multiparticle quantum correlationschep.iisc.ac.in/meetings/cqiqc/icqiqc/talks/jan09_sende.pdf ·...
TRANSCRIPT
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Multiparticle Quantum Correlations
& its application in Quantum Communication
Aditi Sen (De)
Harish-Chandra Research Institute, Allahabad
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Multiparticle Quantum Correlations
& its application in Quantum Communication
Aditi Sen (De)
Harish-Chandra Research Institute, Allahabad
Collaborators: Utkarsh Mishra, R. Prabhu, Ujjwal Sen
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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
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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
![Page 5: Multiparticle Quantum Correlationschep.iisc.ac.in/Meetings/CQIQC/ICQIQC/talks/Jan09_SenDe.pdf · Multiparticle Quantum Correlations & its application in Quantum Communication Aditi](https://reader030.vdocuments.us/reader030/viewer/2022041109/5f0dc1547e708231d43bece3/html5/thumbnails/5.jpg)
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
![Page 6: Multiparticle Quantum Correlationschep.iisc.ac.in/Meetings/CQIQC/ICQIQC/talks/Jan09_SenDe.pdf · Multiparticle Quantum Correlations & its application in Quantum Communication Aditi](https://reader030.vdocuments.us/reader030/viewer/2022041109/5f0dc1547e708231d43bece3/html5/thumbnails/6.jpg)
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
![Page 7: Multiparticle Quantum Correlationschep.iisc.ac.in/Meetings/CQIQC/ICQIQC/talks/Jan09_SenDe.pdf · Multiparticle Quantum Correlations & its application in Quantum Communication Aditi](https://reader030.vdocuments.us/reader030/viewer/2022041109/5f0dc1547e708231d43bece3/html5/thumbnails/7.jpg)
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
R. Prabhu, ASD, Ujjwal Sen, arXiv:1208.6535
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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
R. Prabhu, ASD, Ujjwal Sen, arXiv:1208.6535
![Page 9: Multiparticle Quantum Correlationschep.iisc.ac.in/Meetings/CQIQC/ICQIQC/talks/Jan09_SenDe.pdf · Multiparticle Quantum Correlations & its application in Quantum Communication Aditi](https://reader030.vdocuments.us/reader030/viewer/2022041109/5f0dc1547e708231d43bece3/html5/thumbnails/9.jpg)
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
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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
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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
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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
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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
R. Prabhu, ASD, Ujjwal Sen, arXiv:1208.6535
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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
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Why Multiparty important?
• Quantum computer is powerful than classical
one: ~ 1000 qubits
• Many-body system: realization of quantum
communication and computation
E.g., the factorization of a 200-digit number requires about 3,500 qubits
J.I. Cirac, P. Zoller, Nature’00
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Why Multiparty important?
• Quantum computer is powerful than classical
one: ~ 1000 qubits
• Many-body system: realization of quantum
communication and computation
E.g., the factorization of a 200-digit number requires about 3,500 qubits
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Preparation of multi-party state in Lab
14 ion trapped linearly, R. Blatt’s Group, Innsbruck, 2011
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Preparation of multi-party state in Lab
14 ion trapped linearly, R. Blatt’s Group, Innsbruck, 2011
Experiments demand immediate investigation
of multiparty state
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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
R. Prabhu, ASD, Ujjwal Sen, arXiv:1208.6535
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Schrödinger Cat
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Schrödinger Cat
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Schrödinger Cat
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Schrödinger Cat
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Schrödinger Cat
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Macroscopic Schrödinger Cat
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Macroscopic Schrödinger Cat
Proposing a new macroscopic Schrödinger Cat
N Particles
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Macroscopic Schrödinger Cat
Proposing a new macroscopic Schrödinger Cat Why they r macroscopically different?
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Macroscopic Schrödinger Cat
Proposing a new macroscopic Schrödinger Cat Why they r macroscopically different?
Ans: violation of local realism
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Macroscopic Schrödinger Cat
Proposing a new macroscopic Schrödinger Cat
More resistant to local decoherence and particle loss
U. Mishra, ASD, U. Sen, arXiv: 1207:5239
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New Schrödinger Cat under Particle Loss
Proposing a new macroscopic Schrödinger Cat
More resistant to local decoherence and particle loss.
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New Schrödinger Cat under Particle Loss
Proposing a new macroscopic Schrödinger Cat
More resistant to local decoherence and particle loss.
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New Schrödinger Cat under Particle Loss
Proposing a new macroscopic Schrödinger Cat
More resistant to local decoherence and particle loss.
