Everything is Quantum Channel
sections 4.5 and 4.6
Ludmila Botelho
Before we start...
ρA⟼ρB=i∑EiρEi†
Kraus representation
i∑EiEi†=IA
-
Noisy Evolution as the Loss of a Measurement Outcome



Kraus Operators!
=N(ρ)
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
-
Trace-out
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
-
Classical-to-Classical Channels

ρ
Krauss Operators
Everything is a quantum channel
-
Classical-to-Classical Channels



Everything is a quantum channel
-
Classical-to-Quantum Channels





preparation + trace-out?
Everything is a quantum channel
-
Quantum-to-classical Channels



Klaus operators?

(measurement channel)
Everything is a quantum channel
-
Quantum-to-classical Channels




Completeness?
Everything is a quantum channel
-
Entanglement-Breaking Channels


Everything is a quantum channel
-
Entanglement-Breaking Channels


Completeness?



Proof of "if" part
Everything is a quantum channel
-
Entanglement-Breaking Channels
Proof of "only if" part


unit-rank

Completeness?


Everything is a quantum channel
-
Entanglement-Breaking Channels



Everything is a quantum channel
-
Entanglement-Breaking 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








independent!
Thank you!
Dziękuję!
Obrigada!
धन्यवाद!
Teşekkür ederim!
Everything is Quantum Channel sections 4.5 and 4.6 Ludmila Botelho
Quantum Channels
By ludmilaasb
Quantum Channels
- 217