Everything is Quantum Channel
sections 4.5 and 4.6
Ludmila Botelho
Before we start...
$$\rho_A \longmapsto \rho_B=\sum_i E_i \rho E_i^{\dagger}$$
Kraus representation
$$\sum_i E_i E_i^{\dagger} = \mathbb{I}_A$$

Noisy Evolution as the Loss of a Measurement Outcome
Kraus Operators!
\(=\mathcal{N}(\rho)\)
Interpretation of quantum channels
Environment
System
Unitary Operator

Noisy Evolution from a Unitary Interaction

Noisy Evolution from a Unitary Interaction
Interpretation of quantum channels

Noisy Evolution from a Unitary Interaction
Interpretation of quantum channels
Preparation Channel
Everything is a quantum channel
Kraus operators:
Kraus operators:

Appending Channel
Preparation Channel
parallel concatenation

Traceout
Everything is a quantum channel

Discarding Channel
Kraus operators:
Kraus operators:

Unitary and Isometric Channels
Everything is a quantum channel

Unitary and Isometric Channels
Everything is a quantum channel

Reversing Unitary channel
Everything is a quantum channel

Reversing isometric channel
Everything is a quantum channel

Reversing isometric channel
Completely positive and trace preserving
Everything is a quantum channel
Everything is a quantum channel

ClassicaltoClassical Channels
$$\rho$$
Krauss Operators
Everything is a quantum channel

ClassicaltoClassical Channels
Everything is a quantum channel

ClassicaltoQuantum Channels
preparation + traceout?
Everything is a quantum channel

Quantumtoclassical Channels
Klaus operators?
(measurement channel)
Everything is a quantum channel

Quantumtoclassical Channels
Completeness?
Everything is a quantum channel

EntanglementBreaking Channels
Everything is a quantum channel

EntanglementBreaking Channels
Completeness?
Proof of "if" part
Everything is a quantum channel

EntanglementBreaking Channels
Proof of "only if" part
unitrank
Completeness?
Everything is a quantum channel

EntanglementBreaking Channels
Everything is a quantum channel

EntanglementBreaking Channels
Everything is a quantum channel

Quantum Instruments
Everything is a quantum channel

Quantum Instruments
Everything is a quantum channel

Quantum Instruments
Everything is a quantum channel

Quantum Instruments
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Quantum Channels
By ludmilaasb
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 115