Post on 30-Dec-2015
description
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
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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’
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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
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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!