Sergey Filippov ¹ , Tom áš Ryb á r ² , M ário Ziman² ¹ Moscow Institute of Physics and...
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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
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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. - PowerPoint PPT Presentation
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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
CEQIP’2011
Content
Local channels Comparison Entanglement-annihilating
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Local channels
12
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Comparison
The aim is to distinguish between non-identical channels twin-identical channels
-distance between channels:
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Scheme
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Local two-qubit channels
Matrix representation for one channel
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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’
-1
+1
– All channels ‘same’ ‘different’
CEQIP’2011
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’
-1
+1
+0.25
0
Entanglement-annihilating
behaviour
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What does EA mean?
is entanglement-annihilating if the output state is separable for all input states
is entanglement-breaking if the state is disentangled with respect to partitioning ‘1+2’|‘anc' for any input state and ancillary system.
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Properties
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Two depolarizing channels
Entanglement-breaking
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Two depolarizing channels
Entanglement-annihilating
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Two depolarizing channels
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
q1
q2
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Pauli channels
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Lemma
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Corollary 1
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How is Corollary 1 useful?
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
q1
q2
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Corollary 2
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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
CEQIP’2011
Conclusion
Local channels ask many questions important for practical Quantum Information
Are participants similar to local channels?
Let us try answer them…
Thank you
for listening!
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