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New Schrödinger Cat under Particle Loss
Proposing a new macroscopic Schrödinger Cat
More resistant to local decoherence and particle loss.
Particle Loss No Entanglement
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New Schrödinger Cat under Local Decoherence
Proposing a new macroscopic Schrödinger Cat
More resistant to local decoherence and particle loss. Decoherence parameter
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New Schrödinger Cat under Local Decoherence
Proposing a new macroscopic Schrödinger Cat
More resistant to local decoherence and particle loss. Decoherence parameter
New Cat state is better than others in the market
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New Schrödinger Cat under Local Decoherence
Proposing a new macroscopic Schrödinger Cat
More resistant to local decoherence and particle loss. Decoherence parameter
New Cat state is better than others in the market
Utkarsh
Mishra’s
Poster
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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
![Page 38: Multiparticle Quantum Correlationschep.iisc.ac.in/Meetings/CQIQC/ICQIQC/talks/Jan09_SenDe.pdf · Multiparticle Quantum Correlations & its application in Quantum Communication Aditi](https://reader030.vdocuments.us/reader030/viewer/2022041109/5f0dc1547e708231d43bece3/html5/thumbnails/38.jpg)
Communication Network
Ali (A)
Bebo(B) Charu (C) Damu (D)
ABCD
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Communication Network
Ali (A)
Bebo(B) Charu (C) Damu (D)
ABCD
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Communication Network
Ali (A)
Bebo(B) Charu (C) Damu (D)
ABCD
Individually
communicate
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Communication Network
Ali (A)
Bebo(B) Charu (C) Damu (D)
ABCD
A individually performs dense
coding with B, C, & D
R.Prabhu’s
Poster
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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)
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Capacity of Dense Coding
A (sender) & B (receiver) share :
Capacity of sending classical information via
quantum channel from A to B is
Coherent Information
S = von Neumann entropy
dA :dimension of A ASD, U. Sen, Physics News (arXiv:1105:2412)
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Capacity of Dense Coding
A (sender) & B (receiver) share :
Capacity of sending classical information via
quantum channel from A to B is
dA :dimension of A
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Capacity of Dense Coding
A (sender) & B (receiver) share :
Capacity of sending classical information via
quantum channel from A to B is
Classical protocol
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Capacity of Dense Coding
A (sender) & B (receiver) share :
Capacity of sending classical information via
quantum channel from A to B is
Coherent Information
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Capacity of Dense Coding
A (sender) & B (receiver) share :
Capacity of sending classical information via
quantum channel from A to B is
Coherent Information > 0
densecodeable
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Capacity of Dense Coding
A (sender) & B (receiver) share :
Quantum advantage in dense coding:
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Quantum advantage in network:
Communication Network:
Advantage in capacity
Ali (A)
Bebo(B) Charu (C) Damu (D)
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Goal
• Connect
Capacity of quantum communication
with
multiparty entanglement
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Goal
• Connect
Capacity of quantum communication
with
multiparty entanglement measures
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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
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Why Multiparty important?
• Quantum computer is powerful than classical
one: ~ 1000 qubits
• Many-body system: realization of quantum
communication and computation
E.g., the factorization of a 200-digit number requires about 3,500 qubits Important to quantify
multipartite entanglement
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Relative Entropy of Entanglement
V. Vedral, M.B. Plenio, M.A. Rippin, P.L. Knight, PRL’97
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Genuine Relative Entropy of Entanglement
V. Vedral, M.B. Plenio, M.A. Rippin, P.L. Knight, PRL’97
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Quantum advantage in network:
Communication Network:
Advantage in capacity
Ali (A)
Bebo(B) Charu (C) Damu (D)
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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
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Theorem: For arbitrary pure or mixed states,
Complementarity between Capacity &
Relative entropy of entanglement
R. Prabhu, ASD, U. Sen, arXiv:1208.6535
![Page 59: Multiparticle Quantum Correlationschep.iisc.ac.in/Meetings/CQIQC/ICQIQC/talks/Jan09_SenDe.pdf · Multiparticle Quantum Correlations & its application in Quantum Communication Aditi](https://reader030.vdocuments.us/reader030/viewer/2022041109/5f0dc1547e708231d43bece3/html5/thumbnails/59.jpg)
Quantum advantage in network:
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Theorem: For arbitrary pure or mixed states,
Complementarity between Capacity &
Relative entropy of entanglement
Suppose
R. Prabhu, ASD, U. Sen, arXiv:1208.6535
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Theorem: For arbitrary pure or mixed states,
Complementarity between Capacity &
Relative entropy of entanglement
Suppose
R. Prabhu, ASD, U. Sen, arXiv:1208.6535
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Theorem: For arbitrary pure or mixed states,
Complementarity between Capacity &
Relative entropy of entanglement
Suppose
R. Prabhu, ASD, U. Sen, arXiv:1208.6535
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Theorem: For arbitrary pure or mixed states,
Complementarity between Capacity &
Relative entropy of entanglement
d: max dimension of recievers
R. Prabhu, ASD, U. Sen, arXiv:1208.6535
![Page 64: Multiparticle Quantum Correlationschep.iisc.ac.in/Meetings/CQIQC/ICQIQC/talks/Jan09_SenDe.pdf · Multiparticle Quantum Correlations & its application in Quantum Communication Aditi](https://reader030.vdocuments.us/reader030/viewer/2022041109/5f0dc1547e708231d43bece3/html5/thumbnails/64.jpg)
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
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How generic?
