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Local two-qubit channels: probability-based comparison of constituents and entanglement-annihilating behavior Sergey Filippov¹, Tomáš Rybár², Mário Ziman² ¹ Moscow Institute of Physics and Technology ² Research Center for Quantum Information, Slovak Academy of Sciences CEQIP’2011

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Content Local channels Comparison Entanglement-annihilating

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CEQIP’2011 Local channels E1E1 E2E2

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CEQIP’2011 Comparison The aim is to distinguish between non-identical channels twin-identical channels -distance between channels:

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CEQIP’2011 Scheme

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CEQIP’2011 Local two-qubit channels Matrix representation for one channel

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CEQIP’2011 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 – All channels ‘same’ ‘different’

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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’

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Entanglement-annihilating behaviour

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CEQIP’2011

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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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CEQIP’2011 Properties

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CEQIP’2011 Two depolarizing channels Entanglement-breaking

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CEQIP’2011 Two depolarizing channels Entanglement-annihilating

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CEQIP’2011 Two depolarizing channels

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CEQIP’2011 Pauli channels

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CEQIP’2011 Lemma

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CEQIP’2011 Corollary 1

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CEQIP’2011 How is Corollary 1 useful?

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CEQIP’2011 Corollary 2

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CEQIP’2011

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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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CEQIP’2011 Conclusion Local channels ask many questions important for practical Quantum Information Are participants similar to local channels? Let us try answer them…

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Thank you for listening!

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