Local two-qubit channels:
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Sergey Filippov ¹ , Tom áš Ryb á r ² , M ário Ziman² ¹ Moscow Institute of Physics and Technology PowerPoint PPT Presentation


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Local two-qubit channels: probability-based comparison of constituents and entanglement-annihilating behavior. Sergey Filippov ¹ , Tom áš Ryb á r ² , M ário Ziman² ¹ Moscow Institute of Physics and Technology ² Research Center for Quantum Information, Slovak Academy of Sciences. CEQIP’2011.

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Sergey Filippov ¹ , Tom áš Ryb á r ² , M ário Ziman² ¹ Moscow Institute of Physics and Technology

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Sergey filippov tom ryb r m rio ziman moscow institute of physics and technology

Local two-qubit channels:probability-based comparison of constituents and entanglement-annihilating behavior

Sergey Filippov¹, Tomáš Rybár², Mário Ziman²

¹Moscow Institute of Physics and Technology

²Research Center for Quantum Information, Slovak Academy of Sciences

CEQIP’2011


Content

Content

  • Local channels

  • Comparison

  • Entanglement-annihilating


Local channels

Local channels

B

E2

A

E1


Comparison

Comparison

The aim is to distinguish between

  • non-identical channels

  • twin-identical channels

-distance between channels:


Scheme

Scheme


Local two qubit channels

Local two-qubit channels

  • Matrix representation for one channel


Example 1

Example 1

  • Input state is

  • POVM has two effects, corresponding to projectors on symm. and antisymm. subspaces

  • The output mean value is

  • Unitary channels

    • ‘same’

    • ‘different’

  • All channels

    • ‘same’

    • ‘different’

-1

+1


Example 2

Example 2

  • Input state

  • POVM has two effects, corresponding to projectors on symm. and antisymm. subspaces

  • The output mean value is

  • All channels

    • ‘same’

    • ‘different’

+0.25

-1

0

+1


Entanglement annihilating

Entanglement-annihilating

behaviour


What does ea mean

What does EA mean?

  • isentanglement-annihilating if the output state isseparable for all input states

  • is entanglement-breaking if the state is disentangledwith respect to partitioning ‘1+2’|‘anc' for any input state andancillary system.


Properties

Properties


Two depolarizing channels

Two depolarizing channels

  • Entanglement-breaking


Two depolarizing channels1

Two depolarizing channels

  • Entanglement-annihilating


Two depolarizing channels2

Two depolarizing channels


Pauli channels

Pauli channels


Lemma

Lemma


Corollary 1

Corollary 1


How is corollary 1 useful

How is Corollary 1 useful?


Corollary 2

Corollary 2


Summary

Summary

  • We have considered

    • Probability-based comparison of qubit channels

    • Entanglement between qubits involved while passing through a local channel

  • Problems to investigate

    • Upper-dimensional systems (qudits)

    • Continuous-variables

    • Multipartite systems

  • Hope you have had some fun 


Conclusion

Conclusion

  • Local channels ask many questions important for practical Quantum Information

  • Let us try answer them…

  • Are participants similar to local channels?


Thank you

Thank you

for listening!


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