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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
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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
Generalized geometric measure
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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.
Possible to compute for arbitrary number of parties
in arbitrary dimensions ASD, U. Sen, PRA 2010
Generalized geometric measure
![Page 69: Multiparticle Quantum Correlationschep.iisc.ac.in/Meetings/CQIQC/ICQIQC/talks/Jan09_SenDe.pdf · Multiparticle Quantum Correlations & its application in Quantum Communication Aditi](https://reader030.vdocuments.us/reader030/viewer/2022041109/5f0dc1547e708231d43bece3/html5/thumbnails/69.jpg)
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.
Possible to compute for arbitrary number of parties
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
ASD, U. Sen, PRA 2010
Generalized geometric measure
![Page 70: Multiparticle Quantum Correlationschep.iisc.ac.in/Meetings/CQIQC/ICQIQC/talks/Jan09_SenDe.pdf · Multiparticle Quantum Correlations & its application in Quantum Communication Aditi](https://reader030.vdocuments.us/reader030/viewer/2022041109/5f0dc1547e708231d43bece3/html5/thumbnails/70.jpg)
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.
Possible to compute for arbitrary number of parties
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
ASD, U. Sen, PRA 2010
Generalized geometric measure
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Quantum advantage in network:
Communication Network:
Advantage ion capacity
Ali (A)
Bebo(B) Charu (C) Damu (D)
Any complementarity
with ?
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Theorem: For arbitrary pure or mixed states,
Complementarity between Capacity & GGM
d: max dimension of receivers
• Yes. Indeed!
R. Prabhu, ASD, U. Sen, arXiv:1208.6535
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Theorem:
Complementarity between Capacity & GGM
d: max dimension of receivers
• Yes. Indeed!
R. Prabhu, ASD, U. Sen, arXiv:1208.6535
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Introduce Macroscopic Schrödinger Cat State:
More resistant to noise
Conclusion
U. Mishra, ASD, U. Sen, arXiv: 1207:5239
Complementarity between
quantum communication network & entanglement
R. Prabhu , ASD, U. Sen, arXiv: 1208.6535
![Page 75: Multiparticle Quantum Correlationschep.iisc.ac.in/Meetings/CQIQC/ICQIQC/talks/Jan09_SenDe.pdf · Multiparticle Quantum Correlations & its application in Quantum Communication Aditi](https://reader030.vdocuments.us/reader030/viewer/2022041109/5f0dc1547e708231d43bece3/html5/thumbnails/75.jpg)
Introduce Macroscopic Schrödinger Cat State:
More resistant to noise
Conclusion
U. Mishra, ASD, U. Sen, arXiv: 1207:5239
Complementarity between
quantum communication network & multipartite entanglement
R. Prabhu , ASD, U. Sen, arXiv: 1208.6535
![Page 76: Multiparticle Quantum Correlationschep.iisc.ac.in/Meetings/CQIQC/ICQIQC/talks/Jan09_SenDe.pdf · Multiparticle Quantum Correlations & its application in Quantum Communication Aditi](https://reader030.vdocuments.us/reader030/viewer/2022041109/5f0dc1547e708231d43bece3/html5/thumbnails/76.jpg)
Introduce Macroscopic Schrödinger Cat State:
More resistant to noise
Conclusion
U. Mishra, ASD, U. Sen, arXiv: 1207:5239
Complementarity between
quantum communication network & multipartite entanglement
R. Prabhu , ASD, U. Sen, arXiv: 1208.6535
Relative entropy of entanglement &
GGM
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QIC Group @ HRI
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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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