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
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Local channels
Comparison
Entanglement-annihilating
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Local channels
E2
E1
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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
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Matrix representation for one channel
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Example 1
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Input state is
POVM has two effects, corresponding to
projectors on symm. and antisymm. subspaces
The output mean value is
–
Unitary
All
channels
channels


‘same’
‘different’
-1
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+1
Example 2
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Input state
POVM has two effects, corresponding to
projectors on symm. and antisymm. subspaces
The output mean value is
–
All channels


+0.25
‘same’
‘different’
-1
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0
+1
Entanglement-annihilating
behaviour
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What does EA mean?
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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
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Entanglement-breaking
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Two depolarizing channels
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Entanglement-annihilating
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Two depolarizing channels
0.0
0.2
0.4
0.6
0.8
1.0
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
q2
0.0
0.0
0.0
0.2
0.4
0.6
q1
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0.8
1.0
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
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0.6
0.8
1.0
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
q2
0.0
0.0
0.0
0.2
0.4
0.6
q1
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0.8
1.0
Corollary 2
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Summary
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We have considered
–
–
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Problems to investigate
–
–
–
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Probability-based comparison of qubit channels
Entanglement between qubits involved
while passing through a local channel
Upper-dimensional systems (qudits)
Continuous-variables
Multipartite systems
Hope you have had some fun 
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Conclusion
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Local channels ask many questions important
for practical Quantum Information

Let us try answer them…
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Are participants similar to local channels?
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Thank you
for listening!