Vedral, M.B. Plenio, M.A. Rippin, P.L. Knight, PRL’97

Genuine Relative Entropy of Entanglement

V. Vedral, M.B. Plenio, M.A. Rippin, P.L. Knight, PRL’97



Advantage in capacity

Ali (A)


Theorem: For arbitrary pure or mixed states,

Complementarity between Capacity &

Relative entropy of entanglement

d: max dimension of receivers

R. Prabhu, ASD, U. Sen, arXiv:1208.6535









Suppose





Suppose





Suppose





d: max dimension of recievers













How generic?

Genuine

Multipartite Entanglement Measure

Introduce a new multiparty measure

(|N) = 1 – (max)2

max(|N) = max |N|

Max is over all pure states | that are not genuinely multiparty entangled.

ASD, U. Sen, PRA 2010

Genuine



(|N) = 1 – (max)2

max(|N) = max |N|



Generalized geometric measure

Genuine



(|N) = 1 – (max)2

max(|N) = max |N|


Possible to compute for arbitrary number of parties

in arbitrary dimensions ASD, U. Sen, PRA 2010


Genuine



(|N) = 1 – (max)2

max(|N) = max |N|



in arbitrary dimensions

Prabhu R. , S. Pradhan, ASD, U. Sen, PRA 2011

MN Bera, Prabhu R., ASD, U. Sen, PRA 2012

MN Bera, Prabhu R., ASD, U. Sen, 1209:1523

A. Biswas, Prabhu R., ASD, U. Sen, arXiv: 1211:3241



Genuine



(|N) = 1 – (max)2

max(|N) = max |N|



in arbitrary dimensions

Prabhu R. , S. Pradhan, ASD, U. Sen, PRA 2011

MN Bera, Prabhu R., ASD, U. Sen, PRA 2012

MN Bera, Prabhu R., ASD, U. Sen, 1209:1523

A. Biswas, Prabhu R., ASD, U. Sen, arXiv: 1211:3241

Manabendra’s Poster





Advantage ion capacity

Ali (A)


Any complementarity

with ?


Complementarity between Capacity & GGM


• Yes. Indeed!


Theorem:

Complementarity between Capacity & GGM


• Yes. Indeed!


Introduce Macroscopic Schrödinger Cat State:


Conclusion



quantum communication network & entanglement

R. Prabhu , ASD, U. Sen, arXiv: 1208.6535



Conclusion



quantum communication network & multipartite entanglement




Conclusion



quantum communication network & multipartite entanglement


Relative entropy of entanglement &

GGM

QIC Group @ HRI

QIC Group @ HRI

QIC@ HRI Arun K Pati Ujjwal Sen R. Prabhu Anindya Biswas Manabendra N Bera Avijit Mishra Utkarsh Misra Shrobona Bagchi Himadri S Dhar Asutosh Kumar Debasish Mondal Uttam Singh Tamoghna Das Debasis Sadhukhan Sudipto Singha Roy ASD

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Multiparticle Quantum Correlationschep.iisc.ac.in/Meetings/CQIQC/ICQIQC/talks/Jan09_SenDe.pdf · Multiparticle Quantum Correlations & its application in Quantum Communication Aditi